Teacher Edition with Resource Masters
CHAPTER
1
Investigate
CHAPTER
0 Start Smart
1 Place Value, Addition, and Subtraction
2 Apply Multiplication and Division Facts
3 Algebraic Patterns
Animations
Vocabulary
Math Songs
4 Multiply by One-Digit Numbers
Multilingual eGlossary
5 Multiply Multi-Digit Numbers
6 Understand Division
7 Organize and Display Data
8 Decimals and Fractions
9 Add and Subtract Fractions and Decimals
Learn
Personal Tutor
Virtual Manipulatives
Audio
10 Identify and Describe Geometric Figures
Foldables
11 Spatial Reasoning
12 Measure Length
13 Measure Capacity, Weight, and Mass
Practice
Self-Check Practice
eGames
Assessment
Leveled Worksheets
Includes Start Smart
Place Value, Addition, and Subtraction
Get ConnectED
INCLUDES Start Smart Chapter Planning Differentiated Instruction Strategies ELL Strategies Essential Questions RtI Lesson Support
Resource Masters Chapter Resources Language Arts Resources Practice & Reinforcement Leveled Lesson Resources Assessment Answers
Get ConnectED ISBN: 978-0-02-103093-4 MHID: 0-02-103093-6
All Resource Masters are available at connectED.mcgraw-hill.com
Digital and Print Solutions Designed for Success Support for Every Learner Support for Every Teacher Data-Driven Decision Making Built on Research
TURN THE PAGE Get ConnectED
for your NEW mathematics curriculum solution . . .
Online Guide
“It’s easy to do my assignments online and quick to find everything I need.”
Get ConnectED connectED.mcgraw-hill.com hill
Investigate Animations present an animation of a math concept or graphic novel. Vocabulary presents visual representations of math concepts. Math Songs reinforce math concepts through songs. Multilingual eGlossary presents key vocabulary in 13 languages.
T2
Built on Research The icons found throughout Math Connects provide you with the opportunity to connect the print textbook with online interactive learning.
Learn
Practice
Personal Tutor presents a teacher explaining step-by-step solutions to problems.
Self-Check Practice allows students to assess their knowledge of foundational skills.
Virtual Manipulatives provides digital ways to explore concepts.
eGames allow students to practice math concepts using interactive games.
Audio recordings provide an opportunity to build oral and listening fluency.
Worksheets provide additional practice and reteach opportunities.
Foldables provide a unique way to enhance students’ study skills.
Online Assessment checks understanding of concepts and terms.
T3
The Next Generation Classroom Seamless Digital and Print Solutions Developing 21st Century Skills
T4 T4
Digital and Print Solutions
Problem-Centered Connections Whole-Class Instruction
Inquiry-Based Learning
Diagnostic, Formative, and Summative Assessment Independent Learning and Practice
Teacher Planning Data Management and Reporting
Parent Communication Professional Development Get ConnectED
T5
Connect to Math NCTM Aligned Curriculum aligns with the K–8 NCTM Focal Points and Process Standards supported by easy-to-use online tools.
Contents in Brief Focal Points Master the epts from Grade
w of conc Start Smart A revie
CH APT ER
3
tion
ition, and Subtrac
1 Place Value, Add and Division Facts cation 2 Apply Multipli 3 Algebraic Patterns it Numbers -Dig One by 4 Multiply ti-Digit Numbers 5 Multiply by Mul sion 6 Understand Divi lay Data 7 Organize and Disp s tion Frac and ls 8 Decima Decimals t Fractions and 9 Add and Subtrac e Geometric Figures and Describ tify Iden 10 ing 11 Spatial Reason 12 Measure Length Weight, and Mass Capacity, 13 SEMeasure Contents in Brief
Get ConnectED
ConnectED
Multi-Part Lessons Chapters contain a smaller number of concepts with greater depth and rigor. PM 3/12/10 12:47
03030.indd iii
iii_FM_CIB_1
Chapter at a Glance Lesson Multi-Part Lesson
A B
T6
1
Pacing 3 days d
Place Value
FPO
Resources Mat eriials l and dM aniipullatives i Materials Manipulatives index cards, base-ten blocks Get ConnectED
Place Value
Place Value
C
Compare and Order Numbers
D
Round Numbers
Leveled Worksheets Explore Worksheet Visual Vocabulary Cards Lesson Animations Daily Transparencies Problem of the Day Self-Check Quiz
SE Chapter at a Glance
Personal Tutor Virtual Manipulatives eGames Math Song Animations Hands-On Activity Tools and Resources
Designed for Success
Engaging Content Content helps students contextualize concepts. Real-life connections motivate students to realize their potential.
The state insect of Washington is the Green Darner dragonfly. It can fly at speeds of more than 50 miles per hour. 27. Suppose 18 nymph dragonflies of maximum length were laid end to end. About how long would they span?
Green Darner arner y Facts Dragonfly Average adult length 74 millimeters Maximum length of nymph
55 millimeters
28. If 32 average adult dragonflies were laid end to end, about how long would they span?
SE Data File
244_247_C05_L01_103030.indd 246
3/1/10 12:51 PM
Data-Driven Decision Making Measure student learning, support RtI, and modify instruction based on balanced assessment. 3 REASSESS CRIBE E AND PRES 2 DIAGNOS ention)
ostic Test.
Administer the Diagn Diagnostic Test
to Interv below to address t, use the charts RtI (Response ostic Assessmen
001_015_C07_101799.indd
ts of the Diagn Based on the resul the chapter. before beginning individual needs
Number of Videos
12/3/09
5. 89, 62, 75, 40, 53
yellow tail
6. 31, 72, 49, 50, 64
Sept.
Oct.
Month 1.
Number of Students
5.
Represent the data in a tally chart. neighborhood to find out their 7. Josh surveyed the people in his football, 10 said baseball, and favorite sports. Fifteen people said basketball was their favorite 10 said soccer. Twenty people said sport and 2 people said wrestling.
Inc.
10 9 8 7 6 5 4 3 2 1 0
4.
6.
7.
Favorite Types of Music
Inc.
there? 7. How many total students are jazz better than 8. How many more students like classical music?
3.
a division of The McGraw-Hill Companies,
question. Use the bar graph to answer each of music? 6. What is the most popular type
2.
Copyright © Macmillan/McGraw-Hill,
a division of The McGraw-Hill Companies,
Aug.
4. 24, 16, 31, 12, 47
sting ray
5. 51, 47, 42, 56, 40
4. 32, 39, 41, 29, 36
Copyright © Macmillan/McGraw-Hill,
50 0
Order from least to greatest.
Tally
shark
Rock
34. Craig visits his grandmother’s house five times. About how many total miles will he travel round trip? (Lesson 1C)
35. Grasshoppers can jump about 20 times their length. About how far could the grasshopper below jump? (Lesson 1C)
Jazz Classical Type of Music
8
Data Grade 4 • Organize and Display
5
001_015_C07_101799.indd
AL
Page 6
12/3/09
06:21 PM u-s008 9:06:21
Name _____________________________
X_SE/Appli... /Volumes/112/GO00396/GO00396_Math_Connects_CRM_NA_G3%0/XXXXXXXXXXXX
Date ________________
Are You Ready
for the Chapter?
appro
Review
ises 1–7,
Order from least to greatest.
or 4 in Exerc students miss 3
If
150 100
Data Grade 4 • Organize and Display
vention Strategic Inter level aching grade
2
200
Types of Fish
Fish eel
3. 74, 69, 67, 72, 80
2. 17, 22, 19, 13, 26
Get Connec
Video Rentals 250
number of videos rented? 1. In which month were the least in August? 2. How many videos were rented rented in October? 3. About how many videos were
for the Chapter?
Fill in the tally chart for the situation. Rose noticed the 1. While looking at an aquarium, past her. Types of different types of fish that swam ray, eel, shark, fish: yellow tail, eel, yellow tail, sting eel. sting ray, yellow tail, yellow tail,
Order from least to greatest.
TIER
Date ________________
Are You Ready Practice
in Exercises 1–7,
rce: choose a resou 324F) Stations (pp. 324E– TE Learning Practice Are You Ready? tED Self-Check Quiz
Then
Test Practice
Date
Name
/Volumes/112/GO00396/GO00396_Math_Connects_CRM_NA_G3%0/XXXXXXXXXXXX
06:20 PM u-s008 9:06:20
Name _____________________________
OL
students miss 2
If
%0/XXXXXXXXXXXXX_SE/Appli... /Volumes/112/GO00396/GO00396_Math_Connects_CRM_NA_G3
u-s008 9:06:22 PM u
Diagnostic Test
5 001_015_C07_101799.indd Page
On Level
1
12/3/09
graph. For Exercises 1–3, use the bar
X_SE/Appli...
TIER
Page 8
1. 7, 3, 10, 4, 2 2. 5, 1, 9, 14, 6 3. 21, 0, 37, 11, 8 4. 54, 32, 97, 65, 9 5. 16, 3, 81, 66, 90, 61
rce: choose a resou Guide (pp. T9, T11) Strategic Intervention Review Are You Ready? tions ED Lesson Anima Get Connect
6. 92, 35, 21, 67, 50, 18 7. 0, 2, 1, 8, 54, 39, 21 8. 2, 3, 4, 3, 3
11. 87, 14, 26, 14, 87, 35, 30
12. 52, 20, 43, 17, 20, 59, 16
If Then
Inc.
3
a division of The McGraw-Hill Companies,
9. 8, 5, 7, 8, 1 10. 43, 29, 12, 7, 12, 26, 12
6
TIER
Copyright © Macmillan/McGraw-Hill,
Then
Data Grade 4 • Organize and Display
vention
Intensive Inter 2
grade level or more years below students miss 5
ises 1–7,
or more in Exerc
phs, an intensive use Math Trium McGraw-Hill program from
n
math interventio
TE Diagnostic Assessment
A. 35 miles
C. 350 miles
F. 80 cm
H. 60 cm
B. 70 miles
D. 700 miles
G. 70 cm
I. 50 cm
SE Test Practice
T7
Inquiry-Based M Learning
ath Connects and IMPACT Mathematics work together to allow a more investigative approach or a more skills-based approach, depending on the needs of your students. The virtual manipulatives allow students and teachers to digitally model mathematical concepts.
A Complete Math Solution Blending Math Connects and IMPACT Mathematics provides teachers maximum flexibility to “test the waters” of an investigative approach, or to completely integrate the two programs. Use the lesson plans in this guide to exchange or enhance Math Connects content with investigations from IMPACT Mathematics. The programs are horizontally aligned so it is easy to move between them.
T8
Support for Every Learner
A Balanced Basal The comprehensive student text supports the NCTM Focal Points and Process Standards. The content is arranged to provide depth and cohesiveness. The organized assignments allow for differentiation and include oral, written, and visual responses.
An Investigative Approach IMPACT Mathematics provides opportunities for investigative instruction through additional inquiry and problem solving.
T9
Engaging M Content
ath Connects is designed to provide students with an engaging, yet balanced approach to mathematics that includes conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
Content that Connects When Will I Use This? Julian and Olivia Musical Math
Graphic Novel
in
Olivia: Hi Julian, what’s up?
Julian: Hi Olivia! I’m just loading some music onto my MP3 player.
A graphic novel in each chapter introduces and revisits a real-world mathematical situation.
INSTANT MESSAGE
When Will I Use This?
17. FIND THE ERROR Candace is finding 67 × 2. Find and correct her mistake.
O: Cool! I want to get an MP3 player too, but I don’t know which kind to get.
O: That’s a lot of songs! I want the same kind of MP3 player you have.
Musical Math
J: The one I have is great! It holds about 4,000 minutes of music.
Candace
67 × 2 −−− 124
J: So far I’ve loaded 467 songs, but there are a lot of songs I still want.
SE Find the Error J: I hope so! I’ll have to find how many minutes are left.
O: Wow, will you be able to fit everything you want on there?
Use the information to solve the problem.
Musical Math Musical Math 210_213_C04_L03_103030.indd 212
rn! Your Tu this thi l You willll solve er er ter. problem in the chap
Remember, Julian is trying to figure out how many minutes are still available on his MP3 player that can hold 4,000 minutes.
Well, I’ve loaded 467 songs. Each song is about 4 minutes long. Now I can find how many minutes I have left.
SE When Will I Use This? 182_184_C04_CO_103030.indd 183
2/25/10 8:24 AM
SE Revisit the Problem
220_223_C04_L03_103030.indd 222
Online Animations Online downloadable animations bring the content to life. Recurring characters captivate students and stimulate their intellectual curiosity.
O: Wow, will you be able to fit everything you want on there?
Get ConnectED
T10
Online Animations
2/25/10 8:40 AM
Support for Every Learner
Problem-Based Learning
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
Problem Solving Problem-solving opportunities embedded in every lesson show students that mathematics is useful in real life. In addition, there are lessons and components solely focused on problem solving.
JEC@P?
SE Real-World Problem-Solving Readers
1
Multi-Part Lesson
Multiples A
PART
B
C
D
wers sw asonable An
g Skill: Re Problem-Solvinther an answer to a problem is reasonable.
Multi-Part Lesson
whe will decide Main Idea I
to a dog dog treats d 3 cases of The dogs eat O ell donate Od 900 treats. has h case has ell says he she s lter. Eac . h month. Od eac ts n one month trea 2,500 for more tha ugh treats donated eno e? abl reason Is his claim
Check
900 treats in each
D
E
F
of the
One bowl of punch serves 35 guests. Isabel is making four bowls of punch. Find how many guests will be served by four bowls of punch.
900
900
Plan Solve
Use a bar diagram to write a number sentence. Multiply the number of guests served by one bowl of punch by the number of bowls being made. You need to find 35 × 4 = . 35 ×4 −−− 20 Multiply 4 × 5. +120 Multiply 4 × 30. −−−− 140 Add.
? guests served 35
35
35
35
guests served by each bowl
So, four bowls of punch will serve 140 guests.
Check
ation, including estim m solving, problem strategies to appropriate
onn lviingg Skill lleesssso SE Problem-Sol 30.indd 194 4_PSS_1030 194_195_C0
Emperor penguins usu ally dive 60 to 70 feet. An average dive lasts 3 to 6 minutes.
You can use repeated addition to check your answer. 35 + 35 + 35 + 35 = 140 So, the answer is correct.
enes and reasonabl
s igit Number ly by One-D 194 Multip
ICE
There are 17 different types of pen guins. Emperor pen guins are the tallest and heavie st penguins. An Emperor penguin is tall and can over 3 feet weigh from 42 to 101 The averag pounds. e Emperor penguin we pounds and ighs 66 can swim 15 miles per hou r. About 200 ,000 pairs of Emperor pen live in 40 dif guins ferent groups Penguins hud in Antarctic a. dle togeth er to share body heat their during the cold winter temperatu res and bit ter winds.
Understand
case
2,700 e t the e to say tha is reasonabl . > 2,500, it one month Since 2,700 longer than last will es three cas . multiplication to check the You can add 00. + 900 = 2,7 900 + 900 t. wer is correc So, the ans
ty of adapt a varie Apply and GLE 0406.1.2 ion. s of the solut
C
YOUR MISSION: Find how many guests four bowls of punch serve.
s ? total treats
9 = 27 THINK 3 × s in the Place 2 zero product.
B
ISABEL: I am making punch for a party. One bowl of punch serves 35 guests. I am going to make four bowls of punch.
? need to find es of treats What do you that the 3 cas able to say ? • Is it reason one month n tha ger will last lon able. na son ount is rea ine if the am . Then determ Find 3 × 900
Solve
A
Main Idea I will choose the best strategy to solve a problem.
w? do you kno What facts d. were donate es of treats • Three cas treats. 900 has e • Each cas h month. eac ts trea ls eat 2,500 • The anima
3 × 900
Emperors
Multiply with Regrouping
Problem-Solving Investigation
Understand
Plan
3
PART
224 Multip ly by One-D igit Number s
AM 2/25/10 8:29 2/2
GLE 0406.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. Also addresses GLE 0406.1.7.
224_225_C0 4_CC_10303 0.indd 224
214 Multiply by One-Digit Numbers
SE Crosss--C C Cuurrrri ric icularr Problem -SSolviing lesson
2/25/10 8:40 AM
214_215_C04_PSI_103030.indd 214
SE Problem-Solving Investigation lesson
Concepts and Skills In multi-part lessons, students use multiple representations to communicate conceptual understanding. Meaningful practice helps students carry out procedures accurately and efficiently.
Depth and Rigor
2/25/10 8:37 AM
Multi-Part Lesson
3
Multiply with Regrouping
PART
A
Main Idea I will use the Distributive Property to make multiplication easier.
B
C
D
E
F
The Distributive Property To multiply greater numbers, the Distributive Property is helpful. The Distributive Property combines addition and d multiplication. Multi-Part Lesson
Get ConnectED GLE 0406.1.3 Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas. SPI 0406.1.1 Verify a conclusion using the commutative, associative, and distributive properties.
3
MP-Title -Title with Regrouping Multiply
PART
Distributive Property
Words
A
The Distributive Property says that hat you can ber and then multiply the addends of a number add the products. 6 × 12 = (6 × 10) + (6 × 2) Main Idea
Symbols
I will mentally multiply a one-digit factor by a two-digit factor.
The Distributive sttributive Property tyy Materials FOOD Chef Cora hard-boils six dozen eggs each day to make egg salad for sandwiches. How many eggs does she hard-boil each day?
Students participate in mathematics discourse and apply higher-order thinking skills. Collaborative activities, writing exercises, and multi-step problems ask students to formulate, represent, reflect upon, and explain their solutions.
+
2 6
Bar Diagrams, which are problem-solving tools that provide visualizations of mathematical relationships, support student understanding throughout the program.
E
F
It may be hard to find a product like 4 × 13 mentally, even if you use counters. If you separate the counters into smaller groups called partial products, it is easier to multiply.
Find 4 × 13 mentally using partial products. 13 Model 4 × 13 by arranging counters in 4 rows and 13 columns. 4 × 13
Get ConnectED
60
+
2
GLE 0406.2.2 Develop fluency with multiplication and singledigit division. Also addresses GLE 0406.1.8.
10
+
3 Separate 13 into two numbers that are each easily multiplied by 4.
4 4 × (10 + 3)
12
10
3
6 × 12 = (6 × 10) + (6 × 2) =
60
=
72
+
(4 × 10) 40
210_213_C04_L03_103030.indd 210
+ +
(4 × 3) 12 =
52
Rewrite 4 × 13 as (4 × 10) + (4 × 3). This is useful since it is easier to find (4 × 10) + (4 × 3) mentally than to find 4 × 13. So, 4 × 13 is 52.
210 Multiply by One-Digit Numbers
SE Lesson Opener
Multiply to find the number of counters in each group. Then add.
4
12
So, Chef Cora hard-boils 72 eggs each day.
BAR DIAGRAM
D
4
10
6
C
counters
There are 12 eggs in one dozen. Find 6 × 12. Think of 6 × 12 as (6 × 10) + (6 × 2). 10
B
Multiply Mentally
About It 2/25/10 8:36 AM
1. To find 4 × 13, you can also find 4 × (9 + 4). Why is it easier to find 4 × (10 + 3) mentally than it is to find 4 × (9 + 4)? 2. Which expression would you use to find 7 × 19 mentally: 7 × (13 + 6) or 7 × (10 + 9)? Explain. 208 Multiply by One-Digit Numbers 2
208_209_C04_EXP_103030.indd 208
2/25/10 8:35 AM
SE Explore Lesson
T11
Differentiated Instruction
AL
Approaching Grade Level
OL
On Grade Level
BL
Beyond Grade Level
ELL
English Language Learners
M
ath Connects fully supports the 3-tier RtI model with print and digital resources to diagnose students, identify areas of need, and conduct short, frequent assessments for accurate data-driven decision making. Every lesson provides easy-touse resources that consider the special needs of all students.
RtI: Response to Intervention
Get ConnectED
TIER
1 Daily Intervention OL ON GRADE LEVEL
BL BEYOND GRADE LEVEL
Core instruction targets on-level students. Comprehensive instructional materials help you personalize instruction for every student. • Diagnostic Teaching
At every step, resources and assignments are available for advanced learners. • Higher-Order Thinking Questions
• Options for Differentiated Instruction
• Beyond-Level Activities
• Data-Driven Decision Making
• Extension Ideas for Games and Chapter Projects
• Enrichment Masters
• Problem-Solving Projects • RWPS Readers 001_015
Are You Ready for the Chapter?
If
students miss 2 or less in Exercises 1–19
Then
choose a resource:
8.
s, Inc.
Chapter Project (p. 182)
ill Companie
TE
9 × 9 −−−
of The McGraw-H
$7 × 5 −−−
Hill, a division
7.
8 × 3 −−−
4. 7 × $8
Are You Ready? Apply
9. Evan’s photo album has 8 pages of pictures. How many photos are in Evan’s album if the same number of photos is on each page?
Get ConnectED
/McGraw-
6.
9 × 4 −−−
AM u-s009 /Volume s/114/G O00397/ GO00397 _Math_C onnects _CRM_NA _G4%0/X XXXXXXX XXXX XXXXX_S
________
_____ Date ________
________
Multiply.
© Macmillan
5.
1:28:38
for the Cha pter? Apply
Multiply. Use models if needed. 3. 5 × 6
12/9/09
________
Take the Quick Check below.
2. 4 × $4
dd Page 7
Are You Ready
You have two options for checking Prerequisite Skills for this chapter.
1. 2 × 3
1796.in
Name ____ ____
eGames: Mount Frost-Multiply Multiples of 10
Copyright
Text Option
Beyond Level
_C04_10
BL
1. Gabb y has 9 How many jewelry boxes. Each bracelets jewelry box does Gabb has 9 brace y have? lets in it. 2. Drew has 6 team pennants. Drew. How Steve has many penna 3 times nts does as many Steve have? pennants 3. Each as movie ticket costs $7. How much will 5 ticket s cost? 4. Lisa has 8 bags of apples. There many apple s does Lisa are 9 apple s in each have? bag. How Solve. 5. Natas ha has 253 marbles. marb
les does She found Natasha 14 more underline have now? marbles. the tens Solve the How many place. exercise, and 6. In the 1930s, there were 16,28 the 1940 s, there were about 2 people living people lived in Virgin 3,000 more in Virgin ia Beach people. and under ia Beach How many . In in the 1940 line the ten thous s? Solve ands place the exerc . ise, 7. Shirle y ran a mile plus 1,000 many feet feet. did Shirle y run? Solve If a mile has 5,280 thousands place. the exerc feet, how ise, and underline the 8. In a bee colon honeycomb y, the worker bees . There are produce Identify wax to build about 55,00 the place the 0 worke value of r bees in each digit a colony. in 55,00 0.
Grade 4 • Multipl y
by One-Di git
Numbers
7
TE Beyond Level Recommendations
Identify the place value of the underlined digit. 10. 1,630
11. $5,367
12. 20,495
13. $89,196
14. Measurement Mount Everest’s tallest peak is 29,035 feet. It is the highest point on Earth. Identify the place value of each digit in 29,035.
Get ConnectED
Online Readiness Quiz
Round each number to its greatest place value. 15. 26
16. $251
17. 4,499
18. $33,103
19. There are 1,366 students at Sunrise Elementary School. Approximately how many students attend the school?
Online Option 184
Take the Online Readiness Quiz.
Multiply by One-Digit Numbers
SE Are You Ready? 182_184_C04_CO_103030.indd 184
T12
2/25/10 8:24 AM
E/Appli
...
Support for Every Learner
ELL
English Language Learners
Comprehensive resources are found throughout Math Connects. • eBook with English and Spanish audio • Student Edition Glossary with words and definitions in English and Spanish • eGlossary with definitions for each vocabulary word in 13 languages • English Language Learners Guide with alternative lessons specifically developed for ELLs • Teacher Edition with strategies to modify activities and lesson content • Family Letters and Activities in English and Spanish • Professional development articles in the Teacher Resource Handbook
TIER
2 Strategic Intervention
AL APPROACHING GRADE LEVEL
Teachers can choose from a myriad of intervention tips and ancillary materials to support struggling learners. • Learning Stations Small Group Option • Options for Differentiated Instruction • Alternate Teaching Strategies
TIER
3 Intensive Intervention
AL FAR BELOW GRADE LEVEL
Access Point Activities support special education students. For students who are far below grade level, Math Triumphs provides step-by-step instruction, vocabulary support, and scaffolded practice.
• Strategic Intervention Guide • Hands-On Activity Tools and Resources • Online animations and Personal Tutors The Personal Tutors provide students an opportunity to approach content from another teacher’s perspective.
Get ConnectED
Online Personal Tutor
T13
Teacher M Success
ath Connects offers teachers many ways to plan and deliver quality instruction, from the Teacher Edition to online assets to quality professional development. At-aglance planning and scheduling tools show the mathematics objectives, suggested pacing, and vertical alignment. Robust teaching materials help you build rigorous lessons that address concepts in depth. The seamless integration of print and digital tools puts the teacher in control.
Plan, Teach, and Assess Online is the online all-in-one portal that allows you to • build lesson plans with easy-to-find print and digital resources • search for activities to meet a variety of learning modalities • personalize instruction with print and digital resources • teach with technology by providing virtual manipulatives, lesson animations, whole-class presentations, and more • provide students with anywhere, anytime access to student resources and tools, including eBooks, tutorials, animations,and the eGlossary • access AdvanceTracker, which allows you to assign online assessments, track student progress, generate reports, and differentiate instruction • access ExamView®, an assessment customization tool where you can assess your state standards in a variety of test formats Get ConnectED
My Home Schedule Content Classroom Bookmarks Assessments Reports Communication Profile
T14
connectED.mcgraw-hill.com
Support for Every Teacher
Professional Development McGraw-Hill Professional Development (MHPD) provides comprehensive programs for growth in mathematics education that target teachers, math coaches, and administrators. Support includes initial and on-going training.
INSERVICE A program walkthrough of Math Connects components, technology, and ancillaries. CLIPS VIDEO LIBRARY Videos for specific concepts and general instructional strategies including demonstrations and commentaries by experts in the field. CONSULTANT WEBSITE Provides customized, online support to educators using Math Connects.
WORKSHOPS ONSITE Onsite, coach-led video and activity-based workshops. TECH TRAINING Short animated or video modules that explain the use of Math Connects technology components.
Ready-Access Math More than 200 lessons allows for a custom professional development series, or a special 45–60 minute after-school session.
T15
Comprehensive Assessment M
ath Connects offers a variety of frequent and meaningful assessment built into the curriculum structure and teacher support materials. Digital assessment solutions offer the same quality assessments, plus options to create, customize, administer, and instantly grade assessments.
ou Readery? Are Yth e Chapt
cking options for che You have two lls for this chapter. Ski Prerequisite
for
w. ck Check belo Take the Qui
Text Option Multiply. Use 1. 2 × 3
5.
ded. models if nee 2. 4 × $4
6.
9 4 × −−−
3. 5 × 6
7.
8 3 × −−−
$7 5 × −−−
4. 7 × $8
8.
1
9 9 × −−−
8 pages of to album has 9. Evan’s pho tos are in w many pho pictures. Ho e number of sam the if Evan’s album e? each pag photos is on
Identify the 10. 1,630
erlined digit. 12. 20,495
of the und place value 11. $5,367
15. 26
atest place ber to its gre 16. $251
value. 9 99 ,49 4,4 17. 4
Initial Assessmen Assessment nt Assess students’ knowledge know wledge at the beginning of the year with Diagnostic and Placement Tests. The results and scoring guides identify students who may need additional resources to meet grade-level standards.
Entry-Level Assessment
13. $89,196
Assess students’ prior knowledge at the beginning of a chapter or lesson.
t. is 29,035 fee tallest peak e of each unt Everest’s the place valu rement Mo th. Identify 14. Measu point on Ear t hes hig It is the . digit in 29,035
num Round each
Diagnostic
3,103 18. 18 $33 1
School. Elementaryy ts at Sunrise ooll?? choo sch sc 1,366 studen ts attend the 19. There are many studen how tely ima Approx
Online Optio
n
z. uiz. Qui ss Q ine Readine Take the Onl
mbers One-Digit Nu M ltiply by
y? SE Are You Read
AM 2/25/10 8:24
30.indd 184
4_CO_1030
182_184_C0
Get ConnectED
T16
AdvanceTracker: Chapter Readiness Quiz
Data-Driven Decision Making
2
Mid-Ch Check apter Multip (Lesson
ly. Use basic fa cts and pattern
1B)
s.
1. 3 × 4 3 × 40 3 × 40 0 3 × 4,00 0
Formative
9. BAR DIAGRA M Juan 264 pa plans to ges a m read onth to book in complet 6 month e his s. Abou pages ar t how m e in his any book? (Lesson
2. 12 × 5 12 × 50 12 × 50 0 12 × 5, 000
3. A tri ceratops 1C) weighs pounds 2 × 7,00 . How m 10. Mea 0 uch do weigh? suremen es a tri ceratops t Each ga paint co vers ab llon of 4. Kyra out 350 Chandr needs 29 square a estim 2 toothp feet. ated th project. paint w icks for at 3 ga A box ho ould be a llons of lds 150 Is it reas en 1,400 sq ough to toothpick onable uare fe cover to buy s. Explain. et. Will enough 2 boxe Ch (Lesson an pa s? dra have int? Expl 1D) ain. (Le 5. Mar sson 1D a and Bi ) lly have balloon 6 bags 11. MUL s. Is it re of 12 TIPLE CH asonab have m OICE Th le to sa of marke ore than er y e they are 21 rs in th 75 ballo Explain. boxes e art ro ons? holds th (Lesson om. Ea 1D) e marke ch box rs show markers n. How are in th many e art ro (Lesson 2C) om?
Progress Monitoring Determine if students are progressing adequately as you teach each lesson. Use the assessments to differentiate lesson instruction and practice.
Estimat
e each produc t. (Lesso 6. 3 × n 1C) 252 7. 5 × 7,493 8. MUL
TIPLE CH OICE Ja a year in da pays ca
r paym $1,875 much m ents. Ab oney w out how ill she pa 5 years? y in (Lesson
A. $5,0 00 B. $7,5 00
F. 108 G. 160 12.
E
H. 168 I.
248
WRITE
MATH Cassie followin got g proble m wrong the math te st. Expl on her ain her (Lesson mistake. 1B)
1C)
C. $9,3 75 D. $10, 000
50 ×8 −− − 40
205_C0
4_MCC_ 103030 .indd 205
Mid-C
SE Mid hapter Check 205 -Chapter Check 2/25/10
Get ConnectED
8:33 AM
Self-Check Quiz
SE Practice Chap ter Test
3
Practice Chapter Test Multipl ti y. Use bas ic facts and patt erns. 1. 5 × 4 2. 9 × 6 5 × 40 9 × 60 5 × 400 9 × 600 5 × 4,000 9 × 6,000 Multiply. Use mental math. 3. 2 × 60 4. 4 × 50
Summative
5. 6 × 800
6. 8 × 9,000
8. MULT LTIPLE CHOICE Which pair of numbers b best completes the equ q ati atio on? n?
Assess student success in learning the concepts in each chapter. Use remediation suggestions to address problem areas.
× 100 = A. 65 and 650 B. 65 and 6,50 0 C. 605 and 6,50 0 D. 650 and 6,50 0 9. Fiona makes $25 a day bab ysittting ing.. Is it reasonable to say she will have more than $20 0 at the end of a week? Explain. Estimate each product. 10. 4 × 657
11. 7 × 9,431
13. 9 × 7,005
14. Hakeem take s 60-minute tenn is lessons twice a week. How many minutes of tenn is lessons doe s Hakeem take in four weeks?
Algebra Find the value of eac h expression if n = 6. 15. n × 827
7. Scho ool supplies cost $30. Is it reaso onable for 9 stud ents to purchas supp e plies with $30 0? Explain.
Summative Assessment
Multiply. 12. 5 × 604
16. $3,285 × n
Multiply. 17. 4 × 226
18. 8 × 591
Algebra Copy and com
plete. 19. If 3 × = 21, then 30 × = 2,100. 20. If 8 × = 48, then 80 × = 4,800. 21. MULTIPLE CHOICE A plane carries 234 passengers . If the plane mak es 4 trips a day, how many pas sengers does the plan e transport a day? F. 826 H. 936 G. 926 I. 981 22. E WRIT E MATH Joshua does not understand why 4,200 is not a reasonable esti mate for 681 × 7. Explain. Practice Ch
231_235_C04_
SGR_103030.i
ndd 235
2/25/10 8:44 AM
Get ConnectED
ExamView® Assessment Suite
T17
The
C Research
Base
ontinuous research with teachers, students, academics, and leading experts builds a solid foundation for Math Connects. Expert authors, reviewers, and consultants contributed their knowledge and experience throughout the program development.
Developmental Research
Formative Research
Pre-Development
Pre-Publication
• State and local standards evaluation
• Pedagogical research base
• Relevant data from recognized sources
• Classroom field tests
• Qualitative market research
• Teacher advisory boards
• Current academic content research
• Academics, authors, consultants, and reviewers
Percentage Correct
Student Data from Classroom Field Tests 66 64 62 60 58 56 54 52 50 0
Pre-Test Post-test
64%
60%
51%
50%
Math Connects
Control
Classroom Types
Students using a field test version of the Math Connects program (experimental group) had higher pre-test to post-test gains than students using other textbook programs (control group).
T18
Built on Research
Summative Research Post-Publication • Evidence of increased test scores • Quasi-experimental program efficacy research • Longitudinal studies • Qualitative program evaluations
Math Connects National Field Study
Final Report: Student Learning, Student Attitudes and Teachers’ Reports on Program Effectiveness October 2009
Macmillan/McGraw- Hill and Glencoe
Get ConnectED
Find detailed information about our classroom research results at connectED.mcgraw-hill.com. T19
True PreK–12
Content Design Students experience an articulated, coherent sequence of content from elementary to high school. Content is introduced, reinforced, and assessed at appropriate steps in each grade and throughout the series, eliminating gaps and unnecessary duplication.
Vertical Alignment
Instructional Design A uniform approach to presenting concepts and skills, along with common authors, vocabulary, technology, lesson planning, and manipulatives, allows smooth transitions for students between grade levels and less reteaching for teachers.
Multi-Part Lesson
2
Addition and Subtraction Relationships
PART
Multi-Part Lesson
Name
PART
A
Main Idea
4
B
C
A
D
I will explore addition and subtraction equations.
E
Add in Any Order
Materials cup counters
Get Ready I will add in any order.
Get ConnectED
3+6=6+3
3
+
6
=
addend
sum
6
3
9
+
Addition and Subtraction Equations An equation is a sentence like 4 + 5 = 9 that contains an equals sign (=). The equals sign shows that the expressions on each side of it are equal. Equations sometimes have a missing number. 4+x=9
=
addend
GLE 0406.3.1 Extend understanding of a variable to equations involving whole numbers, fractions, decimals, and/or mixed numbers. Also addresses GLE 0406.1.4, GLE 0406.3.3.
Step 2
sum
Step 3
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Write the addends. Use 1.
to add. 2.
2
+
4
=
6
Model the expression on the left side. To model n + 3, use a cup to show n and 3 counters. Model the expression on the right side. Place 5 counters on the right to show 5. An equals sign shows that both sides are the same. Find the value of n. Put enough counters in the cup so that the number of counters on each side of the equals sign is the same.
+
=
+
=
+
=
The value of n that makes n + 3 = 5 true is 2. So, n = 2.
+
+
140 Algebraic Patterns
140_141_C03_EXP_103030.indd 140
+
k-1=7
10 - m = 6
Solve n + 3 = 5. S
Step 1
9
addend
addend
C
When you find the value of the missing number that makes the equation true, you solve the equation.
You can change the order of the addends and get the same sum.
Main Idea
B
2/25/10 7:34 AM
=
3. E Talk Math Tell how you can show that 1 + 9 has the same sum as 9 + 1. GLE 0106.3.2 Understand that addition and subtraction are inverse operations.
Addition Strategies to 20
209_212_C05_L4_103027.indd 209
PRIMARY
T20
two hundred nine
209 3/5/10 1:17 PM
INTERMEDIATE
Built on Research
Visual Design The student pages have a consistent visual design—elementary through high school. This logical page design makes student reading and learning easier. Common labels and color schemes support student progress from grade to grade.
Solving Multi-Step Equations Then
Now
Why?
You solved singlestep equations.
1
Solve equations involving more than one operation.
2
Solve equations involving consecutive integers.
The Tour de France is the premier cycling event in the world. The map shows the 2007 Tour de France course. If the length of the shortest portion of the race can be represented by k, the expression 4k + 20 is the length of the longest stage or 236 kilometers. This can be described by the equation 4k + 20 = 236
(Lesson 2-2)
Multi-Part Lesson
1
PART
Gand Paris Chablis
FRANCE
Tallard
Addition and Subtraction Equations A
Main Idea Write and solve addition and subtraction equations using bar diagrams.
B
C
D
NewVocabulary
Solve Addition and Subtraction Equations with Bar Diagrams
multi-step equation consecutive integers number theory
Alabama Course of Study A7.0 Solve multistep equations and inequalities, including linear, radical, absolute value, and literal equations.
Get ConnectED
A7.2 Formulating the design of application-based problems by developing and solving equations and inequalities, including those involving direct and inverse variation
What do you need to find? how many states did not have a cell phone law for school bus drivers You can represent this situation with an equation.
states that do not have a law ?
Original equation Add 4 to each side.
33 11x _ =_
Simplify.
x=3
Simplify.
11
11
Divide each side by 11.
a+7 b. _ = 5 a+7 _ =5
(
8
8
)
a + 7 = 40 -________ 7=-7 a = 33
Write an equation from the bar diagram. Let x represent the states that do not have a cell phone law for school bus drivers.
Original equation Multiply each side by 8. Simplify. Subtract 7 from each side. Simplify.
You can check your solutions by substituting the results back into the original equations.
GuidedPractice
15 + x = 50
Solve each equation. Check your solution.
Use the work backward strategy to solve the equation. Since 15 + x = 50, x = 50 - 15. So, x = 35. Check
a. 11x - 4 = 29 11x - 4 = 29 11x - 4 + 4 = 29 + 4 11x = 33
a+7 8 _ = 8(5)
50 states
15
Solve each equation. Check your solution.
8
Draw a bar diagram that represents the total number of states and how many have passed a law.
states with a law
Since the above equation requires more than one step to solve, it is called a multi-step equation. To solve this equation, we must undo each operation by working backward.
Example 1 Solve Multi-Step Equations
CELL PHONES In a recent year, 15 of the 50 states had a law banning the use of handheld cell phones while driving a school bus. How many states did not have this law?
GLE 0706.3.7 Use mathematical models involving linear equations to analyze real-world phenomena. GLE 0706.3.8 Use a variety of strategies to efficiently solve linear equations and inequalities. Also addresses GLE 0706.1.4, GLE 0706.1.8, SPI 0706.3.7.
1 Solve Multi-Step Equations
1A. 2a - 6 = 4 5
15 + 35 = 50
n+1 1B. _ = 15 -31 -2
connectED.mcgraw-hill.com
91
So, 35 states did not have a law banning the use of cell phones by bus drivers. 091_096_CH02L3_892242.indd 91
29/01/10 12:54 PM
the Results 1. Suppose nine more states adopt similar laws. How would the equation change? 2. How would the diagram change if the U.S. Virgin Islands and Puerto Rico were counted with the United States? 204 Equations and Inequalities
204_213_C04L1_895130.indd 204
12/31/09 3:55 PM
MIDDLE GRADES
HIGH SCHOOL
Get ConnectED
A complete Scope & Sequence can be found in the Teacher Handbook or at connectED.mcgraw-hill.com. T21
Authors O
ur lead authors ensure that the Macmillan/McGrawHill and Glencoe/McGraw-Hill mathematics programs are truly vertically aligned by beginning with the end in mind—success in Algebra 1 and beyond. By “backmapping” the content from the high school programs, all of our mathematics programs are well articulated in their scope and sequence.
Lead Authors
John A. Carter, Ph.D.
Gilbert J. Cuevas, Ph.D.
Assistant Principal for Teaching and Learning Adlai E. Stevenson High School Lincolnshire, Illinois
Professor of Mathematics Education Texas State University—San Marcos San Marcos, Texas
Areas of Expertise: Using technology and manipulatives to visualize concepts; mathematics achievement of English language learners
Areas of Expertise: Applying concepts and skills in mathematically rich contexts; mathematical representations
Roger Day, Ph.D., NBCT
Carol Malloy, Ph.D.
Mathematics Department Chairperson Pontiac Township High School Pontiac, Illinois
Associate Professor University of North Carolina at Chapel Hill Chapel Hill, North Carolina
Areas of Expertise: Understanding and applying probability and statistics; mathematics teacher education
Areas of Expertise: Representations and critical thinking; student success in Algebra 1
Get ConnectED
T22
Meet the authors at connectED.mcgraw-hill.com.
Built on Research
Program Authors
Ellen C. Grace
Mary Behr Altieri
Don S. Balka
Philip D. Gonsalves
Putnam/Northern Westchester BOCES Yorktown Heights, New York
Professor Emeritus Saint Mary’s College Notre Dame, Indiana
Mathematics Coordinator Alameda County Office of Education and California State University East Bay Hayward, California
Consultant Albuquerque, New Mexico
Stephen Krulik
Rhonda J. Molix-Bailey
Lois Gorden Moseley
Brian Mowry
Professor Emeritus Mathematics Education Temple University Cherry Hill, New Jersey
Mathematics Consultant Mathematics by Design Desoto, Texas
Staff Developer NUMBERS: Mathematics Professional Development Houston, Texas
Independent Math Educational Consultant/Part-Time Pre-K Instructional Specialist Austin Independent School District Austin, Texas
Christina L. Myren
Jack Price, Ed. D.
Mary Esther Reynosa
Rafaela M. Santa Cruz
Consultant Teacher Conejo Valley Unified School District Thousand Oaks, California
Professor Emeritus California State Polytechnic University Pomona, California
Instructional Specialist for Elementary Mathematics Northside Independent School District San Antonio, Texas
SDSU/CGU Doctoral Program in Education San Diego State University San Diego, California
Contributing Author
Lead Consultant
Robyn Silbey
Kathleen Vielhaber
Math Content Coach Montgomery County Public Schools Gaithersburg, Maryland
Mathematics Consultant St. Louis, Missouri
Dinah Zike
Viken Hovsepian
Educational Consultant Dinah-Might Activities, Inc. San Antonio, Texas
Professor of Mathematics Rio Hondo College Whittier, California
T23
Consultants T and Reviewers
hese professionals were instrumental in providing valuable input and suggestions for improving the effectiveness of the mathematics instruction.
Consultants Mathematical Content
Graphic Novels
Grayson H. Wheatley, Ph.D. Emeritus Professor Florida State University Tallahassee, Florida
Douglas Fisher, Ph.D. Macmillan/McGraw-Hill Treasures Author Associate Professor in the College of Education Department of Teacher Education San Diego State University San Diego, California
Dr. Michaele Chappell Professor of Mathematics Education Middle Tennessee State University Murfreesboro, Tennessee
Differentiated Instruction Jennifer Taylor-Cox, Ph.D. Educational Consultant Innovative Instruction: Connecting Research and Practice in Education Severna Park, Maryland
Reading in the Content Areas Sue Z. Beers President/Consultant Tools for Learning, Inc. Jewell, Iowa
Reading and Vocabulary Donald R. Bear, Ph.D. Macmillan/McGraw-Hill Treasures Author Director, E.L. Cord Foundation Center for Learning and Literacy Professor of Educational Specialties College of Education University of Nevada, Reno Reno, Nevada
T24
Family Involvement Paul Giganti, Jr. Children’s Author Director, Math Festival Program California Math Council Albany, California
Literature David M. Schwartz Children’s Author, Speaker, Storyteller Oakland, California
English Learners Kathryn Heinze Graduate School of Education Hamline University St. Paul, Minnesota Gladis Kersaint, Ph.D. Associate Professor of Mathematics Education, K–12 University of South Florida Tampa, Florida
Cognitively Guided Instruction Susan B. Empson, Ph.D. Associate Professor of Mathematics and Science Education University of Texas at Austin Austin, Texas
Built on Research
Tennessee Advisory Board
Lisa M. Baranoski
Tracy Benson
Stephen W. Blessing
Dr. Allison Clark
Numeracy Coach Antioch High School Nashville, TN
Math Intervention Specialist (Grades 4-6)/Read 180 Catlettsburg Elementary School Sevierville, TN
Director of Curriculum, 6-12 Coffee County Schools Manchester, TN
Mathematics Curriculum Specialist Shelby County Schools Memphis, TN
Dr. Brenda P. Dean
Ashley Donoho
Jane Hudgins
Assistant Superintendent Morristown, TN
3rd Grade Teacher Dresden Elementary School Dresden, TN
Assistant Principal/ Literacy Leader Martin Elementary School Martin, TN
Tamora L. Jackson, B.B.A., M.A.T., Ed.D. 6th/7th Grade Teacher Bellevue Middle School Memphis, TN
Timothy Jones
Randall B. Kincaid
Leslie Mattern
Gary A. Petko
Exemplary Teacher Shelby County Schools Memphis, TN
Supervisor of Instruction, PreK-3 Sevier County Board of Education Sevierville, TN
Math Teacher Sevier County High School Sevierville, TN
Mathematics Specialist Knox County Schools Knoxville, TN
Sherleta Sanders 2nd Grade Teacher LaVergne Lake Elementary LaVergne, TN
Ernestine Saville-Brock Math Coordinator Metro-Nashville Public Schools Nashville, TN
Leah B. Tomlinson
Jerry L. Whitaker
8th Grade Math Teacher West Wilson Middle School Mt. Juliet, TN
Mathematics Curriculum Coordinator Washington County Jonesborough, TN
T25
Tennessee’s Mathematics Curriculum Framework, Grade 4 Correlated to Tennessee Math Connects, Grade 4 Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
Standard 1 – Mathematical Processes GLE 0406.1.1
Use mathematical language, symbols, and definitions while developing mathematical reasoning.
Throughout the text; for example, 2-1B, 5-2B, 7-2D, 8-2B, 10-1A, 13-2D
76–77, 253–254, 343–344, 402–403, 496–497, 655–656
GLE 0406.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
1-2B, 1-2C, 1-3D, 2-3C, 3-1C, 3-3D, 4-1C, 4-1D, 4-3D, 5-1B, 5-4B, 6-2B, 6-3F, 7-3D, 8-3C, 9-2A, 9-2B, 9-3C, 10-3C, 11-1E, 11-2D, 12-1B, 12-3B, 13-1D, 13-2B, 13-3B
36–39, 40–41, 54–55, 104–105, 134–135, 158–159, 190–193, 194–195, 214–215, 244–247, 268–269, 292–294, 312–313, 358–359, 426–427, 456–459, 460–463, 474–475, 518–519, 544–545, 556–557, 587–589, 606–607, 636–637, 644–647, 662–663
SPI 0406.1.4
Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument.
12-1B, 12-2A, 12-2B, 13-2B
587–589, 594–595, 596–598, 644–647
✔ 0406.1.1
Understand the relationship between use of answers and the accuracy of the number.
1-2B, 1-2C, 12-1A
36–39, 40–41, 586
✔ 0406.1.2
Identify the range of appropriate estimates, including over-estimate and under-estimate.
4-1C, 4-1D, 5-1B, 6-2B
190–193, 194–195, 244–247, 292–294
✔ 0406.1.5
Measure using ruler, meter stick, clock, thermometer, or other scaled instruments.
7-2E, 12-1A, 12-1B, 12-2A, 12-2B, 12-4A, 12-4B, 13-2A, 13-2B, 13-2D, 13-3A
345–346, 585–586, 587–589, 594–595, 596–598, 608–609, 613, 642–643, 647, 654, 658
✔ 0406.1.6
Identify geometric or physical attributes that are appropriate to measure in a given situation.
10-2B, 10-3A, 12-1C, 12-2B, 12-3A, 12-4B
506–508, 510–513, 591, 597, 602–604, 610–613
GLE 0406.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
1-2A, 4-3C, 5-1A, 5-2A, 7-4A, 12-4A
32–35, 210–213, 241–243, 250–251, 362–363, 608–609
SPI 0406.1.1
Verify a conclusion using the commutative, associative and distributive properties.
1-2A, 2-1D, 2-3B, 2-3D, 4-3C, 4-4B
32–35, 80–83, 100–102, 106–109, 210–213, 228–230
Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning.
1-2A, 2-1D, 2-3B, 2-3D, 4-3B, 4-3C, 4-4B, 5-1A, 5-2A, 5-3A
32, 80–83, 100–102, 106–109, 208–209, 228, 241–243, 250–251, 256–257
GLE 0406.1.4
Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.
2-2B, 2-3B, 3-2A, 3-2B, 3-2C, 3-3A, 3-3C, 3-4C, 4-2B
86–89, 100–102, 136–139, 140–141, 142–144, 148–150, 154–157, 168–169, 198–199
SPI 0406.1.2
Compare decimals using concrete and pictorial representations.
8-1E
396–398
✔ 0406.1.7
Translate the details of a contextual problem into diagrams and/or numerical expressions, and express answers using appropriate units.
3-1C, 3-2A, 3-3A, 3-3C, 3-3D, 7-4B, 8-2C
134–135, 136–139, 148–150, 155–157, 158–159, 364–366, 404–405
✔ 0406.1.8
Match the spoken, written, concrete (including base ten blocks), and pictorial representations of decimals.
8-1A, 8-1B, 8-1C
383–384, 385–387, 388–391
✔ 0406.1.9
Develop a story problem that illustrates a given multiplication or division number sentence.
2-2B, 2-3B, 4-3F, 4-4B, 6-3B
89, 102, 223, 230, 302
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
2-3A, 4-1B, 5-1C, 6-2A, 10-1C
98–99, 187–189, 248–249, 288–291, 502–503
✔ 0406.1.4
GLE 0406.1.5
T26
Correlated to Tennessee Math Connects, Grade 4
Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
GLE 0406.1.6
Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
Throughout the text; for example, 1-3C, 3-3C, 6-3E, 8-3B, 11-2B, 13-3A
50–53, 104–105, 308–310, 422–423, 549–550, 658–661
GLE 0406.1.7
Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
1-3A, 2-3D, 3-2C, 4-3D, 4-3F, 5-2B, 6-1B, 7-1A, 8-2F, 9-3E, 10-2B, 11-2C, 12-1C,13-1C, 13-3A
44–47, 106–109, 142–144, 214–215, 220–223, 252–254, 283–285, 327–329, 414–418, 478–481, 506–508, 552–555, 590–591, 632–634, 668–661
SPI 0406.1.3
Determine the correct change from a transaction.
9-2B, 9-3C, 9-3E
462, 475, 480–481
✔ 0406.1.3
Connect operations with decimals to money and make estimates.
9-2B, 9-3B, 9-3E
461–463, 471–473, 480–481
✔ 0406.1.10
Use age-appropriate books, stories, and videos to convey ideas of mathematics.
1-3A, 2-3D, 3-2C, 4-3F, 5-2B, 6-1B, 7-1A, 8-2F, 9-3E, 10-2B, 11-2C, 12-1C, 13-1C
46, 108, 144, 222, 254, 285, 329, 417, 480, 508, 554, 591, 634
1-3B, 2-1A, 4-1A, 4-2A, 4-3A, 4-3B, 4-4A, 5-1A, 6-3C, 11-3B
48–49, 73–74, 185–186, 196–197, 206–207, 208–209, 226–227, 241–243, 303, 563
GLE 0406.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
TE pages: 16D, 17, 19a, 19b, 32a, 32b, 44a, 44b, 60, 70D, 71, 73a, 73b, 84a, 84b, 94, 96a, 96b, 110a, 124D, 125, 127a, 127b, 136a, 136b, 146, 148a, 148b, 160a, 160b, 182D, 183, 185a, 185b, 196a, 196b, 206a, 206b, 206c, 224, 226a, 238D, 239, 241a, 241b, 250a, 256a, 262, 264a, 278D, 239, 241a, 241b, 250a, 256a, 262, 264a, 278D, 279, 281a, 281b, 288a, 296a, 296b, 296c, 314, 324D, 325, 327a, 334a, 334b, 348a, 3348b, 360, 362a, 362b, 380D, 381, 383a, 383b, 399a, 399b, 399c, 420a, 420b, 424, 442D, 443, 445a, 445b, 456a, 456b, 468a, 468b, 482, 492D, 493, 495a, 495b, 504a, 510a, 510b, 520, 530D, 531, 533a, 533b, 546a, 546b, 560a, 564, 566a, 566b, 582D, 583, 585a, 585b, 594a, 600, 602a, 608a, 608b, 624D, 625, 627a, 627b, 642a, 642b, 652, 658a
Standard 2 – Number and Operations GLE 0406.2.1
Understand place value of numbers from hundredths to the hundred-thousands place.
1-1A, 1-1B, 1-1C, 1-1D, 8-1A, 8-1B, 8-1C, 8-1D
19, 20–23, 24–27, 28–31, 383–384, 385–387, 388–391, 392–395
SPI 0406.2.1
Read and write numbers from hundredths to hundred-thousands in numerals and in words.
1-1B, 8-1B, 8-1C, 8-1D
20–23, 385–387, 388–391, 392–395
SPI 0406.2.3
Identify the place value of a specified digit in a number and the quantity it represents.
1-1B
20–23
✔ 0406.2.1
Compose and decompose quantities according to place value.
1-1A, 1-1B, 2-4A, 4-3B
19, 20–23, 110–113, 208–209
✔ 0406.2.2
Understand decimal notation as an extension of the base-ten number system.
8-1A, 8-1B, 8-1C
383–384, 385–387, 388–391
GLE 0406.2.2
Develop fluency with multiplication and singledigit division.
2-1A, 2-1B, 2-1C, 2-1D, 2-2A, 2-2B, 2-2C, 2-3A, 2-3B, 2-3C, 2-3D, 4-1A, 4-1B, 4-2C, 4-3B, 4-3E, 6-1B, 6-2A
73–74, 75–77, 78–79, 80–83, 84–85, 86–89, 90–92, 96–99, 100–102, 104–105, 106–109, 185–186, 187–189, 200–203, 208–209, 216–219, 283–285, 288–291
SPI 0406.2.11
Solve problems using whole number multi-digit multiplication.
4-2C, 4-3F, 4-4A, 4-4B, 5-1A, 5-1C, 5-2A, 5-2B, 5-3A, 5-3B, 5-4A, 5-4B
200–203, 220–223, 226–227, 228–230, 241–243, 248–249, 250–251, 252–254, 256–257, 258–261, 264–266, 268–269
SPI 0406.2.12
Solve problems using whole number division with one- or two-digit divisors.
6-1A, 6-1B, 6-3A, 6-3B, 6-3D, 6-3E
281–282, 283–285, 296–299, 300–302, 304–307, 308–310
✔ 0406.2.3
Multiply two- and three-digit whole numbers.
4-2C, 4-3C, 4-3E, 5-1A, 5-1B, 5-1C, 5-2A, 5-2B, 5-3A, 5-3B, 5-4B
200–203, 210–213, 216–219, 241–243, 244–247, 248–249, 250–251, 252–254, 256–257, 258–261, 268–269
✔ 0406.2.4
Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently.
4-2B, 4-3F, 4-4A, 4-4B, 5-1A, 5-3B, 5-4A, 6-2A, 6-3A, 6-3E
199, 220–223, 227, 228–230, 241–243, 258–261, 264–266, 288–291, 296–299, 308–310
T27
Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
✔ 0406.2.5
Understand that division by zero is undefined.
2-1D
81
✔ 0406.2.6
Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper.
6-3A, 6-3B, 6-3D
297–299, 300–302, 304–307
✔ 0406.2.10
Use models to understand division as the inverse of multiplication, partitioning, and repeated subtraction.
2-1A, 2-1B, 2-1C, 2-2B, 2-3A, 2-3B, 6-3C
73–74, 75–77, 78–79, 86–89, 96–99, 100–102, 303
✔ 0406.2.14
Understand the role of the remainder in division.
6-1B, 6-3B, 6-3E
283–285, 301–302, 309–310
GLE 0406.2.3
Identify prime and composite numbers.
2-4B
114–115
SPI 0406.2.4
Find factors, common factors, multiples, and common multiples of two numbers.
2-4A, 2-4B, 8-2E
110–113, 114–115, 410–413
Identify factors of whole numbers and model factors and products beyond basic multiplication facts using arrays and area models.
2-4A, 2-4B, 4-1A, 4-2B, 4-3F, 5-2A, 5-3A
110–113, 114–115, 185–186, 198–199, 220–221, 250–251, 256–257
GLE 0406.2.4
Understand and use the connections between fractions and decimals.
8-3A, 8-3B, 8-3D, 8-3E
420, 421–423, 428–429, 430–432
SPI 0406.2.2
Locate and place mixed numbers on the number line.
8-2F
414–418
SPI 0406.2.5
Generate equivalent forms of common fractions and decimals and use them to compare size.
8-2A, 8-2B, 8-2C, 8-3D, 8-3E
399–400, 401–403, 404–405, 428–429, 430–432
SPI 0406.2.6
Use the symbols < , > and = to compare common fractions and decimals in both increasing and decreasing order.
8-1E, 8-2D
396–398, 406–409
SPI 0406.2.7
Convert improper fractions into mixed numbers and/or decimals.
8-2F
414–418
Generate equivalent forms of whole numbers, 1 1 1 3 decimals, and common fractions (e.g., _, _, _, _).
8-2A, 8-2B, 8-2E, 8-3D, 8-3E
399–400, 401–403, 410–413, 428–429, 430–432
Compare equivalent forms whole numbers, fractions, and decimals to each other and to benchmark numbers.
8-1E, 8-2D
396–398, 406–409
✔ 0406.2.11
Use models, benchmarks, and equivalent forms to compare fractions/decimals and locate them on the number line.
8-1E, 8-2D
396–398, 406–409
✔ 0406.2.12
Understand and use decimal numbers up to hundredths and write them as fractions.
8-3A, 8-3B
420, 421–423
GLE 0406.2.5
Add and subtract fractions with like and unlike denominators.
9-1A, 9-1B, 9-1C
445–447, 448–451, 452–455
SPI 0406.2.8
Add and subtract proper fractions with like and unlike denominators and simplify the answer.
9-1A, 9-1B, 9-1C
445–447, 448–451, 452–455
GLE 0406.2.6
Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations.
1-2A, 1-2C, 1-3A, 1-3B, 1-3C, 1-3E, 2-3C, 5-1C, 6-1C, 6-3F, 8-3C, 9-3A, 9-3B, 9-3C, 9-3D, 9-3E, 12-1D, 13-3B
32–35, 40–41, 44–47, 48–49, 50–53, 56–59, 104–105, 248–249, 286–287, 312–313, 426–427, 468–469, 470–473, 474–475, 476–477, 478–481, 592–593, 662–663
SPI 0406.2.9
Add and subtract decimals through hundredths.
9-3A, 9-3B, 9-3C, 9-3D, 9-3E
468–469, 470–473, 474–475, 476–477, 478–481
SPI 0406.2.10
Solve contextual problems using whole numbers, fractions, and decimals.
1-2C, 1-3D, 2-2A, 4-1D, 4-3D, 5-1C, 5-4B, 6-1C, 6-3F, 7-2A, 7-3D, 8-2C, 8-3C, 9-2C, 9-3C, 11-2D, 12-1D
40–41, 54–55, 84–85, 194–195, 214–215, 248–249, 268–269, 286–287, 312–313, 334–335, 358–359, 404–405, 426–427, 464–465, 474–475, 556–557, 592–593
Solve multi-step problems of various types using whole numbers, fractions, and decimals.
1-3D, 4-3D, 6-1C, 6-3F, 9-1A, 9-3E, 13-3B
54–55, 215, 287, 312–313, 446–447, 480–481, 662–663
✔ 0406.2.7
✔ 0406.2.8
10 4 2 4
✔ 0406.2.9
✔ 0406.2.13
T28
Correlated to Tennessee Math Connects, Grade 4
Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
Standard 3 – Algebra GLE 0406.3.1
Extend understanding of a variable to equations involving whole numbers, fractions, decimals, and/or mixed numbers.
3-2B, 3-2C, 3-3B, 3-3C, 8-2B, 8-2E, 9-1C
140–141, 142–144, 152–153, 154–157, 403, 412, 455
SPI 0406.3.1
Use letters and symbols to represent an unknown quantity and write a simple mathematical expression.
3-2A, 3-3A
136–139, 148–150
✔ 0406.3.1
Find an unknown quantity in simple equations using whole numbers, fractions, decimals, and mixed numbers.
3-2B, 3-2C, 3-3B, 3-3C, 8-2B, 8-2E, 9-1C
140–141, 142–144, 152–153, 154–157, 403, 412, 455
✔ 0406.3.2
Translate between symbols and words to represent quantities in expressions or equations.
3-2A, 3-2C, 3-3A, 3-3C
137–138, 143–144, 149–150, 155–156
GLE 0406.3.2
Use mathematical language and modeling to develop descriptions, rules and extensions of patterns.
3-1A, 3-1B, 3-1C, 3-3D, 3-4A, 3-4B, 3-4C, 3-4D, 7-2A, 7-3D, 10-1C, 10-3C
127–129, 130–133, 134–135, 158–159, 160–163, 164–167, 168–169, 170–173, 334–335, 358–359, 502–503, 518–519
SPI 0406.3.2
Make generalizations about geometric and numeric patterns.
3-1A, 3-1B, 3-3D, 10-1C
127–129, 130–133, 158–159, 502–503
SPI 0406.3.3
Represent and analyze patterns using words, function tables, and graphs.
3-1B, 3-4A, 3-4B, 3-4C, 3-4D
130–133, 160–163, 164–167, 168–169, 170–173
Create, explain and use a rule to generate terms of a pattern or sequence.
3-1B, 3-1C, 3-4A, 3-4B, 3-4C, 3-4D
130–133, 134–135, 160–163, 164–167, 168–169, 170–173
Translate between different forms of representations of whole number relationships.
3-1B, 3-1C, 3-2A, 3-2B, 3-2C, 3-3A, 3-3B, 3-3C
130–133, 134–135, 136–139, 140–141, 142–144, 148–150, 152–153, 154–157
Translate between symbolic, numerical, verbal, or pictorial representations of a whole number pattern or relationship.
3-1B, 7-2A
130–133, 334–335
✔ 0406.3.3 GLE 0406.3.3 ✔ 0406.3.4
Standard 4 – Geometry and Measurement GLE 0406.4.1
Understand and use the properties of lines, segments, angles, polygons, and circles.
10-1A, 10-1B, 10-2A, 10-2B, 10-3A, 10-3B, 11-1A, 11-1B, 11-1C
495–499, 499–501, 504–505, 506–508, 510–513, 514–517, 533, 534–535, 536–539
SPI 0406.4.1
Classify lines and line segments as parallel, perpendicular, or intersecting.
11-1B, 11-1C
534–535, 536–539
SPI 0406.4.4
Identify acute, obtuse, and right angles in 2-dimensional shapes.
10-3A
510–513
SPI 0406.4.5
Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes.
10-1A, 10-1B
497, 501
✔ 0406.4.1
Identify the basic parts of circles.
10-1A
498
✔ 0406.4.2
Understand the definition of degree as it relates to the circle.
10-2A, 10-2B
504–505, 506–508
✔ 0406.4.3
Classify angles and triangles as obtuse, acute, or right.
10-2A, 10-2B, 10-3A
504–505, 506–508, 510–513
✔ 0406.4.4
Measure and draw angles.
10-2B
508
✔ 0406.4.5
Determine if a figure is a polygon.
10-1A
495–497
Recognize two-dimensional faces of threedimensional shapes.
10-1B
499–501
Understand and use measures of length, area, capacity, and weight.
12-1A, 12-1B, 12-1C, 12-2A, 12-2B, 12-3A, 12-4A, 13-1A, 13-1B, 13-1C, 13-1E, 13-2B, 13-2C, 13-2D
585–586, 587–589, 590–591, 594–595, 596–598, 602–604, 608–609, 627, 628–631, 632–634, 638–640, 644–647, 648–651, 654–657
✔ 0406.4.21 GLE 0406.4.2
T29
Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
SPI 0406.4.6
Determine situations in which a highly accurate measurement is important.
12-1A, 12-2B
585–586, 596–598
SPI 0406.4.7
Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight.
12-1B, 12-2B, 13-1B, 13-1E, 13-2B, 13-2D
587–589, 596–598, 628–631, 638–640, 644–647, 654–656
✔ 0406.4.6
Recognize the use of decimals in metric measures.
8-1E, 9-3E
394, 478–480
✔ 0406.4.7
Measure liquids using both standard units and metric units.
13-1A, 13-1E
627, 638–640
✔ 0406.4.8
Recognize that a measure of area represents the total number of same-sized units/that cover the shape without gaps or overlaps.
12-4A, 12-4B
608–609, 610–613
✔ 0406.4.9
Recognize that area does not change when 2-dimensional figures are cut apart and rearranged.
12-4B, 12-4C
612, 615
✔ 0406.4.10
Connect area measure to multiplication using a rectangular area model.
12-4A, 12-4B
608–609, 610–613
✔ 0406.4.13
Compare objects with respect to a given attribute such as length, area, and capacity.
12-1B, 12-1C, 12-2B, 13-2B
589, 590–591, 598, 644–647
GLE 0406.4.3
Solve problems that involve estimating and measuring length, area, capacity and weight.
12-1B, 12-2B, 12-3A, 12-3B, 12-4B, 12-4C, 13-1B, 13-1D, 13-2A
587–589, 596–598, 602–604, 606–607, 610–613, 614–615, 628–631, 636–637, 642–643
SPI 0406.4.8
Convert measurements within a single system that are common in daily life (e.g., hours and minutes, inches and feet, centimeters and meters, quarts and gallons, liters and milliliters).
12-1C, 13-1C, 13-2C, 13-2D
590–591, 632–634, 648–651, 654–657
SPI 0406.4.9
Solve problems involving area and/or perimeter of rectangular figures.
12-3A, 12-3B, 12-4B, 12-4C
602–604, 606–607, 610–613, 614–615
✔ 0406.4.11
Estimate areas of rectangles in square inches and square centimeters.
12-4A, 12-4B, 12-4C
608–609, 610–613, 614–615
✔ 0406.4.12
Estimate the size of an object with respect to a given measurement attribute (length, perimeter, area, or capacity).
12-1A, 12-2A, 12-3A, 12-4C, 13-1B, 13-2A, 13-2B, 13-2D
585–586, 594–595, 602–604, 614–615, 628–631, 642–643, 644, 654–656
GLE 0406.4.4
Understand the representation of location and movement within the first quadrant of a coordinate system.
11-1D, 11-1E, 11-4A, 11-4B, 11-4C
540–543, 544–545, 566–567, 568–571, 572–574
SPI 0406.4.2
Graph and interpret points with whole number or letter coordinates on grids or in the first quadrant of the coordinate plane.
11-1D
540–543
SPI 0406.4.3
Construct geometric figures with vertices at points on a coordinate grid.
11-1D
543
SPI 0406.4.10
Identify images resulting from reflections, translations, or rotations.
11-2A, 11-2B, 11-2C, 11-2D, 11-3A
546–547, 548–551, 552–555, 556–557, 560–562
✔ 0406.4.14
Explain how the components of a coordinate system are used to determine location.
11-1D
540–543
✔ 0406.4.15
Explore properties of paths between points.
11-1D, 11-1E
541–542, 544–545
✔ 0406.4.16
Examine transformations in the coordinate plane.
11-2A, 11-2B
546–547, 548–551
✔ 0406.4.17
Predict the results of a transformation of a geometric shape.
11-2A, 11-2B
546–547, 548–551
✔ 0406.4.18
Determine whether a geometric shape has line and/ or rotational symmetry.
11-4A, 11-4B, 11-4C
566–567, 568–571, 572–574
✔ 0406.4.19
Design and analyze simple tilings and tessellations.
11-2C
552–555
✔ 0406.4.20
Draw lines of symmetry in 2-dimensional figures.
11-4B
568–571
T30
Correlated to Tennessee Math Connects, Grade 4
Grade Level Expectation (GLE), State Performance Indicator (SPI), and Check for Understanding (✔)
Lesson(s)
Page(s)
Standard 5 – Data, Probability and Statistics GLE 0406.5.1
Collect, record, arrange, present, and interpret data using tables and various representations.
7-1A, 7-2B, 7-2C, 7-2D, 7-2E, 7-3A, 7-3B, 7-3C
327–329, 336–339, 340–341, 342–344, 345–346, 348–351, 352–353, 354–356
SPI 0406.5.1
Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs).
7-1A, 7-2C, 7-2E, 7-3B
327–329, 340–341, 345–346, 352–353
SPI 0406.5.2
Solve problems using estimation and comparison within a single set of data.
7-2D, 7-3A, 7-3C
342–344, 348–351, 354–356
SPI 0406.5.3
Given a set of data or a graph, describe the distribution of the data using median, range, or mode.
7-1B, 7-2B
330–333, 336–339
✔ 0406.5.1
Create and label appropriate scales for graphs.
7-2E, 7-3B
345–346, 352–353
✔ 0406.5.2
Evaluate how well various representations show the collected data.
7-2B
337
✔ 0406.5.3
Interpret and prepare pie charts using appropriate measurements of angles.
7-3A, 10-2B
351, 508
✔ 0406.5.4
Develop and use stem-and-leaf plots.
7-2C
340–341
✔ 0406.5.5
Use measures of central tendency to compare two sets of related data.
7-1B, 7-3B, 7-3C
333, 352–353, 354–356
GLE 0406.5.2
Use probability to describe chance events.
7-4C
368–371
SPI 0406.5.4
List all possible outcomes of a given situation or event.
7-4A, 7-4B, 11-1E
362–363, 364–367
✔ 0406.5.6
Determine a simple probability.
7-4C
368–371
✔ 0406.5.7
Express a probability pictorially.
7-4C
370
T31
NCTM Process Standards Correlated to Tennessee Math Connects, Grade 4
NCTM Process Standard
Lesson(s)
Page Number(s)
Problem Solving Tennessee Math Connects addresses problem solving throughout the text and in Graphic Novels, Problem-Solving Strategy lessons, Problem-Solving Investigation lessons, and Cross-Curricular features. Build new mathematical knowledge through problem solving.
Throughout the text; for example, 1-2C, Ch. 2 CC, 4-3D, 7-2A, 12-1D
Throughout the text; for example, 40–41, 94–95, 214–215, 334–335, 592–593
Solve problems that arise in mathematics and in other contexts.
Throughout the text; for example, Ch. 1 GN, Ch. 3 GN, 7-3D, Ch. 12 GN, 13-1C
Throughout the text; for example, 17, 46, 125, 144, 358–359, 583, 634
Apply and adapt a variety of appropriate strategies to solve problems.
Throughout the text; for example, 2-3C, 5-4B, 10-3C, 11-1E, 13-3B
Throughout the text; for example, 104–105, 268–269, 518–519, 544–545, 663–664
Monitor and reflect on the process of mathematical problem solving.
Throughout the text; for example, 2-2A, 4-1D, 6-1C, 10-1C, 13-1D
Throughout the text; for example, 84–85, 194–195, 286–287, 502–503, 636–637
Reasoning and Proof Tennessee Math Connects addresses reasoning and proof in every lesson. See Talk Math and H.O.T. Problems: Challenge, Find the Error, Number Sense, Open Ended, Which One Doesn’t Belong, Write Math. Also see Reflect and Clarify in the teacher support of the Explore lessons. Recognize reasoning and proof as fundamental aspects of mathematics.
Throughout the text; for example, 1-2A, 5-4A, 6-3E, 8-3B, 11-2B
Throughout the text; for example, 33–34, 266, 310, 422–423, 549–550
Make and investigate mathematical conjectures.
Throughout the text; for example, 2-3D, 3-4A, 6-2A, 8-2B, 12-4A
Throughout the text; for example, 108, 161–162, 291, 402–403, 608–609
Develop and evaluate mathematical arguments and proofs.
Throughout the text; for example, 1-2B, 2-4A, 8-2E, 10-3B, 13-2B
Throughout the text; for example, 37, 39, 112, 411–412, 516, 645
Select and use various types of reasoning and methods of proof.
Throughout the text; for example, 2-2C, 3-4B, 5-1B, 8-2D, 10-1B
Throughout the text; for example, 92, 165–166, 247, 409, 501
KEY
T32
CC: Cross Curricular GN: Graphic Novels
Correlated to Tennessee Math Connects, Grade 4
NCTM Process Standard
Lesson(s)
Page Number(s)
Communication Tennessee Math Connects addresses communication in every lesson. See Talk Math and H.O.T. Problems: Challenge, Find the Error, Number Sense, Open Ended, Which One Doesn’t Belong, Write Math. Organize and consolidate their mathematical thinking through communication.
Throughout the text; for example, 1-3A, 4-4B, 7-1A, 8-2F, 12-2B
Throughout the text; for example, 46–47, 229–230, 328–329, 416–417, 597–598
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Throughout the text; for example, 1-1C, 3-1A, 6-1B, 8-1E, 10-1A
Throughout the text; for example, 26–27, 128–129, 284–285, 397–398, 497
Analyze and evaluate the mathematical thinking and strategies of others.
Throughout the text; for example, 3-2A, 5-3B, 7-4C, 9-1A, 13-2D
Throughout the text; for example, 137–138, 260, 369–370, 446–447, 655
Use the language of mathematics to express mathematical ideas precisely.
Throughout the text; for example, 2-1D, 5-2B, 6-3D, 8-1C, 10-2B
Throughout the text; for example, 82–83, 253–254, 305–306, 389–390, 507–508
Connections Tennessee Math Connects addresses connections throughout the text by including real-world application problems. In addition, Cross-Curricular features are found in each chapter. Recognize and use connections among mathematical ideas.
Throughout the text; for example, 2-1B, Ch. 5 CC, Ch. 6 CC, 12-4C, 13-2C
Throughout the text; for example, 77, 262–263, 314–315, 614–615, 648–650
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Throughout the text; for example, Ch. 3 CC, Ch. 5 CC, Ch. 7 CC, Ch. 9 CC, Ch. 12 CC
Throughout the text; for example, 146–147, 262–263, 360–361, 482–483, 600–601
Recognize and apply mathematics in contexts outside of mathematics.
Throughout the text; for example, Ch. 1 CC, 4-3F, Ch. 8 CC, Ch. 11 CC, 12-1B
Throughout the text; for example, 60–61, 222, 424–425, 564–565, 587–589
Representation Tennessee Math Connects addresses multiple representations throughout the text by incorporating manipulatives, diagrams, charts, tables, symbols, and graphs. Create and use representations to organize, record, and communicate mathematical ideas.
Throughout the text; for example, 3-1C, 7-3B, 7-4B, 8-2A, 13-3A
Throughout the text; for example, 134–135, 352–353, 364–366, 399–400, 658
Select, apply, and translate among mathematical representations to solve problems.
Throughout the text; for example, 3-4D, 5-1C, 7-3A, 9-1B, 13-1B
Throughout the text; for example, 170–173, 248–249, 348–351, 448–450, 630
Use representations to model and interpret physical, social, and mathematical phenomena.
Throughout the text; for example, 1-1A, 2-1A, 4-1A, 10-2A, 11-1B
Throughout the text; for example, 19, 73–74, 185–186, 504–505, 534–535
KEY
CC: Cross Curricular GN: Graphic Novels
T33
Cou rse 1
Cou rse 2
†
•
•
•
Blending Math Connects and IMPACT Mathematics
•
•
•
•
•
•
•
•
•
IMPACT Mathematics*
•
•
•
•
•
•
•
•
•
Hands-On Activity Tools and Resources
•
•
•
•
•
•
•
•
•
ELL Guide
•
•
•
•
•
•
•
•
•
Real-World Problem-Solving Readers*
•
•
•
•
•
• •
•
•
Quick Review Skills Workbook
•
•
•
Study Notebook
•
•
•
•
•
•
Real-World Problem Solving Graphic Novels Strategic Intervention Guide*
Learning Station Cards*
•
•
•
•
•
•
•
•
•
•
•
Quick Review Math Handbook Alphabet Cards*
•
Activity Flipchart
•
Student Edition Flipbook
•
•
Math Routines on the Go*
•
•
•
Robot Puppet
•
•
•
Transition Blackline Masters
•
Game Boards*
•
•
•
•
•
•
Visual Vocabulary Cards*
•
•
•
•
•
•
•
•
•
Family Letters and Activities*
•
•
•
•
•
•
•
•
•
Diagnostic and Placement Tests*
•
•
•
•
•
•
•
•
•
StudentWorks™ Plus CD-ROM or DVD
•
•
•
•
•
•
•
•
•
TeacherWorks™ Plus CD-ROM or DVD
•
•
•
•
•
•
•
•
•
ExamView®
•
•
•
•
•
•
•
•
•
Interactive Classroom PowerPoint™
•
•
•
•
•
•
•
•
•
Online Games
•
•
•
•
•
•
Math Songs CD-ROM*
•
•
•
•
•
• •
•
•
Assessment Suite CD-ROM
eSolutions Manual CD-ROM WorkMats*
•
•
•
•
•
•
Individual Manipulative Kit
•
•
•
•
•
•
•
•
•
Classroom Manipulative Kit
•
•
•
•
•
•
•
•
•
Overhead Manipulative Kit
•
•
•
•
•
•
•
•
•
Dinah Zike’s Teaching with Foldables®
•
•
•
•
•
•
•
•
•
Professional Development
•
•
•
•
•
•
•
•
•
* Available in Spanish
T34
Cou rse 3
de 5 Gra
†
de 4 Gra
†
de 3 Gra
†
de 2 Gra
†
Chapter Resource Masters
de 1 Gra
†
Components
de K Gra
Components and Manipulatives
† Available in Teacher Edition
Cou rse 2
Cou rse 3
8
2
6
3
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
grid paper
•
•
•
•
•
•
•
•
Money
real money, construction paper
•
•
•
•
•
JODIFT
Ruler
straightedge, book
•
•
•
•
•
Fraction Circles
construction paper
•
•
•
•
•
•
•
•
Fraction Tiles
construction paper
•
•
•
•
•
•
Geoboards
dot paper
•
•
•
•
•
•
Compass
paper clip
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Attribute Buttons
real buttons, pasta
•
•
Color Tiles
blocks, buttons
•
•
Graphing Mats
poster board
•
•
Attribute Blocks
pasta, buttons
•
•
Student Clock
paper plate, brads
•
•
•
•
•
•
Demonstration Clock
paper plate, brads
•
•
•
•
•
•
Connecting Cubes
paper clips
•
•
•
•
•
•
•
Number Cubes
spinner, cards
•
•
•
•
•
•
Spinners
construction paper, paper clip, pencil
•
•
•
•
•
Two-Color Counters
buttons, coins, beans
•
•
•
•
Pattern Blocks
construction paper
•
•
•
Geometric Solids/Models
cans, boxes, balls
•
•
Bucket Balance
ruler, paper cups, string
•
•
Base-Ten Blocks
•
•
•
•
Protractor
•
•
•
Plastic Cups
paper cups
Algebra Tiles
block, buttons, coins
•
•
•
Equation Mats
construction paper
•
•
•
Measuring Cups
paper cups
•
•
•
•
•
•
Geomirrors
mirror
•
•
•
•
•
•
•
•
•
Stopwatch '
Gra de 5
•
Gra de 4
•
Gra de 3
•
•
Gra de 2
•
•
Gra de 1
•
Gra de K
•
Bears in a Boat
PreK
Cou rse 1
Suggested Alternative
•
Manipulative
$
m
m
m
m
m
m
m
m
m
Thermometers
•
•
•
m
T35
Suggested Pacing for Tennessee’s Math Connects, Grade 4 Chapter
Days
Start Smart
Optional
Chapter
1
Place Value, Addition, and Subtraction
12
Chapter
2
Apply Multiplication and Division Facts
14
Chapter
3
Algebraic Patterns
12
Chapter
4
Multiply by One-Digit Numbers
12
Chapter
5
Multiply Multi-Digit Numbers
Chapter
6
Understand Division
11
Chapter
7
Organize and Display Data
12
Chapter
8
Decimals and Fractions
13
Chapter
9
Add and Subtract Fractions and Decimals
10
Chapter 10
Identify and Describe Geometric Figures
9
Chapter 11
Spatial Reasoning
13
Chapter 12
Measure Length
10
Chapter 13
Measure Capacity, Weight, and Mass
13
9
Projects
Optional Total
150
Copyright © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning. Send all inquiries to: Macmillan/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-02-103092-7 (Teacher Edition Program Overview) MHID: 0-02-103092-8 (Teacher Edition Program Overview) ISBN: 978-0-02-103030-9 (Student Edition) MHID: 0-02-103030-8 (Student Edition) Tennessee Math Connects, Grade 4 Printed in the United States of America. 1 2 3 4 5 6 7 8 9 10 WEB 18 17 16 15 14 13 12 11 10
Teacher Edition
Table of Contents
Authors Carter • Cuevas • Day • Malloy Altieri • Balka • Gonsalves • Grace • Krulik • Molix-Bailey • Moseley • Mowry Myren • Price • Reynosa • Santa Cruz • Silbey • Vielhaber
Contents
Refer to the Teacher Resource Handbook to further explore: • 22 Professional Development articles • Program Scope and Sequence • Research Bibliography • Teacher’s Annotated Glossary • Vocabulary Scope and Sequence
You may want to use these optional lessons to refresh key prerequisite skills taught in previous grades.
ii
1
The Four Step Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2
Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3
Patterns and Function Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
4
Analyze Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
1
Place Value, Addition, and Subtraction
Investigate
Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Multi-Part Lesson
1
A B C D Multi-Part Lesson
Place Value Expl plo ore Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Compare and Order Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Round Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
A B C
Practice
Every chapter and every lesson has a wealth of interactive learning opportunities.
Addition and Subtraction Addition Properties and Subtraction Rules . . . . . . . . . . . . . . . . . . . . 32 Estimate Sums and Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Problem-Solving Skill: Estimate or Exact Answer . . . . . . . . . . . . . 40 Game Time: Make a Big Difference. . . . . . . . . . . . . . . . . . . . . . 42
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Multi-Part Lesson
A B C D E
3
Add and Subtract Whole Numbers Add Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Expl plo ore Subtract Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Subtract Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . . 54
Subtract Across Zeros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Problem Solving in Science: Ready, Set, Click . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
iii
CHAPTE R
2
Apply Multiplication and Division Facts
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Multi-Part Lesson
1
A B C D Multi-Part Lesson
Relate Multiplication and Division Expl plo ore Meaning of Multiplication and Division . . . . . . . . . . . . . . . 73 Relate Multiplication and Division Facts . . . . . . . . . . . . . . . . . . . . . . 75 Relate Division to Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Multiplication Properties and Division Rules . . . . . . . . . . . . . . . . . . . 80
2
A B C
Multiplication and Division Facts Through 9 Problem-Solving Skill: Choose an Operation . . . . . . . . . . . . . . . . 84 Multiply and Divide Through 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Multiply and Divide Through 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Problem Solving in History: Pop Culture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Multi-Part Lesson
3
A B
Multiply and Divide by 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Multiply and Divide by 11 and 12 . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Game Time: Multiplication Bingo . . . . . . . . . . . . . . . . . . . . . . 103 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 104
C D Multi-Part Lesson
A B
Multiplication and Division Facts Greater Than 9
Multiply Three Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4
Factors and Multiples Determine Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Prime and Composite Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
iv
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
3
Investigate
Algebraic Patterns Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Multi-Part Lesson
1
A B C Multi-Part Lesson
Patterns
Practice
Nonnumeric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Numeric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Problem-Solving Skill: Draw a Picture . . . . . . . . . . . . . . . . . . . . . 134
2
A B C
Every chapter and every lesson has a wealth of interactive learning opportunities.
Addition and Subtraction Relationships Addition and Subtraction Expressions . . . . . . . . . . . . . . . . . . . . . . . 136 Expl plo ore Addition and Subtraction Equations . . . . . . . . . . . . . . . . . 140 Solve Equations with Addition or Subtraction . . . . . . . . . . . . . . . . . 142
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Problem Solving in Science: Do Flying Squirrels Really Fly? . . . . . . . . . . . . . . 146
Multi-Part Lesson
3
A
Multiplication and Division Expressions. . . . . . . . . . . . . . . . . . . . . . 148 Game Time: Expression Race. . . . . . . . . . . . . . . . . . . . . . . . . . 151 Expl plo ore Multiplication and Division Equations. . . . . . . . . . . . . . . . 152 Solve Equations with Multiplication or Division . . . . . . . . . . . . . . . 154
B C D Multi-Part Lesson
A B C D
Multiplication and Division Relationships
Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 158
4
Function Tables Find a Rule with Addition or Subtraction . . . . . . . . . . . . . . . . . . . . . 160 Find a Rule with Multiplication or Division . . . . . . . . . . . . . . . . . . . 164 Expl plo ore Functions with Two Operations . . . . . . . . . . . . . . . . . . . . . 168 Function Tables with Two Operations . . . . . . . . . . . . . . . . . . . . . . . 170
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
v
CHAPTE R
4
Multiply by One-Digit Numbers
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Multi-Part Lesson
1
A B C D Multi-Part Lesson
Multiples Expl plo ore Multiples of 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Round to Estimate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Problem-Solving Skill: Reasonable Answers . . . . . . . . . . . . . . . . 194
2
A B C
Multiply Without Regrouping Expl plo ore Use Models to Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Expl plo ore Use Area Models and Partial Products to Multiply. . . . . . 198 Multiply by One-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Game Time: Estimation Station . . . . . . . . . . . . . . . . . . . . . . . . 204
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Multi-Part Lesson
3
A B C D E F
Multiply with Regrouping Expl plo ore Use Models to Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Expl plo ore Multiply Mentally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 214 Multiply Two-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Multiply Multi-Digit-Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Problem Solving in Science: Emperors of the Ice . . . . . . . . . . . . . . . . . . . . . . 224
Multi-Part Lesson
A B
4
Multiplication with Zeros Expl plo ore Multiply Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 Multiply Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
vi
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
5
Multiply Multi-Digit Numbers
Investigate
Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Multi-Part Lesson
1
A B C Multi-Part Lesson
Multiplication with Tens
Practice
Multiply by Tens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Estimate Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Problem-Solving Strategy: Make a Table. . . . . . . . . . . . . . . . . . . 248
2
A B
Every chapter and every lesson has a wealth of interactive learning opportunities.
Two-Digit Multiplication Expl plo ore Multiply Two-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . 250 Multiply Two-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Multi-Part Lesson
3
Three-Digit Multiplication
A B
Expl plo ore Multiply Three-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . 256 Multiply Three-Digit Numbers by Two-Digit Numbers . . . . . . . . . . 258 Problem Solving in Geography: A Walk in the Park . . . . . . . . . . . . . . . . . . . . 262
Multi-Part Lesson
A B
4
Multi-Digit Multiplication Multiply Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Game Time: Greatest Products . . . . . . . . . . . . . . . . . . . . . . . . 267 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 268
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
vii
CHAPTE R
6
Understand Division
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Multi-Part Lesson
1
A B C Multi-Part Lesson
Model Division Expl p ore Model Division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Division with Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Problem-Solving Strategy: Guess, Check, and Revise . . . . . . . . 286
2
A B
Use Mental Math to Divide Divide Multiples of 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . 288 Estimate Quotients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Multi-Part Lesson
A B C D E
3
Divide Whole Numbers Two-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Three-Digit Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 Exte end Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Quotients with Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Divide Greater Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Game Time: Division Shuffle . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 312 F Problem Solving in Science: A Desert Safari . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
viii
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
7
Organize and Display Data
Investigate
Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Multi-Part Lesson
1
A B Multi-Part Lesson
Collect and Organize Data
Practice
Collect and Organize Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Find Mode, Median, Outliers, and Range. . . . . . . . . . . . . . . . . . . . . 330
2
A B C D E
Line Plots and Line Graphs
Every chapter and every lesson has a wealth of interactive learning opportunities.
Problem-Solving Strategy: Make a Table. . . . . . . . . . . . . . . . . . . 334 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Exte end Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Line Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Exte end Make a Line Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Multi-Part Lesson
3
A B C
Bar Graphs Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Expl plo ore Make Double Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Double Bar Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Game Time: Graph Race . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 D Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 358 Problem Solving in Science: A Head Above the Rest . . . . . . . . . . . . . . . . . . . 360
Multi-Part Lesson
A B C
4
Probability Expl plo ore Possible Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Determine Possible Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
ix
CHAPTE R
8
Decimals and Fractions
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Multi-Part Lesson
1
A B C D E Multi-Part Lesson
Decimals Expl p ore Place Value Through Tenths and Hundredths . . . . . . . . . 383 Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Hundredths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Decimals Greater Than One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Compare and Order Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
2
A B C D E F
Fractions Expl p ore Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Problem-Solving Strategy: Make a Model . . . . . . . . . . . . . . . . . . 404 Compare and Order Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Simplest Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Multi-Part Lesson
3
Relate Fractions and Decimals
A B
Expl p ore Fractions and Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Problem Solving in Music: Decimal Note-ation . . . . . . . . . . . . . . . . . . . . . . . . 424
C D E
Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 426 Expl p ore Model Fraction and Decimal Equivalents . . . . . . . . . . . . . 428 Fraction and Decimal Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . 430 Game Time: Fraction and Decimal Game. . . . . . . . . . . . . . . . 433
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
x
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
9
Add and Subtract Fractions and Decimals
Investigate
Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Multi-Part Lesson
1
A B C Multi-Part Lesson
Add and Subtract Fractions
Practice
Add and Subtract Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Add Unlike Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Subtract Unlike Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
2
A B C
Every chapter and every lesson has a wealth of interactive learning opportunities.
Round and Estimate with Decimals Round Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 Estimate Decimal Sums and Differences . . . . . . . . . . . . . . . . . . . . . 460 Problem-Solving Strategy: Use Logical Reasoning . . . . . . . . . . . 464 Game Time: Match Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Multi-Part Lesson
A B C D E
3
Add and Subtract Decimals Expl plo ore Add Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 Add Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 474
Expl plo ore Subtract Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Subtract Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Problem Solving in History: Olympic Games . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
xi
CHAPTE R
10
Identify and Describe Geometric Figures
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Multi-Part Lesson
1
A B C Multi-Part Lesson
Two- and Three-Dimensional Figures Two-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Problem-Solving Strategy: Look for a Pattern . . . . . . . . . . . . . . . 502
2
A B
Angles Expl plo ore Classify Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
Multi-Part Lesson
A B C
3
Triangles and Quadrilaterals Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 518 Problem Solving in Art: Making Mosaics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 Game Time: Geometry Sketch . . . . . . . . . . . . . . . . . . . . . . . . . 522 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
xii
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
11
Investigate
Spatial Reasoning Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 Multi-Part Lesson
1
A B C D E Multi-Part Lesson
Lines Expl plo ore Lines, Line Segments, and Points . . . . . . . . . . . . . . . . . . . 533 Expl plo ore Parallel and Intersecting Lines . . . . . . . . . . . . . . . . . . . . . . 534 Lines, Line Segments, and Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 Find Points on a Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
Practice
Every chapter and every lesson has a wealth of interactive learning opportunities.
Problem-Solving Strategy: Make an Organized List . . . . . . . . . . 544
2
A B C D
Transformations Expl plo ore Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 Identify Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548 Tessellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 556
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 Game Time: Geometry Match . . . . . . . . . . . . . . . . . . . . . . . . . 559 Multi-Part Lesson
3
A B
Congruent Figures Congruent Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
Exte end Congruent Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Problem Solving in Social Studies: Congruent Cases . . . . . . . . . . . . . . . . . . 564
Multi-Part Lesson
A B C
4
Symmetry Expl plo ore Line and Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . 566 Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
xiii
CHAPTE R
12
Measure Length
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Multi-Part Lesson
1
A B C D Multi-Part Lesson
Customary Measurement Expl p ore Estimate and Measure Lengths . . . . . . . . . . . . . . . . . . . . . 585 Customary Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Convert Customary Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . 590 Problem-Solving Strategy: Solve a Simpler Problem . . . . . . . . . 592
2
A B
Metric Measurement Expl p ore Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Problem Solving in Science: Coral Reefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
Multi-Part Lesson
3
A
Measure Perimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 Game Time: Perimeter Guess . . . . . . . . . . . . . . . . . . . . . . . . . 605 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 606
B Multi-Part Lesson
A B C
Perimeter
4
Area Expl p ore Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Measure Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 Exte end Perimeters and Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
xiv
Contents
Get ConnectED connectED.mcgraw-hill.com
CHAPTE R
13
Measure Capacity, Weight, and Mass
Investigate
Learn
Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 Multi-Part Lesson
1
A B C
Capacity Expl plo ore Estimate and Measure Capacity. . . . . . . . . . . . . . . . . . . . . 627 Customary Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628 Convert Customary Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . 632 Game Time: Capacity Estimates . . . . . . . . . . . . . . . . . . . . . . . 635 Problem-Solving Strategy: Work Backward . . . . . . . . . . . . . . . . . 636
D E
Practice
Every chapter and every lesson has a wealth of interactive learning opportunities.
Metric Units of Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
Multi-Part Lesson
2
Weight and Mass
A B C
Expl plo ore Estimate and Measure Weight . . . . . . . . . . . . . . . . . . . . . . 642 Customary Units of Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
D
Metric Units of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654
Convert Customary Units of Weight . . . . . . . . . . . . . . . . . . . . . . . . . 648 Problem Solving in Science: Tide Pool Ecosystems . . . . . . . . . . . . . . . . . . . . . 652
Multi-Part Lesson
A B
3
Elapsed Time Elapsed Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658 Problem-Solving Investigation: Choose a Strategy . . . . . . . . . . 662
Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670
xv
End-of-Year Projects You may want to use these Problem-Solving Projects to finish the school year.
Problem-Solving Projects Make a Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 Plan a Family Celebration . . . . . . . . . . . . . . . . . . . . . . . . . . 676 Make Your Home Your Own . . . . . . . . . . . . . . . . . . . . . . . . 678 Plan a Trip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680
xvi
Contents
Get ConnectED connectED.mcgraw-hill.com Investigate
Student Handbook
Learn
Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EP2 Practice
Reference Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R1 English-Spanish Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R3 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R27
Every chapter and every lesson has a wealth of interactive learning opportunities.
xvii
ii_xvii_PO_TOC_103092.indd xvii
4/29/10 1:56 PM
Reading and Language Arts Support Why Integrate Reading and Language Arts in the Math Classroom? A Primer for Reading and Language Arts Support by Sue Z. Beers
I
posed the question: “Who would like to learn how to read story problems so you can solve them faster and have a better chance to respond correctly?” Every hand in the classroom went up. I continued, “Let me share a story problem with you. Listen closely, and be ready to provide the answer at the end.” The room was silent; every student listened intently. “The bus left the station with 5 people on board. It stopped at Locust Street, where 3 people got on and 1 person got off. Then it went on to State Street where 5 people got off and 4 people got on. It continued to First Street, where 7 people got on and 1 person got off. It ended on Fourth Street, where 5 people got on and 2 people got off. What’s the answer?” “15!” several students shouted in unison. I responded, “I’m sorry. That’s not the right answer.” One enterprising student shouted, “16! We forgot the bus driver!” “Good thinking, but that’s not the right answer,” I told them. “The answer is First Street.” Puzzled looks stared at me. “Well, you didn’t ask me what the question was. The question was, ‘What was the third stop?’ This is why reading a story problem is different from other kinds of reading. When you were taught to read, where did you learn that the main idea is located in a paragraph?” The students quickly answered that it was the first sentence. “The main idea of a story problem is usually the question at the end.” A boy at the front of the class looked at me for awhile, slapped his hand on the table, and said, “Why didn’t somebody tell us this at the beginning of the year?” Mathematics is a language. To learn math efficiently, students must be able to read, talk, and listen using math language. Learning in math is about sharing knowledge and understanding of what is being learned. Being able to communicate about math concepts means that students are thinking like mathematicians.
A2
Reading and Language Arts Support
How Language Arts and Reading Connect to Math Learning in any subject demands that students continually make connections between what they already know and the new concepts and skills being taught. Math is not just numbers and calculations; it is also patterns and logic. Recognizing patterns and logic in literature helps students see universal math concepts. Reading and writing in mathematics helps students: • Use language to understand and solve problems • Communicate ideas clearly • Organize their thinking and connect related ideas • Incorporate other perspectives into their understanding • Examine their own problem-solving processes • Represent ideas in different and meaningful ways • Interpret ideas in ways that make sense • See math as an important life subject, not just a school subject. Using Language Arts to Teach Math Vocabulary Using stories and poetry, students can understand math terms beyond a textbook definition. They are more playful in delivery and help students retain concepts in more meaningful ways for a longer period. When students write their own descriptions of words and share their understandings with others, they develop effective ways to express what the words and symbols mean to them.
Table of Contents Place Value, Addition, and Subtraction . . . . . . . . . . . . A6 Apply Multiplication and Division Facts . . . . . . . . . . . . . A9
When – And How – To Use This Appendix In determining when and how to use these activities, you might consider some of the following possibilities: • Use the literature activity to introduce the concept and build interest. • Differentiate instruction for students by using some of the activities as extended learning opportunities. • Allow students to choose an activity that appeal to them and to complete it either in small groups or individually. • Designate a “Math Arts” time once a week in which a math and language arts activity are completed. • Select at least 1 activity for each math unit, providing a mix of reading, writing, talking, and thinking activities across units. You might pick 1 activity for the whole class and then allow individuals or groups of students to pick a second one. • Create a math center that includes activities from this section. Allow students to choose the activities, or direct an individual or group of students to a specific activity that would help them. • Use the activities for integrated homework assignments. • Select some of the activities to include in a parent newsletter as ideas for parents to use at home with their children.
Algebraic Patterns . . . . . . . . . . . . . . . . . . . . . . . A13 Multiply by One-Digit Numbers . . . . . . . . . . . . . . . . A17 Multiply Multi-Digit Numbers . . . . . . . . . . . . . . . . . A21 Understand Division . . . . . . . . . . . . . . . . . . . . . . A25 Organize and Display Data . . . . . . . . . . . . . . . . . . A28 Decimals and Fractions . . . . . . . . . . . . . . . . . . . . A32 Add and Subtract Fractions and Decimals . . . . . . . . . . . A35 Identify and Describe Geometric Figures . . . . . . . . . . . A36 Spatial Reasoning . . . . . . . . . . . . . . . . . . . . . . . A41 Measure Length . . . . . . . . . . . . . . . . . . . . . . . . A45 Measure Capacity, Weight, and Mass . . . . . . . . . . . . . A45
Sue Z. Beers During her 31-year career in education, Sue Z. Beers has been a middle and high school teacher, technology coordinator, and school administrator. She is currently the Director of the Mid-Iowa School Improvement Consortium, which serves over 100 school districts in Iowa. Sue has worked with over 400 school districts in the areas of secondary reading strategies, effective teaching, Dimensions of Learning, student assessment, and school improvement.
Reading and Language Arts Support
A3
Helping Students Read Mathematics Texts Reading math text is a challenge even for able readers. Math text contains more concepts per word, per sentence, and per paragraph than any other content-area text. Students must shift from words, numbers, and symbols, and decode them to solve the mathematical problem. Reading math text requires unique knowledge and skills not taught in other areas, such as reading from right to left or top to bottom and vice versa, and reading diagonally, such as in charts. Reading mathematics is the ability to make sense of everything on the page. Reading and writing are fundamentally thinking tools. They help organize the students’ schema about how ideas fit together and relate. If students do not integrate and process ideas, they will have difficulty recalling what they have learned, or applying their learning later. Math text “holds still” for students. The words are always there, waiting for the reader to process and review them as many times as it takes to understand them. Front-loading new vocabulary prior to reading will aid students’ understanding. It helps anchor new learning to students’ prior knowledge. Calling on students’ prior learning about the new topic and giving them a brief introduction to new vocabulary before they begin to read will increase comprehension of math text. Before students learn a new math concept, teachers can: • Activate prior knowledge by reviewing prior concepts related to the new learning • Ask questions to arouse curiosity • Preview the text
Four Categories to Frame Math and Reading/Language Arts Suggestions for having students read, write, talk, and think about mathematics are provided in these four categories:
Reading math text helps strengthen math vocabulary. Using literature related to math concepts builds interest and helps students connect math to their everyday lives.
e Included in th e d ra Grade 4 T Book Library
Writing is the ultimate form of thinking. When students write about the thinking processes they use when solving math problems, it helps solidify their understanding of math concepts.
Verbalizing thinking will clarify what students know and help them formulate questions they still have about math.
Critical thinking involves asking questions that require students to seek clarification, discover errors in their thinking, and connect between ideas.
• Front-load key vocabulary • Provide a purpose that will guide reading or listening • Identify text features that will help reinforce understanding, such as examples, pictures, graphs, and diagrams. As students process the text, they can: • Organize knowledge with the use of graphic organizers. • Guide practice with modeling • Write the thought processes used to solve math problems • Refine their understanding of key vocabulary with multiple exposures to terms, connecting concepts, visualizing concepts, and describing terms in their own words. Reading math with understanding starts with students’ attitudes. By making connections with real-life applications, students learn to value math. Students’ willingness to read math will increase as they find success in their efforts. By preparing students to read math text and helping them process it in meaningful ways, teachers will help students interpret math text and learn math concepts effectively.
A4
Reading and Language Arts Support
Activities Embedded Include: • Literature Activity • • Math in the News • • Math in Our World • • Using Math Vocabulary • Get ConnectED
Examining Math Problem Solving in Math Extending Our Learning Math in Action
You can find more detailed information about these activities at macmillanmh.com
Reading Graphic Novels Text Features Specific to Graphic Novels Graphic novels motivate students to learn about new math concepts by presenting information in a fun and interesting format. To help students understand how to read graphic novels, provide them with guidance in how to use the text features unique to this genre: • Visual clues provide important information that may be necessary to solve the math problem presented. Ask students to identify information presented in the artwork and discuss why the artist may have included specific items in the frames. Remind students that the story is told by art and words. • Dialogue tells the “story” of the graphic novel. Because there is only a small space to include the dialogue, it must be very concise. Help students identify how thought and speech balloons are used to indicate spoken words as well as thoughts. • Non-verbal cues, such as facial expressions, enhance the story line and provide clues about the characters’ thoughts. Ask students how these non-verbal cues help them understand what is happening in the graphic novel. • Frames identify the series of events in the graphic novel. Discuss with students how these frames are sequenced. Help them think about how sequencing affects the ideas presented.
Using Comprehension Strategies with Graphic Novels Reading a graphic novel requires students to employ the same kinds of skills they would use to read text. To comprehend the story, they must: • Make inferences about what is happening, and fill in details from their own experience and knowledge • Think ahead to what might happen in the next frame, and predict what will happen next • Periodically summarize what has happened • Interpret text features to enhance understanding and gain clues about the story’s meaning • Look for clues that help sequence the story • Use visual and word clues that will unlock the meaning of new words • Evaluate how accurately they have interpreted the story. Helping students think about how a graphic novel is like reading text will help students understand the complex process of comprehension. Point out how these same skills are used when they read math problems!
Reading and Language Arts Support
A5
Reading and Language Arts Support
USE WITH
Chapter: Place Value, Addition, and Subtraction Multi-Part Lesson 1
Reading GLE 4.1.06.a The student will build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Literature Activity Read aloud with students How Much Is a Million? by David Schwartz. Then have students use flash cards to create several sets of Matching Game cards. Each set needs seven cards with place value names on them (ones, tens, hundreds, and so on through millions) and seven cards showing a 7-digit number with a different place value indicated on each card. (1,234,567; 1,234,567; 1,234,567; and so on) Divide the class into groups of four. Distribute a set of cards to each group. Have groups place their cards facedown in an array, and take turns matching place value names with their examples. Have groups identify strategies for organizing the values of each number.
Reading GLE 4.1.03.a The student will develop awareness of the sounds of language through repeated exposure to a variety of auditory experiences (e.g., poetry, music lyrics, books on tape, sound effects, read alouds).
Poem
Millions By Chandler Tyrrell
7 digits in a row; 1 million’s a mighty numb
er.
Imagine 1 million trees: That’s an awful lot of lumbe
r.
But is 1 million trees abou
t
e Included in th e Grade 4 Trad Book Library.
A single mountain’s worth
?
Or is that number way too More trees than there are
Reading GLE 4.1.06.f The student will foster word consciousness (e.g., word play, word walls and word sorts).
Using Math Vocabulary Display a word web for students. Write million in the center oval, and then work as a class to come up with related words, phrases, or examples to complete the surrounding ovals. Have students think of things they can conceptualize as a million. For example, have students consider how a million pennies can be expressed as a value in terms of dollars. Reading GLE 4.1.10.b The student will locate information using available text features (e.g., maps, charts, graphics, appendices, and tables of contents).
Q
".&3*$"/4
.07&
#?R? L?JWQGQ
A6
Reading and Language Arts Support
What about 1 million secon
ds?
Would they go by in just a
year?
If I counted for a century, Would I even be getting ne
ar?
1 million of whatever is a lot to count—don’t doub
t it. But if I had 1 million bucks nt it.
MJTGLE
,?RF ?LB2 MAG?J 2RSBGC
on Earth.
I’d pay someone else to cou
Extending Our Learning Refer to pages 19 and 20 in Americans on the Move. Display a copy of Place-Value Chart (Millions to Ones) found on page 100 in Hands-On Activity Tools and Resources. Rewrite each number from the table on page 19 using the place-value chart. Ask students how many zeros are represented by the word million when it is used in the table. Then have them rewrite each number 0/5)& from the table on page 20 in words. (For example, one milllion, three-hundred thirty-six, two-hundred dollars) Finally, point out to students that the numbers in the second chart show money spent in millions. Remind them that in the previous table, this meant the 6 zeros needed to be added to each number. Do the same here to show the actual amounts referred ers RWPS Read levels 3 to in the table. For example, Air: available in . sh $137,000,000,000 and in Spani 1C?J 6MPJB/PM@JCK2
much—
Math in Our World Read the poem aloud with students. Ask students to share their own ideas about how much 1 million is. Have them write a critique of the examples of 1 million that this writer uses. Which examples does he use? trees, seconds, dollars Have students compare and contrast the different examples of 1 million—their weight, value in society, importance to an adult versus importance to a fourth grader. How do students rate the value of each example?
USE WITH
Reading GLE 4.1.07.a The student will set a purpose for reading (e.g., to understand, to enjoy, to solve problems, to locate specific information/facts).
Reading GLE 4.1.09.g The student will retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
Literature Activity Before reading, distribute 40 counters to each student. Then read aloud Too Many Kangaroo Things to Do by Stuart J. Murphy. On the pages showing the total number of things each animal has to do, have students follow along with the totals by placing the corresponding number of counters in front of them. Demonstrate the Associative Property by adding the numbers in different orders, each time asking students whether the total number of counters change or stay the same each time. It stays the same.
Math in the Content Areas Have students compare the maps on pages 6–7 and 12–13 in Riding the Mail Trail. Ask, How do these maps add to your understanding of the text? They help me see clearly how much farther it was to reach the West Coast by ship versus over land. Then have students share any experiences they have had using maps or describing other maps they have seen.
On the page showing 40 dingo things to do, also demonstrate the Distributive Property. On the board, write (4 × 1) + (4 × 2) + (4 × 3) + (4 × 4) = 4 × (1 + 2 + 3 + 4) = 4 × 10 = 40 Ask students if they think the Distributive Property will work on the other problems from the book. Have them pair up and use their counters to test the Distributive Property using the other problems in the book.
Understanding Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 of Hands-On Activity Tools and Resources. Write estimate in the center rectangle, and work as a class to complete the surrounding squares. Then have students get into groups of four and write a short paragraph describing the steps they would take to estimate the total number of students in their school.
Math and Science
Real-World Problem
Reading and Language Arts Support
Chapter: Place Value, Addition, and Subtraction Multi-Part Lesson 2
Solving
s Math and Socia l Studie
Math and Social Studies
Number and Operations 8/2/07 2:24:02 PM
Next, have students pair up and turn to the he bar graph on page 16 in the reader. Ask them to round the number of stations in each state to the nearest 10, and then add to estimate the total number of stations. 230 Come together again as a class, and find the exact total. 227 Ask students if estimating is a good strategy for doing math quickly. Have them explain how it helps them. d ii Cover_B9_G04LEV_106234x.ind
Extending Our Learning Tell the class that a younger student needs help. He gave 3 marbles each to two of his friends, and he has 7 marbles left. He wants to know how he could find out how many marbles he had to begin with. Have students write a short paragraph describing what they would tell the younger student. Next, have them exchange papers to check for punctuation and spelling errors. Finally, ask several students to share what they wrote.
Reading and Language Arts Support
A7
Reading and Language Arts Support
USE WITH
Chapter: Place Value, Addition, and Subtraction Multi-Part Lesson 3
Reading GLE 4.1.12.a The student will read, view, and recognize various literary (e.g., poetry, novels, historical fiction, nonfiction) and media (e.g. photographs, the arts, films, video) genres.
Literature Activity Read aloud with students Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Cindy Bickel through page 16. Then work as a class to compare the weights of Matthew and T.J. as shown in the bar graph. Week 0: 3 – 3 = 0; Week 6: 14 – 10 = 4; Week 10: 19 – 13 = 6 Then use subtraction to compare their weight gains from 0 to 6 weeks, Matthew: 14 – 3 = 11; T.J.: 10 – 3 = 7; 11 – 7 = 4; Matthew gained 4 pounds more than T.J. from 6 to 10 weeks, Matthew: 19 - 14 = 5; T.J.: 13 - 10 = 3; 5 - 3 = 2; Matthew gained 2 pounds more than T.J. and overall. Matthew: 19 - 3 = 16; T.J.: 13 - 3 = 10; 16 - 10 = 6; Matthew gained 6 pounds more than T.J. overall Next, have students spend several minutes writing a short description of what it would be like to have a baby tiger as a pet. Encourage them to consider how they would need to accommodate their pet’s growth. Have them write about how much space the tiger might need and how much food it might eat. Ask several volunteers to share what they wrote. Have them explain how they determined the amount of space and food the tiger might need.
Reading GLE 4.1.10.a The student will develop and maintain vocabulary specific to content and to current events.
Reading Graphic Novels Have students revisit “Recycling CAN Make a Difference,” or distribute copies from page 1 of Hands-On Activity Tools and Resources. Point out to them that the dialoguee is written in speech balloons. Explain that these graphic features help readers separate which characters are speaking within a frame. Then explain that a frame is a single image surrounded by lines called frame borders. Have a volunteer tell how many frames are in this graphic novel. 8 frames Ask how the speech balloon is different in the fifth panel. It has bubbles instead of a point. Explain that this kind of speech balloon indicates what a character is thinking, not what he or she is saying. Tell students to imagine that the students in Carmen’s class collected 254 cans in May. Create and solve an addition problem to find out how many cans total the student collected in April and May. 178 cans + 254 cans = 432 cans Have students determine how many more were collected in May than April. 254 cans – 178 cans = 76 cans
A8
Reading and Language Arts Support
Reading GLE 4.1.02.b The student will use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Math in Our World Have students browse Solving the Pyramid Puzzle for words in boldface print, and list them on the board. Ask students to tell why these words are in boldface print. It tells the reader that the word is listed in the glossary. Have students use context clues and previous knowledge to create definitions for the words. Then turn to the glossary to compare their definitions to those in the reader.
1C?J 6MPJB/PM@JCK2MJTGLE ,?RF?LB 2AGCLAC
&CMKCRPW
Next, have students pair up. Tell them to list the pyramids referred to in the reader and their current heights in order from shortest to tallest. Students will use only whole numbers and ignore any decimals or fractions. Finally, have pairs use subtraction to compare each pyramid’s height to the height of the pyramid above it in their list. Ask them which of the two pyramids in their list had the greatest difference in height. The Transamerica Building is 404 feet taller than the Great Pyramid Then ask which had the least difference. The Great Pyramid is 3 feet taller than Khafre’s Pyramid.
USE WITH
Reading GLE 4.1.08.a.8 The student will derive meaning while reading by drawing conclusions based on evidence gained.
Reading GLE 4.1.01.a The student will listen attentively by facing the speaker, asking questions, and paraphrasing what is said.
Literature Activity Read aloud to students the spread in Hottest Coldest Highest Deepest by Steve Jenkins that shows the world’s highest waterfall. Display (or make copies) for students the diagram on the spread that compares the heights of three different waterfalls in the world to the height of the Empire State Building in New York City. To aid diagram reading, explain that each white band represents the height of a particular falls.
Using Math Vocabulary Display a copy of the Describe and Draw graphic organizer found on page in Hands-On Activity Tools and Resources. Write common factor in one example. Ask volunteers to share how they would draw or describe this word. Then have them complete the rest of the page with the following terms from this chapter: factor, common factor, and Distributive Property of Multiplication. Have volunteers share their descriptions in front of the class. Encourage volunteers in the audience to ask the speaker questions.
Point out that the height of the tallest falls is 3,212 feet. Have a volunteer explain how many times smaller Victoria Falls is than Angel Falls, and ask how they know. About 10 times; divide the height of Angel Falls by the height of Victoria Falls
Reading GLE 4.1.07.b The student will organize prior knowledge using a variety of strategies (e.g., webbing, mapping, brainstorming, listing).
Reading GLE 4.1.09.h The student will develop an awareness of the effects of media (e.g., television, print materials, radio, internet, magazines) on daily life.
Extending Our Learning Discuss with students what role multiplication and division play in helping to plan efficient use of space. Might it be easier or harder to work with even numbers or odd numbers? Have volunteers provide examples.
Math in Our World Ask students what kinds of considerations our media might make when publishing a newspaper. cost of paper used; size of paper used; what stories to write; how frequently to publish Tell them that newspaper publishers must think carefully about how to present the information in their publications.
Next, refer to pages 7 and 12 in Class Project. Ask students to get into pairs, and then distribute 12 counters to each pair. Have them arrange their counters in arrays that show how Miguel divides his 12 trophies equally onto 4 shelves. Then work as a class to create a fact family that demonstrates the arrangement.. 12; 12 ÷ 3 = 4; 12 ÷ 4 = 3 Repeat the exercise to show Emily’s 12 mugs arranged equally on 2 shelves. 2 × 6 = 12; 6 × 2 = 12; 12 ÷ 2 = 6; 12 ÷ 6 = 2 Ask students whether they think Emily’s mugs would be easier or more difficult to arrange if she had 11 mugs instead of 12.
Reading and Language Arts Support
Chapter: Apply Multiplication and Division Facts Multi-Part Lesson 1
Display a single sheet from a newspaper, and count with students to determine the total number of pages it contains. 4 On the whiteboard, write a series of multiplication sentences showing the numbers of sheets in relation to the number of pages. 1 sheet × 4 = 4 pages; 2 sheets × 4 = 8 pages; and so on through 20 pages Divide the class into groups of four, and then distribute three sheets of paper to each group. Explain that each group will be creating a newspaper. Have students stack their sheets and fold them using a hamburger fold as used in their Foldables activities. Lead a brief discussion about common newspaper names and the main sections found in most newspapers. Tell students that they will choose a name for their newspaper and write it on the front page. Then they will choose four sections to include in their paper. Next, they must calculate the number of total pages for each section so that all sections are equal. 3 Finally, each group will label their sections and create one headline per page. Ask students why they arranged their newspaper’s sections and stories in a particular order. Have a volunteer explain how this is similar to presenting reports, papers, and other assignments.
Reading and Language Arts Support
A9
Reading and Language Arts Support
USE WITH
Chapter: Apply Multiplication and Division Facts Multi-Part Lesson 2
Reading GLE 4.1.01.c The student will understand, follow, and give oral multi-step directions which may include illustrations.
Literature Activity Read aloud with students the “Square Deal” page in Math Appeal by Greg Tang. Ask them to group objects on their page and then write a number sentence to represent how they counted. Some of them may write 5 + 5 + 5 + 5 + 5 = 25, while others write 5 × 5 = 25. Ask students why both number sentences work. Then have them create their own visual math riddles. They should draw a group of objects that totals a multiple of 5, and then write instructions for how to group the objects by fives in order to count using multiplication. Afterward, encourage students to repeat the activity as listed above, using division instead of multiplication.
Reading GLE 4.1.02.c The student will recognize different forms of text (e.g., poems, plays, drama, letters, ads, biographies).
Poem
Gardening With Snai ls by Betsy Franco
Two rows of daisies, With three in each row. I dug and I watered And left them to grow. I planted some pumpkins In four rows of two. I built a big scarecrow And then I was through. At night, twenty snails Marched out on the lawn, And early next morning My plants were all gone. I’ll have to find plants
Reading GLE 4.1.09.g The student will retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
That the snails don’t attack
Examining Math Refer to page 21 in Riding the Mail Trail. Work as a class to create a chart comparing the original cost of sending mail by Pony Express to what it cost by the middle of 1861. The chart should show the costs per ounce, up to 10 ounces. Column 1: $5, $10, $15, $20, $25 . . . $50; Column 2: $1, $2, $3, $4, $5 . . . $10 Then add a third column showing the savings. $4, $8, $12, $16, $20, . . . $40 Ask students what pattern they see in the savings column. Finally, discuss with students how they could find out the cost per ounce of mail today.. Real-World Problem
Solving
s Math and Socia l Studie
Math and Science
8/2/07 2:24:02 PM
A10
rden’s
A great midnight snack!
Math in Action Before you read, ask students why people might choose to grow plants in arrangements of equal rows and columns. there is space to walk around and tend to the plants Have students explain whether they think it would be more challenging to monitor the progress of plants that were not grown in a pattern.
Math and Social Studies
Number and Operations
Cover_B9_G04LEV_106234x.ind
, ‘cause they think that my ga
d ii
Reading and Language Arts Support
Read the poem aloud with students. Next, divide the class into groups of four. Distribute 30 counters to each group. Have students create an array to show the arrangement of daisies in the garden and write a corresponding multiplication sentence. 2 × 3 = 6 Then have them use the counters to show how 20 snails can be distributed evenly according to rows of daisies and write a corresponding division sentence. 20 ÷ 2 = 10 Have students repeat the exercise with the rows of pumpkins, showing how the snails can be distributed evenly this time by rows or columns of pumpkins. 4 × 2 = 8; 20 ÷ 4 = 5; 20 ÷ 2 = 10 Afterward, reinforce for students that math is used in many contexts in daily life.
USE WITH
Literature Activity Read aloud some of the riddles from The Grapes of Math by Greg Tang. Choose riddles that are based on 11s and 12s. (“Large Pizza to Go,” “For the Birds,” “Scallop Surprise,” and “Flying Seeds”) Ask students to group the objects and write a number sentence to represent how they counted. Next have students create their own visual math riddles using groups of objects with totals that are multiples of 11 or 12. Ask students to include instructions for how to group these objects so they can be counted using multiplication. Have students trade papers to check their instructions for subject/verb and noun/ pronoun agreement.
Reading GLE 4.1.06.a The student will build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Problem Solving in Math Have students imagine that they make regular visits to relatives or friends living in other cities. Then read the following story once, and repeat it. Direct students to complete the Four-Step Problem-Solving graphic organizer found on page 19 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.) Miho and her two brothers piled into the backseat of the car. As usual, Miho sat in the middle. She had to be a human barrier. Otherwise, her brothers would poke, prod, and tease each other for the next two hours. Miho’s family was headed to her grandparents’ house. They had been making this same trip once a month for Miho’s entire life, but this visit was special. It was Miho’s 9th birthday. She couldn’t wait to see the cake her grandmother had made. During the ride, Miho’s mind began to wander. She wondered, “How many times since I was born have I made this trip? It must be a pretty big number.”
Reading GLE 4.1.08.a.6 The student will derive meaning while reading by making inferences.
Reading Graphic Novels Have students revisit “Dog Walking Dollars,” or display it on the whiteboard. Ask them what is unusual about the seventh panel. There is a speech balloon without a character attached to it. Tell students to infer which character is speaking the dialogue in this balloon, and to explain how they know. The balloon points out of the frame to the left, where Teresa appears in the previous frame. Based on what is said in the balloon, and the direction the balloon is pointing, it is Teresa who is saying this dialogue.
Reading and Language Arts Support
Chapter: Apply Multiplication and Division Facts Multi-Part Lesson 3
Examining Math Refer to the chart on page 17 in Expanding the United States. Have students get into pairs. Instruct them to rewrite the chart showing prices in the West if they know that a shirt costs $11, boots costs $9, and 60 eggs cost $20 in the East. Remind them that they must first find the number of times greater each item costs in the West than in the East. 36 ÷ 4 = 9; 16 ÷ 2 = 8; 2 ÷ 2 = 1 Second, they need to calculate the new price per dozen eggs. 60 ÷ 12 = 5; 20 ÷ 5 = 4 Finally, they can calculate the new prices for their charts. Shirt: 11 × 9 = $99; Boots: 9 × 8 = $72; 1 dozen eggs: 4 × 3 = $12 MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
Q
&YQBOEJOHUIF
-SK@CPQ?LB .NCP?RGMLQ
Work as a class to answer the question. 1 visit per month × 12 months = 12 visits per year; 12 visits per year × 9 years = 108 visits Then calculate the number of hours Miho has spent in the car during the trip. 2 hours there + 2 hours back = 4 hours per trip; 108 visits × 4 hours = 108 + 108 + 108 + 108 = 432 hours
Reading and Language Arts Support
A11
Reading and Language Arts Support
USE WITH
Chapter: Apply Multiplication and Division Facts Multi-Part Lesson 4
Reading GLE 4.1.12.b The student will determine the problem of a story, discover its solution, and consider alternate solutions.
Literature Activity Read aloud with students pages 11–13 in The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan. Ask them why it was impossible for the brothers to divide the 35 camels in half (2 equal groups), thirds (3 equal groups), or ninths (9 equal groups). It is not possible to divide 35 evenly by halves, thirds, or ninths. Next discuss the groupings of people who could share 35 camels evenly. 1, 7, 5, 35 Point out that all of these numbers are factors of 35. Distribute 36 counters each to pairs of students and have them find the factors for 36. Ask students what conclusion they can draw about factors and multiples from this activity.
Reading GLE 4.1.12.a The student will read, view, and recognize various literary (e.g., poetry, novels, historical fiction, nonfiction) and media (e.g. photographs, the arts, films, video) genres.
Math in Action Read the poem aloud with students. Ask them if the poem’s mood is silly or serious and how the author’s word choices help the reader understand the intended mood. Then work together to answer the question. 5,000 ÷ 50 = 100; She flew 5,000 miles in 50 days, or 100 miles per day. Have students identify factors and multiples related to the equation.
The Polka-D ot
Poem
Pajama Bird
by J. Patrick Le
wis
In 50 days the po Pajama bird had From a polka-do
lka-dot
flown
tted birdhouse To the park at Ye llowstone. She didn’t stop at birdbaths, Puddles, pools, or water fountain s Until she reache d the Pink Pajam a Polka-dotted mou ntains. The flight? 5,000 How far did Mis
miles or so.
s Pajama go On average each of 50 days To bag pink polk a-dotted rays?
A12
Reading and Language Arts Support
Using Math Vocabulary Create two number cubes, one containing odd numbers to 11, and the other containing even numbers to 12. On the whiteboard, write is a factor of and is a multiple of . Then have students form two lines. The student at the front of one line rolls the two cubes. He or she then uses one of the numbers to complete the first sentence and the other number to complete the other sentence. Student rolls 7 and 10; 2 is a factor of 10. 28 is a multiple of 7. Then the student at the front of the other line takes a turn. Continue the exercise until all students have had a turn. Afterward ask students how they thought of the factors and multiples in their examples.
Reading GLE 4.1.01.b The student will use established rules for conversation (e.g., do not interrupt, ask questions, provide appropriate feedback).
Extending Our Learning Refer to the table on page 7 in The Olympic Games. Divide the class into groups of four. Have students calculate the number of points each country earned in each medal category. Then have students determine which category for which country had the highest point total. 38 points for Greece’s silver medals Ask if anyone can explain what a prime number is. If necessary, tell students that a prime number is a number with only two factors— itself and 1. Then tell students that more than half the numbers in the table are prime numbers. Challenge the groups to identify them most quickly. Afterward, have students explain the relationship between total medals and total points. The highest medal level, gold, earns the most points. Discuss with students why simply considering the total number of medals won is an inaccurate way to determine which country won the most events.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
4HE
-SK@CPQ?LB .NCP?RGMLQ
Q
USE WITH
Reading GLE 4.1.08.b.8 The student will check for understanding after reading by identifying cause and effect relationships.
Literature Activity Read aloud with students A Cloak for a Dreamer by Aileen Freidman. Discuss the story, focusing on causeand-effect relationships in the text. Then have students identify different objects in the classroom. Do they notice objects displayed in a pattern? books on shelves, decorative border around a bulletin board Do they notice patterns within an object? book cover, design on a logo Tell students that patterns can be found everywhere. Ask them to explain why they think patterns are so important. help to organize our lives Have volunteers tell what goes into creating a pattern.
Reading Graphic Novels Have students revisit the graphic novel “School Carnival Challenge.” Discuss with students what patterns they notice in the graphic novels they have read in their textbooks. stories told frame by frame, each frame tells the story visually, each story is read left to right and top to bottom Have students explain what patterns they notice in this story. there are 3 frames per row, the Mega Dudes and monkeys are organized in rows, Tai’s points are accumulating in a particular pattern
Reading and Language Arts Support
Chapter: Algebraic Patterns Multi-Part Lesson 1
Poem Reading GLE 4.1.10.a The student will develop and maintain vocabulary specific to content and to current events.
Using Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28: in Hands-On Activity Tools and Resources. Write the word pattern in the center rectangle, and then work as a class to complete the surrounding squares. Have students search the classroom for nonnumeric patterns and then describe the patterns. Encourage students to use pictures and drawings as well as words in order to describe patterns.
Reading GLE 4.1.10.b The student will locate information using available text features (e.g., maps, charts, graphics, appendices, and tables of contents).
Extending Our Learning Divide students into groups of four, and then distribute to each group a copy of the Two-Column Chart graphic organizer found on page 24 in Hands-On Activity Tools and Resources. Tell them to label the left column Patterns and the right column Not Patterns. Groups will browse Americans on the Move for graphic 0/5)& organizers containing numbers and categorize them using their charts. For example, the timeline on page 11 follows a pattern, but the table on page 20 does not. Each group will choose one number pattern from the reader and extend it by 4 more digits. Discuss each group’s lists. Some graphic organizers from the reader could appear in either column. Allow students to defend their choices of categorization. MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
Q
".&3*$"/4
.07&
#?R? L?JWQGQ
Nature Knows Its M ath by Joan Bransfield Grah
am
Divide the year into seasons, four, subtract the snow then add some more green, a bud, a breeze, a whispering behind the trees, and here beneath the rain-scrubbed sky orange poppies multiply.
Math in Our World Read the poem aloud with students. Discuss the author’s word choice and how it affects the mood of the poem. Then ask students what they think is meant by the line “subtract the snow”? by the line “add the green”? Then ask them to suggest other patterns they have seen in nature.
Reading and Language Arts Support
A13
Reading and Language Arts Support
USE WITH
Chapter: Algebraic Patterns Multi-Part Lesson 2
Reading GLE 4.1.08.b.12 The student will check for understanding after reading by reflecting upon comprehension strategies utilized to make meaning from text.
Reading GLE 4.1.07.a The student will set a purpose for reading (e.g., to understand, to enjoy, to solve problems, to locate specific information/facts).
Literature Activity Read aloud with students Whales by Gail Gibbons. Have them compare what they learned earlier about blue whales with what they learned in this book about other whales. Then have students use number sentences to compare the lengths of different whales individually and in combinations. For example, you might ask, Which is longer, the sperm whale or the pilot whale, or the beluga whale and killer whale combined? Have students work in groups to create graphs that compare the lengths of each type of whale.
Problem Solving in Math Read the following story once, and repeat it. Direct students to complete the Four-Step Problem-Solving graphic organizer found on page 20 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.) Every Friday after school, Antonio visits the public library. As soon as he walks in the door, he hands the books he’s finished reading to the librarian. Then Antonio spends the next hour carefully searching the shelves for the books he will read during the coming week. With his head turned sideways, Antonio slowly walks up one aisle and down the next. Before he checks out, Antonio stops at the shelves filled with DVDs. The number of books he checks out varies from week to week, but Antonio always gets 2 videos to watch over the weekend. If Antonio checked out 10 items, how many of them were videos? Use the whiteboard to write an equation that will answer the question, and then work as a class to solve it. For further practice, have students suggest other scenarios based on the number of items checked out from a library.
Reading GLE 4.1.06.g The student will continue to use context clues to determine the correct meaning/usage of multiple meaning words.
Using Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 in Hands-On Activity Tools and Resources. Write the word rule in the center rectangle, and then work as a class to complete the surrounding squares. Then have students spend several minutes writing a short persuasive essay about a nonmath rule they think is unfair, including a supporting argument with details. Ask volunteers to share what they have written. Extend this activity by asking students to tell why rules—that is, directives that guide action or behavior—are important in mathematics. Ask students if they find rules in mathematics to be frustrating or if they find them helpful, and to explain their reasoning.
A14
Reading and Language Arts Support
Math Investigations Refer to page 8 in Solving the Pyramid Puzzle. Create an equation showing that the height of the Great Pyramid today is about 30 feet less than it was originally. 481 – 30 = 451 Work as a class to create a function table that uses a similar equation. x – 30 Have students complete the table with a series of 3-digit numbers. Then lead a discussion about possible reasons why the Great Pyramid has lost a significant amount of its height during the last several thousand years.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
&CMKCRPW
USE WITH
Reading GLE 4.1.12.b The student will determine the problem of a story, discover its solution, and consider alternate solutions.
Reading GLE 4.1.01.d The student will formulate and respond to questions from teachers and other group members.
Literature Activity Read aloud with students Mailing May by Michael O. Tunnel. Discuss the problem that May faced and how it was resolved. Ask students if they can think of any other resolutions the author could have used. In the story, a train ticket costs $1.55, which is the amount May’s father says he makes working all day. If this amount were his actual wage, have students write and solve equations showing how much he makes in 5 days, with x as the unknown variable. 5 × $1.55 = x; or x ÷ 5 = $1.55; x = $7.75 Have students repeat the exercise with daily wages of $2.25 and $2.75.
Problem Solving in Math Read the following story once, and repeat it. Direct students to complete the Four-Step Problem-Solving graphic organizer found on page 20 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.)
As an extension, compare how much the ticket would cost today for someone earning minimum wage.
For two days, Ty had been selling raffle tickets to raise money for his school’s band. Each ticket cost $3, but everyone who bought one had a chance to win a pizza party at Cheeseria’s Pizzeria, the best pizza place in town. Ticket holders also got to attend a performance by the school band, which included Ty on drums. Ty sold 32 tickets the second day, which was more than he sold on the first day. If Ty sold a total of $156 in tickets, how many tickets did he sell the first day?
Reading and Language Arts Support
Chapter: Algebraic Patterns Multi-Part Lesson 3
Work as a class to create an equation that can be used to answer the question. [a + 32] × 3 = 156, in which a is the number of tickets sold the first day Solve the equation, and then ask students if they play any instruments or have ever attended a concert.
Reading GLE 4.1.09.c The student will use current technology as a research and communication tool for personal interest, research, and clarification.
Math in Our World Ask students what they know about the Celsius scale, such as the boiling and freezing points of water, where it is used in the world, and so on. Next, distribute copies of a newspaper’s Weather section, or display a Web site showing local weather. Have students locate the high and low temperatures forecast for the next day. On the whiteboard, write the following function: (F° – 32) × 5 ÷ 9 = C°. Work as a class to convert the temperatures from Fahrenheit to Celsius. Round numbers wherever necessary to avoid fractions or decimal numbers. Finally, have students point out which parts of the weather page are facts and which are opinions. Have them explain their choices.
Math in Action Distribute an index card to each student. On one side, have students describe two key learnings about algebra that they feel they understand well. On the other side, have them describe two key learnings that they feel they don’t understand as well. Collect the cards, and then randomly choose several key learnings that they feel they understand well to read aloud. Then review any key learnings that students are having trouble with.
Reading and Language Arts Support
A15
Reading and Language Arts Support
USE WITH
Chapter: Algebraic Patterns Multi-Part Lesson 4
Reading GLE 4.1.12.j The student will explore the concept of theme.
Reading GLE 4.1.09.f The student will skim materials to develop a general overview of content or to locate specific information.
Literature Activity Read aloud with students Once Upon a Dime by Nancy Kelly Allen. Then work as a class to create a function with two operators that will help students calculate the total amount of money harvested from the tree before the leaves turned into Chinese dollars, or yuan. For example, (100 × a) + (100 × b), in which a and b represent the amounts in cents of two different coins, can be used to show the total of two kinds of coins from the story. Practice using this function with different pairs of coins. Finally, ask students to recall the stories they have read so far this year. Discuss which themes and topics that have appeared most or least often in these books.
Math in Our World Distribute copies of a newspaper’s classified ads showing apartments for rent, and have students circle the rental prices shown in several of the ads. Create a chart on the whiteboard listing these amounts, along with other information about the apartment, such as number of bedrooms, amenities, square footage, and so on. Next, work as a class to create an expression that will show the amount of rent paid over a year. Use this expression to calculate the yearly cost in rent for each apartment listed on the whiteboard. Lead a discussion about which apartment seems like the best deal.
To extend, have students create new story problems using American coins.
Reading GLE 4.1.07.f The student will relate text to prior personal and historical experiences, current events, as well as previously read print and non-print media.
Reading GLE 4.1.06.d The student will determine the meaning of unfamiliar words using context clues, dictionaries, glossaries, and other resources.
Math in Action Lead a discussion with students about what they know about gold. Have volunteers explain how the discovery of gold in the United States affected our country’s history. Then refer to pages 19 and 20 in Expanding the United States. As a class, discuss the table on page 19, and then use the whiteboard to rewrite it as a function table that can be used to calculate totals for additional dollar amounts. Divide the class into groups of four, and distribute pieces of paper to each group. Have students &YQBOEJOHUIF use the information on page 20 to create a function table comparing the numbers of real ounces to digger’s ounces.
Using Math Vocabulary Display a copy of the Four-Step Problem Solving Plan graphic organizer found on page 20 in Hands-On Activity Tools and Resources. Across the top of the whiteboard, write the following vocabulary words from this chapter: variable, expression, equation, function. Below the words, write 3 × a × 8 = 48. Work as a class to fill in the graphic organizer as students discuss each step in solving the equation for a. Underline vocabulary words as they are used during the discussion. Encourage students to use each word at least once during the exercise. Be sure students label each part of the equation as they solve. If time permits, review Visual Vocabulary Cards 22, 25, 30, and 72.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
Afterward, ask students to consider whether similar falsification occurs today with modern money. -SK@CPQ?LB .NCP?RGMLQ
A16 Reading and Language Arts Support
Q
ISBN: 978-0-02-101741-6 MHID: 0-02-101741-7
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.
USE WITH
Reading GLE 4.1.08.b.2 The student will check for understanding after reading by selecting main idea and supporting details from text.
Reading GLE 4.1.06.g The student will continue to use context clues to determine the correct meaning/usage of multiple meaning words.
Literature Activity Ask students what they know about whales, and then read aloud Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells. Afterward, discuss with students the main idea of the book and the details that support it. Then, if a blue whale measures 100 feet in length, work as a class to calculate the length of 5 blue whales in a row. Then calculate the length for 50, 500, and 5,000 whales.
Using Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 in Hands-On Activity Tools and Resources. Write the word round in the center rectangle and complete the surrounding squares.
Discuss the pattern that emerges when multiplying by multiples of 10. Ask students if they think the same pattern would apply to calculating lengths of 40, 400, and 4,000? 70, 700, and 7,000? Have them explain their reasoning.
Discuss with the class different meanings of the word round. Then have students brainstorm other words that have both math and nonmath meanings, such as place, equal, and rule. Finally, discuss how context clues can help students understand which meaning is correct.
Reading GLE 4.1.10.b The student will locate information using available text features (e.g., maps, charts, graphics, appendices, and tables of contents).
Reading GLE 4.1.01.f The student will summarize orally what has been learned or accomplished after completing an activity or assignment.
Math in Our World Lead a discussion about local recycling programs, and conduct a survey of students to see what they recycle. Ask students if thinking about the amount of waste produced during a given time might persuade a person to recycle. Have volunteers explain how numbers can be used as a means of persuasion.
Math in Action Ask students to imagine that they have 25 marbles. Be sure to show a marble or find a photograph to show to the class to ensure common background knowledge. Tell students that they are going to write about the marbles. Encourage students to think creatively about what the marbles look like, where they could be stored, what they could be used for, and so on. After students have been writing for several minutes, tell them that they now have 1,000 times as many marbles. Ask students to begin writing again, this time describing what it would be like to have 25,000 marbles, where they would be stored, what they could be used for, and so on. Ask volunteers to share their descriptions, and have the class discuss how increasing the number of marbles caused them to reevaluate how they would store and use the marbles.
Refer to page 14 in What Is Recycling? Work as a class to calculate the total kitchen waste produced by the class each year. Round the number of students in class and the days of the year to the nearest 10. Allow volunteers to do the math in their heads before confirming the answers with multiplication sentences written on the whiteboard. Display results of the class survey in a chart.
Reading and Language Arts Support
Chapter: Multiply by One-Digit Numbers Multi-Part Lesson 1
Extending Our Learning Tell students to imagine that that they are at a sold-out high school football game. The stadium has 8 sections, and each section contains 20 rows. There are 14 seats in each row. Have students write a detailed description of how they could get a good estimate of the total attendance without counting every single person in the stands. Afterward, have students share how they solved this problem. Ask if anyone would modify their strategies once they listened to the problem-solving strategies of other students. Remind students that they should reexamine their approaches to problem solving in math.
Reading and Language Arts Support
A17
Reading and Language Arts Support
USE WITH
Chapter: Multiply by One-Digit Numbers Multi-Part Lesson 2
Reading GLE 4.1.06.i The student will build vocabulary by reading from a wide variety of text and literary genres.
Reading GLE 4.1.01.a The student will listen attentively by facing the speaker, asking questions, and paraphrasing what is said.
Literature Activity Read aloud with students Spaghetti and Meatballs for All by Marilyn Burns. Then ask them if they have read or heard any other similar stories. How were those stories similar to or different from this one? Next, tell students that the tables in a restaurant seat 4 people each. Then have them write number sentences showing how many tables are needed to seat 32 people. Next, ask students to write multiplication sentences showing twice as many, and 3 times as many, as 32. Then have them write number sentences showing the number of tables needed for both new totals.
Problem Solving in Math Read the following story once, and repeat it. Direct students to complete the Four-Step Problem-Solving graphic organizer found on page 20 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.)
Have students offer suggestions for how best to configure space in a restaurant. Is it better to have many small tables, or a few large ones?
Kylie Kay is a local DJ. Every Saturday night, she hosts a 30-minute show in which she plays her favorite new songs. Seven minutes of each show are taken up by commercials. After editing out the commercials, Kylie Kay recorded 12 of her most recent shows onto CDs. If each CD holds up to 80 minutes of music, how many shows did Kylie Kay fit on each CD? How many total CDs did she use? Work as a class to answer the questions from the story. 23 minutes per show × 3 shows = 69 minutes total; 12 shows ÷ 3 shows per CD = 4 CDs total
Reading GLE 4.1.10.a The student will develop and maintain vocabulary specific to content and to current events.
Math in Action Ask students to write a few sentences justifying how the local weather affects their lives. What does the weather enable them to do? How can the local weather prevent them from doing what they want to do? Encourage them to think about their favorite outdoor activity as they write.
Discuss with students if they would recommend other technology to Kylie Kay to help her save her work more efficiently. Save it to an MP3 player; stream the show as a podcast and use the audio display to edit the unnecessary portions of the show.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
Q
Rivers s Mountain and
of the
United States
Refer to the table on page 16. Using the whiteboard, work as a class to multiply each temperature by 2 and then by 3. 43° × 2 = 86°; 82° × 2° = 164°; 7° × 2 = 14°; 43° × 3 = 129°; 82° × 3 = 246°; 7° × 3 = 21° Discuss how the different temperatures compare to the weather where students live. -SK@CPQ?LB .NCP?RGMLQ
Extending Our Learning Have students get into pairs. Distribute three index cards to each pair. Have the groups write one key learning about multiplication or division on each card. Collect the cards, and then choose random cards to read aloud. Ask for a volunteer to provide an example of each key learning. As time allows, continue to choose cards at random to read aloud. Reading GLE 4.1.13.d The student will relate literary experiences (e.g., book discussions, literacy circles, writing, oral presentations, artistic expressions).
Math in Our World Have students talk about their favorite books. Ask each student to explain why they enjoy this book. Afterward, discuss with the class what traits in a book might get it included on a bestseller list. Next, distribute copies of a bestseller list for books from a newspaper or magazine. Lead a discussion about which books are most or least popular on the lists. Direct students’ attention to the column showing each book’s previous ranking. Using the whiteboard, work as a class to calculate where some of the books would be if their rankings had changed by four times as much.
A18
Reading and Language Arts Support
USE WITH
Reading GLE 4.1.05.c The student will participate in guided oral reading.
Reading GLE 4.1.08.b.7 The student will check for understanding after reading by locating information to support opinions, predictions, and conclusions.
Literature Activity Read aloud with students Too Many Kangaroo Things to Do by Stuart J. Murphy. Discuss how the book would be different without illustrations. Would it be more or less informative? More or less entertaining? The same? Then work as a class to create number sentences showing totals of flowers, candles, oranges, and so on mentioned in the book. If there is time, repeat the exercise on the pages about koalas and dingoes.
Math in Our World Read the poem aloud to students, but stop before the final line. Work as a class to answer the poem’s riddle. Poem
Father and S on by Charles F. Li
nn My father’s age I just found out. He’s four times as old as me, But after only fiv e more years His age’ll be min e times three.
Reading GLE 4.1.09.f The student will skim materials to develop a general overview of content or to locate specific information.
Math Investigations Browse Strange But True with students, looking for 2-digit numbers. Use these numbers and information from the reader to create multiplication problems that require regrouping. For example, based on the information from page 5, ask students how many ounces of fish a pelican would eat in one week. 64 ounces per day × 7 days = 448 ounces per week Have students look at page 14. Work with them to calculate the number of meters they would travel in 9 seconds if they could move at 23 meters per second. 23 × 9 = 207 meters Use the whiteboard to demonstrate regrouping. Afterward, discuss with students the possible relationships between how much an animal eats and how fast it moves. What other relationships can they think of between an animal’s appearance and its behavior?
Reading and Language Arts Support
Chapter: Multiply by One-Digit Numbers Multi-Part Lesson 3
You can sure gu ess what I’ll ask of you, So speak withou t delay. My father’s age— and also mine— Quick now, wha t do you say? (Pa is forty and I’m ten…but gaining on him.)
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
Distribute copies of the poem from page 38 in Hands-On Activity Tools and Resources. Then reread the poem aloud, including the final line. Have students use multiples of their own ages to calculate how many times older a parent, guardian, or other relative is. Then have students write their own versions of the poem, using numbers based on the age of a relative or parent.
JEC@P?
Math in Our World Display a copy of the Two-Column Chart found on page 24 in Hands-On Activity Tools and Resources. Label the left column Without Regrouping and the right column With Regrouping. Tell students that they are going to calculate classroom totals for a few body parts. Use the whiteboard to multiply the total number of students times 1 head, 2 eyes, 4 limbs, and 5 holes in the head. Have students record each result in the column of the chart that describes how they solved the problem.
Understanding Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 of Hands-On Activity Tools and Resources. Write Distribute Property in the center rectangle, and then work as a class to fill in the surrounding squares. Have students get into pairs, and ask them to create four of their own examples of the Distributive Property. Then have pairs exchange papers to check their work.
Reading and Language Arts Support
A19
Reading and Language Arts Support
USE WITH
Chapter: Multiply by One-Digit Numbers Multi-Part Lesson 4
Reading GLE 4.1.08.b.3 The student will check for understanding after reading by identifying the author’s purpose (e.g., to entertain, to inform, to explain).
Literature Activity Read aloud with students Each Orange Has 8 Slices by Paul Giganti, Jr. Ask them if the author’s purpose was to inform, entertain, or explain. Is it possible for the author to have more than a single purpose? Then refer to the first page of the book, and have students answer the questions. 3 red flowers, 18 pretty petals, 36 tiny bugs Then have students calculate the total number of tiny bugs if there were 20 on each petal, as well as the total number of petals if there were 30 per flower. Ask them to explain how they found their answers. What distinction can students make between multiplying by zeroes versus multiplying by other numbers?
Reading GLE 4.1.12.a The student will read, view, and recognize various literary (e.g., poetry, novels, historical fiction, nonfiction) and media (e.g. photographs, the arts, films, video) genres.
Math in Our World Divide the class into groups of four. Distribute to each group a copy of a newspaper’s local news section. Have students search for and circle 2- and 3-digit numbers. Each group will choose three of the circled numbers, and multiply each one by 5. Then have them add a zero in between one pair of digits in each number. For example, 256 could become 2,056 or 2,506. Have students multiply each number by 5 again. Each group will repeat the process, adding 2 zeros and then 3 zeros. Have groups exchange papers and check each other’s calculations. Then come together again as a class and lead a discussion about the local news stories students saw. Ask students if they noticed particular types of stories or topics that include numbers.
Reading GLE 4.1.09.g The student will retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
Reading GLE 4.1.01.b The student will use established rules for conversation (e.g., do not interrupt, ask questions, provide appropriate feedback).
Extending Our Learning Display a world map to students prior to this activity, focusing on Norway in particular. Then refer to page 24 in The Olympic Games. Use the numbers in the tables to practice multiplication across zeros. Wherever necessary, add zeros between pairs of digits to create relevant numbers for the exercise.
Math in Action Have students work in pairs, and then distribute an index card to each pair. Have them discuss the similarities and differences between multiplication and division. Each pair will record two similarities on one side of their index card and two differences on the other side.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF ?LB2 MAG?J 2RSBGC
Discuss with students the information in the tables. Ask why they think that the United States has so many more Summer Olympic medals compared to other countries. Why might Norway have such a successful record in the Winter Olympics?
Q
4HE
Finally, have students spend a few minutes considering which Olympic sport they would most like to compete in or be interested in watching. Have them explain why they chose that particular sport. Do they enjoy watching it? Encourage students to respond, considering the sport’s history, heroes, and importance to the Olympic broadcast. -SK@CPQ?LB .NCP?RGMLQ
A20
Reading and Language Arts Support
Collect the cards, and then come together again as a class to discuss what students have written. Have students write paragraphs on the Journal in page 21 of Hands-On Activity Tools and Resources, explaining how this activity helped them better understand the relationship between multiplication and division. Reading Graphic Novels Reread with students the graphic novel “Musical Math.” Ask them to volunteer examples of their experiences using instant messaging. Do they think it is realistic for Julian and Olivia to write to each other about MP3 players? Distribute copies of the blank “Musical Math” from page 2 in Hands-On Activity Tools and Resources. Tell students they will write their own conversation between Olivia and Julian. Encourage them to make the scenario they write realistic. Challenge students to create a problem-solving situation as with the original.
USE WITH
Literature Activity Ask students to listen for the lesson in Melisande by Elizabeth Nesbit, and then read the story aloud. After reading, discuss with them what they thought the story’s lesson was. Next, tell students that Melisande’s hair is 24 inches long.
Math in Our World Distribute copies of a newspaper’s Travel section to students. As a class, search for listings of airplane ticket prices. On the whiteboard, create a list of several destinations and the price per ticket. Survey the class to see which destination is most popular. Then round the number of students to the nearest ten, and calculate the total cost of tickets for the class.
Work as a class to calculate her hair’s length if it grew 10 times as long, 20 times as long, and 50 times as long. Discuss strategies for multiplying by tens during each calculation. Ask them if multiplying by tens helps them make predictions about Melisande’s hair length? Students might suggest that estimating by tens helps them make calculations more easily.
Discuss alternative methods of transportation that could get the class to their destination, including students’ thoughts about the cost, travel time, convenience, and so on. Ask students how this activity illustrates the considerations that adults must make when arranging travel plans. Ask students if they would reprioritize any future travel plans based on this activity.
Reading GLE 4.1.08.b.2 The student will check for understanding after reading by selecting main idea and supporting details from text.
Reading and Language Arts Support
Chapter: Multiply Multi-Digit Numbers Multi-Part Lesson 1
Reading GLE 4.1.10.b The student will locate information using available text features (e.g., maps, charts, graphics, appendices, and tables of contents).
Reading GLE 4.1.01.f The student will summarize orally what has been learned or accomplished after completing an activity or assignment.
Math in Action Have each student create a multiplication sentence in which a 3-digit number is multiplied by a 2-digit multiple of 10. Then have them spend several minutes writing detailed descriptions of how they completed their problems. Afterward, ask students if they used the four-step problem solving plan. Ask volunteers to tell how they can apply what they learned to division.
Extending Our Learning Refer to page 9 in Ancient Giants of the Forest. Have students look at the map. Point out the key, and explain to students that a key is a graphic feature that explains symbols or codes shown on a map. Tell students the key in this map shows how each color corresponds to champion trees. Divide the class into groups of four. Have groups choose one state each from the two different colors used as a key in the map. Students should calculate the total number of champion trees for their two states. Have one student from each group present his or her group’s states and totals.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
,C?QSPCKCLR
Reading GLE 4.1.04.d The student will understand, recognize, and use spelling patterns and word families to decode words.
Reflective Writing Have students imagine that they are at a huge art museum. The walls of every room they walk into are filled with paintings and drawings. In one room, they count 15 pieces of art on 2 of the walls, 16 on another, and 18 on the 4th wall. The museum has 30 rooms. Have students calculate the approximate total number of pieces of art in the museum. An average of 16 pieces per wall × 4 walls × 30 rooms = 1,920. Afterward, have students write a paragraph reflecting on how an art museum curator (that is, the person who is in charge of choosing the art in a museum) might choose which art to display. Then have students exchange paragraphs to check them for punctuation errors.
Reading and Language Arts Support
A21
Reading and Language Arts Support
USE WITH
Chapter: Multiply Multi-Digit Numbers Multi-Part Lesson 2
Reading GLE 4.1.08.a.8 The student will derive meaning while reading by drawing conclusions based on evidence gained.
Literature Activity Before reading Sea Squares by Joy N. Hulme, cover the answers in the book with sticky notes. Read the story aloud, and have students answer each multiplication problem before revealing its answer. Then extend the problems from the story with greater numbers, and show students how to use model squares for solving. Have students demonstrate this using their own problems, or problems they copied from this chapter.
Reading GLE 4.1.09.i The student will gather and record information on a research topic using two different sources.
Math in Our World Refer to pages 18 and 19 in Trapped in Tar. Have students work in pairs to calculate the total length of 22 Columbian mammoths’ tusks laid end to end. If necessary, remind them that each mammoth has 2 tusks. 22 mammoths × 2 tusks apiece × 16 feet = 704 feet Next have each student pair write a short essay describing at least two similarities and two differences between mammoths and modern elephants. Be sure students conduct research to determine the tusk size of modern elephants. Challenge each pair to formulate a theory for the difference in tusk sizes between each type of elephant. Math and Scienc e
Real-World Problem
Math and Social Studies
8/2/07 2:37:27 PM
ii
Reading GLE 4.1.06.f The student will foster word consciousness (e.g., word play, word walls and word sorts).
Using Math Vocabulary Write six math vocabulary words on the sides of a blank number cube. Then have students work in groups of four. Each member of the groups will take turns rolling the cube and describing or giving an example of the word that appears. Encourage students to draw an example for a word, if that is more appropriate. Continue until all students have had a turn.
A22
Reading and Language Arts Support
Two-Digit Fish Math by Suzanne Korner
Clyde is a fish who likes mu ltiplication. Starting with the ones place, he tells me, is the easy part. Those two-digit answers spa rk his imagination! Want to see how he does it? OK let’s start! Start with the ones place— come on, you know how! Multiply by both numbers at the top. What’s that—you’ve finished ? You’re asking what now? Move to tens, just like Clyde —now that you’ve started, you cannot stop. Now add the answers togeth er, from the tens and the ones. (Don’t forget for a place ho lder use zero.) You have to admit, really it’s kind of fun. Now check it, if your answ er is right you’ll be a hero.
Solving
Math and Scienc e
Algebra
4.indd COVER_B12_G04LEV_106237
Poem
So now you can multiply by two digits Look at what’s coming up next! Uh—oh, what to do? Clyde is worried, and he’s beginning to fidget. Multiplying by three numb ers? Let’s leave that to his friend, Rue.
Extending Our Learning Distribute copies of this poem on page 54 in Hands-On Activity Tools and Resources. Read the poem aloud with students. Lead a discussion with students about how reading this poem helped them understand the steps involved in multiplying two-digit numbers.
USE WITH
Reading GLE 4.1.02.b The student will use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Reading GLE 4.1.09.f The student will skim materials to develop a general overview of content or to locate specific information.
Literature Activity Read aloud with students Snakes: Long Longer Longest by Jerry Pallotta, and then refer to the page with the snake and cheetah. Ask students how far the black mamba snake would travel in 5 days if it moved at 12 miles per hour without stopping. 24 hours × 5 days = 120 hours; 120 hours × 12 m.p.h. = 1,440 miles Then ask students how far a sprinter would travel in a week running nonstop at 27 miles per hour. 7 days × 24 hours = 168 hours; 168 hours × 27 m.p.h. = 4,536 miles Ask students if they notice a relationship between top speed and the way an animal moves.
Math in Our World Divide the class into groups of four, and then distribute to each group copies of appliance or electronics ads. Tell students to browse the ads for items priced with 3-digit dollar amounts. Each group will select two of the items to use in the exercise.
Reading GLE 4.1.01.c The student will understand, follow, and give oral multi-step directions which may include illustrations.
Math in Action Have students work in pairs. Distribute three index cards to each pair. Have them write one key learning from this chapter on each card. Collect the cards, and then choose random cards to read aloud. Ask for volunteers to provide examples of the key learnings. As time allows, continue to choose cards at random to read aloud. Ask students to listen for repeated key learnings to find the most important things to remember about the chapter.
Tell students that a store sells an average of 15 of each item per month. Have each group calculate the yearly total sales for each item. $225 washing machine × 15 per month × 12 months = $40,500 Have groups share their totals with the class.
Reading and Language Arts Support
Chapter: Multiply Multi-Digit Numbers Multi-Part Lesson 3
Lead a discussion about how this money is not all profit but is used to pay for business expenses such as rent, utilities, employees’ salaries, wholesale costs, and so on. Extending Our Learning Refer to page 22 in What Is Recycling? Work as a class to calculate the total consumption of items listed in the reader for 999 families. 999 × 180 gallons of soda = 179,820; 999 × 30 gallons of juice = 29,970; 999 × 105 gallons of milk = 104,895; 999 × 25 gallons of bottled water = 24,975 Then have students find the total number of gallon containers used. 339,660 Discuss these numbers in relation to the total number off families in students’ city or town. Ask students for suggestions of ways to reduce the number of containers used and ways they might be able to reuse the containers. Reading GLE 4.1.08.a.6 The student will derive meaning while reading by making inferences.
Reading Graphic Novels Have students look at “Basketball Brainteaser,” focusing on frames 2 and 3. Ask how they know what happens as a result of these frames. Carmen scores the winning 2 points, and someone shouts, “We win!” Then explain to students that good readers use information from the text, along with their personal experience, to reach a more comprehensive understanding of a story’s plot, characters, and meaning. Ask students what they can infer about Carmen based on this graphic novel. she is a good athlete; she is focused
Reading and Language Arts Support
A23
Reading and Language Arts Support
USE WITH
Chapter: Multiply Multi-Digit Numbers Multi-Part Lesson 4
Reading GLE 4.1.07.f The student will relate text to prior personal and historical experiences, current events, as well as previously read print and non-print media.
Reading GLE 4.1.03.b The student will understand rhyming patterns in printed materials.
Literature Activity Lead a discussion with students about the Titanic, including what they know and what questions they have. Then turn to pages 32 and 33 in 882½ Amazing Answers to Your Questions About the Titanic by Hugh Brewster and Laurie Coulter. Discuss how this book’s structure is similar to or different from other books, and ask students why they think the authors structured it the way they did. Work as a class to calculate the number of pounds each in 40 tons of potatoes and 3 tons of tomatoes. 80,000 pounds of potatoes; 6,000 pounds of tomatoes Then ask students to find the number of ounces in 1,120 pounds of jams and marmalades. 17,920 ounces Have them select one other item on the ship and calculate the total for the ship or the trip.
Extending Our Learning Read the poem aloud with students. Ask them to identify the end rhymes and how often they occur. inside/ decide/pride/tried; every third line rhymes Then display a large container, such as a 5-gallon bucket or a large cardboard box. Place a box of paper clips next to the container. Ask students to imagine that the container is filled with paper clips. Work as a class to estimate the total number of paper clips that the large container could hold. Ask students to tell how they arrived at their estimates.
Have students discuss what this activity shows them about what is involved in preparing a trip on a large ship. Reading GLE 4.1.07.a The student will set a purpose for reading (e.g., to understand, to enjoy, to solve problems, to locate specific information/facts).
Math in Action Ask students if they have ever wondered why certain areas in the United States—or even in their community—are more populated than others. Ask them to keep this in mind during the following activity. Refer to the table on page 23 in Life in the United States. Divide the class into groups of four. Have students multiply the population per square mile by the number of square miles for each region. (Instruct students to ignore any digits to the right of decimals.) Come together again as a class and compare students’ answers with each region’s total population as it appears in the table. Lead a discussion about why they are different. Ask students to explain how this activity helped them understand the relationship between population and size of land regions. What conclusions can they draw about how populations are distributed across the United States? Real-World Problem
Solving
s Math and Socia l Studie
Math and Science
“How Many?”
Author Unknown I’m looking at a candy jar And wondering How many are inside. I take a long and steady loo k. It’s time to guess And yet I can’t decide. Some kids can always get it right. Their guesses match. Their faces beam with pride . I think my guess will win thi s time. My answer is… One thousand… Well, I tried.
Math and Social Studies
Number and Operations
2951.indd COVER_B13_G04LEV_SE_106
Poem
ii
8/6/07 12:01:42 PM
Math in Action Display a globe, and point out the equator. Tell students that the equator is 38,622 kilometers long, and that 1 kilometer is equal to 3,280 feet. As a class, use the whiteboard to calculate the equator’s distance in feet. 38,622 × 3,280 = 126,680,160 feet Then discuss countries a traveler would pass through while following the equator around Earth, including Brazil, Colombia, Equador, Indonesia, Somalia, Kenya, Uganda, Democratic Republic of Congo, Republic of Congo, and Gabon. Ask students which continents the equator does not pass through. Next, have students compare the distance around the equator to something familiar in their lives. For example, if it is 40 kilometers to their cousin’s house, then 38,622 kilometers ÷ 40 kilometers would be the equation they could use to conclude that it would take almost 500 round trips to their cousin’s house and back to equal the distance around the equator.
A24
Reading and Language Arts Support
USE WITH
Reading GLE 4.1.08.b.1 The student will check for understanding after reading by indicating sequence of events in fiction and nonfiction selections.
Reading GLE 4.1.10.a The student will develop and maintain vocabulary specific to content and to current events.
Literature Activity Read aloud with students A Remainder of One by Elinor J. Pinczes, and then ask them to explain what happened in the book. Next, ask students to pretend that there are 125 ants. Work as a class to see if the ants can be divided into 2 rows without any remainders. Have students explain why it is not possible. Then repeat the exercise to see whether the ants can be divided into 3, 4, 5, or 6 rows without remainders. Ask students to tell you how they could check to see if they divided correctly.
Using Math Vocabulary Write several division equations on the whiteboard. Have students identify the name of each part of the equation you point to at random. dividend, divisor, quotient Be sure to write equations using the ÷ symbol as well as within brackets.
Reading and Language Arts Support
Chapter: Understand Division Multi-Part Lesson 1
Reading GLE 4.1.12.k The student will recognize and understand basic literary devices (e.g., imagery, simile, metaphor, personification).
Poem
A Microscopic Topic Author Unknown
I am a paramecium
If I’d an eye, I’d surely cry
That cannot do a simple sum,
About the way I multiply
And it’s a rather well-known fact
For though I’ve often tried and tried,
I’m quite unable to subtract.
I do it backward…and divide.
Math in Our World Read the poem aloud with students. Ask students to explain how the author used personification in this poem and to recall examples from other stories they know. Then explain that the class will translate addition, subtraction, and multiplication sentences into division sentences that the paramecium can solve. On the whiteboard, write the following math sentences: 3 + 3 + 3 + 3 = 12; 6 – 3 – 3 = 0; 15 × 4 = 60. Have students get into pairs and rewrite each math sentence as a division sentence. 12 ÷ 4 = 3; 6 ÷ 3 = 2; 60 ÷ 15 = 4 Then ask students what kinds of microscopic objects they think the paramecium might be counting. Extending Our Learning Refer to pages 6, 10, and 11 in Oceans: Into the Deep. Have students get into groups of four, and then distribute to each group a piece of paper. Explain that each group will be drawing a copy of the diagram shown on pages 10 and 11. In their drawings, however, students will label the depths in fathoms instead of feet. Have them refer to page 6 to find out how many feet are equal to 1 fathom. 6 Finally, have groups browse the remainder of the reader to see which animal lives in each zone. As a class, discuss how each animal has adapted in order to survive.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
Afterward, ask students to draw a picture showing the different levels of the ocean and label the animals that live in each zone. JEC@P?
Reading and Language Arts Support
A25
Reading and Language Arts Support
USE WITH
Chapter: Understand Division Multi-Part Lesson 2
Reading GLE 4.1.13.d The student will relate literary experiences (e.g., book discussions, literacy circles, writing, oral presentations, artistic expressions).
Reading GLE 4.1.01.d The student will formulate and respond to questions from teachers and other group members.
Literature Activity Read aloud with students The Great Divide: A Mathematical Marathon by Dayle Ann Dodds. Have students compare and contrast this selection with other stories they have read about sports. Then reread the story, replacing the beginning number with 1,800. Have students use mental math to find what half would be when they come to the left and right paths in the story. On the page with the boat, replace 40 with 900, and have students use mental math again to find half. Then replace 20 with 450, and so on through the book.
Problem Solving in Math Lead a discussion about kinds of fundraisers, including those that students have participated in or think would be fun to be a part of. Ask them to explain the purpose of a fundraiser. Next, read the following story once, and repeat it. Direct students to complete the Four-Step Problem-Solving graphic organizer found on page 20 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.) It was hot. The sun blazed down, and the parking lot cooked with heat, but everyone sprayed and splashed in the water and suds, so it wasn’t too bad. The High Park Tigers soccer team was holding its annual Clean Machines car-wash fundraiser. For 5 hours, cars were lined up at both cleaning stations, and one by one they took their turns getting scrubbed, rinsed, and dried. The girls had a great time, and, more importantly, they made enough money to buy the new equipment they needed for the season. If the girls made $400, and charged $10 per car, how many cars did they wash per hour? Have students use mental math to answer the story’s question. $400 ÷ 5 = $80; $80 ÷ $10 = 8 cars per hour
Reading GLE 4.1.08.b.7 The student will check for understanding after reading by locating information to support opinions, predictions, and conclusions.
Reading Graphic Novels Have students revisit “Field Trip Fun.” Discuss with students what is happening in this graphic novel. Ashley and Nicholas are visiting the zoo. They are learning about what a zookeeper does to care for the animals in the African Safari exhibit. Have a volunteer identify how many types of animals the zookeeper mentions. 6, plus she takes care of the elephants, which she does not mention Ask students if that number is the result that Nicholas is looking for in frame 8. no How do they know? Nicholas is wondering how many of each animal are in the exhibit. There could be multiple occurrences of the same type of animal in the African Safari. Ask students how many zookeepers feed the animals in the African Safari exhibit. 4 Based on this number, have students discuss how many total animals reside in the exhibit.
A26
Reading and Language Arts Support
Math Investigations On the whiteboard, write 6,573 ÷ 11, and then tell the class that a younger student wants to know how to use mental math to find the answer. Have students spend several minutes writing a detailed explanation of how they would use mental math to solve this equation.
USE WITH
Reading GLE 4.1.08.b.3 The student will check for understanding after reading by identifying the author’s purpose (e.g., to entertain, to inform, to explain).
Reading GLE 4.1.01.i The student will use different voice levels and speech patterns for small groups, informal discussions, and reports.
Literature Activity Read aloud with students The Doorbell Rang by Pat Hutchins. Ask students to identify the author’s purpose—to inform, entertain, or explain—and explain their answers with examples from the story. Then have them pretend that Grandma made 144 cookies instead of 12. Ask them, If there were 2 children, how many cookies would each child get? Have students explain how they got their answer. Then have them divide the cookies by 3, 4, 6, and 12 children. If there is time, have students repeat the exercise for 252 cookies.
Math in Our World Distribute to students copies of a newspaper’s Arts and Entertainment section. Have them browse for ticket prices to live events such as concerts, plays, dance performances, and so on. Tell them that they work for a large company that wants to give away tickets as thank-you gifts to their best salespeople. Students have been given $1,000 for the task. First, they must decide which event would be enjoyed by the most people. Then, they need to calculate the total number of tickets they can buy for that event based on the amount of money they were given. Work as a class to complete the task. Finally, have students discuss when giving someone a formal thank-you note is appropriate. Have volunteers tell about instances when they have written thank-you notes.
Extending Our Learning Refer to page 11 in Growing Goods in a Growing Country. Have students list things made from cotton that they use every day. Then have students pair up, and ask them to calculate how many bales of cotton are equal to 24 tons. If necessary, remind them that 1 ton equals 2,000 pounds. 24 × 2,000 = 48,000; 48,000 ÷ 480 = 100 bales Then have them calculate the total number of dollar bills that can be made from that amount of cotton. 31,360,000 bills
Reading GLE 4.1.02.c The student will recognize different forms of text (e.g., poems, plays, drama, letters, ads, biographies).
Real-World Problem
Solving
s Math and Socia l Studie
Math and Science
Math and Social Studies
Number and Operations
8/2/07 2:41:28 PM
.indd COVER_B14_G04LEV_1062390
ii
Reading and Language Arts Support
Chapter: Understand Division Multi-Part Lesson 3
Reflective Writing Tell the class that a group of college students from Miami, Florida, will be driving to Montreal, Quebec, Canada. Coincidentally, the college students are equal in number to the students in class. Each college student has offered to drive his or her fair share of the 1,415-mile journey. Work as a class to determine how many miles each student will be at the wheel if the driving is divided equally among them. Then look at a map to see what route would be taken and which major cities they would drive through. Could this depend on which route the students choose? Finally, have students spend several minutes writing a brief narrative description of a trip they have taken or would like to take.
Reading and Language Arts Support
A27
Reading and Language Arts Support
USE WITH
Chapter: Organize and Display Data Multi-Part Lesson 1
Reading GLE 4.1.06.g The student will continue to use context clues to determine the correct meaning/usage of multiple meaning words.
Reading GLE 4.1.09.c The student will use current technology as a research and communication tool for personal interest, research, and clarification.
Literature Activity Reread with students Hottest Coldest Highest Deepest by Steve Jenkins. Afterward, return to the list of longest rivers. Explain to students that the mean of a set of numbers is the average. On the board, model for students how to find the mean length of the rivers. 4,145 + 4,007 + 3,964 + 3,710 = 15,826; 15,826 ÷ 4 = 3,956 R2 Say, The mean length of these 4 rivers is 3,956 miles.
Understanding Math Vocabulary Find a Web site, almanac, or newspaper section that lists the average high and low temperatures each day for a given month. Have students get into groups of four, and then distribute or display the list to each group. Assign half the groups to use high temperatures and the other half to use low temperatures. Then review with the class the definitions of mean, mode, median, range, and outliers. Each group will find the mean, mode, median, range, and any outliers of the temperatures from the list. Tell them to record their results using complete sentences. (For example, The range of high temperatures for March was 27 degrees.) Afterward, have each group share one of their statistics. If some groups come up with different values, discuss and model the correct method of calculation.
Next, have students spend several minutes writing about either the hottest, coldest, windiest, or wettest day they can remember. Encourage students to use descriptive adjectives, similes, and metaphors in their writings. Finally, have several volunteers share with the class what they wrote.
Reading GLE 4.1.12.f The student will compare and contrast events and characters using evidence cited from print and non-print text(s).
Reading Graphic Novels Have students revisit “Field Day Decision,” or distribute copies from page 7 of Hands-On Activity Tools and Resources. Remind students that the pictures in a graphic novel tell as much about the story as the words. Point out the second panel. Ask students what is happening. Candace suggests a water balloon fight. Ask students how they know that Ethan does not want a water balloon fight. The panel shows Ethan with a worried look on his face, and a thought balloon has a picture of him getting hit by water balloons. Ask a similar question about Candace and tug of war. Have students suggest a way to tell without words how another character might feel about a sack race. The character would be thinking about falling down in a sack race and have a frown on his or her face. Next, create a tally chart using several of the events listed on the board in the graphic novel. Conduct a survey of students to find out which event they like most. Use the exercise to review tally marks, and then ask students to suggest ways to organize the data into a chart or graph.
A28
Reading and Language Arts Support
Math in Action Have students browse Ancient Giants of the Forest for graphic features. Ask students why graphic features are helpful. They show data in a way that makes it easy to compare.. Discuss how information is displayed in each graphic feature. Next, have students pair up and turn to the table on page 16 in the reader. Have them find the mean, median, and range of the points listed in the table. mean = 1067; median = 1067; range = 492
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
,C?QSPCKCLR
USE WITH
Reading GLE 4.1.08.b.9 The student will check for understanding after reading by distinguishing between fact/opinion and reality/fantasy.
Literature Activity Reread with students Too Many Kangaroo Things to Do by Stuart J. Murphy. Afterward, have students discuss personification in the illustrations of the animals. Ask them how the illustrator made the animals more like humans. They wear hats and clothes, they speak, they cook, and they have parties. Then have them compare the animals in this story to other stories they have read with animal characters. Prompt students to think of any stories in which the animals do not act like humans. Next, have students get into pairs, and distribute a 1–20 number line to each pair. Tell students to look at the pages in the book that contain calculations. Have them create a line plot showing how many times each number appears in the book on these pages. 1: 9 times; 2: 10 times; 3: 10 times; 4: 11 times; 6: 2 times; 8: 2 times; 9: 1 time; 10: 1 time; 12: 2 times; 16: 1 time; 20: 1 time Then ask which number appeared the most times. 4 Have students tell which numbers appeared only once. 9, 10, 16, and 20 Then ask which number was the lowest number that did not appear at all. 5
Reading GLE 4.1.05.a The student will increase confidence and poise in reading aloud (e.g., paired reading, shared reading, choral reading, recorded reading, echo reading).
Poem
Cat Graph
By Shelli Hightshoe
One is brown, one is black One is calico, two are tabbie
s.
All are furry and fluffy.
Reading and Language Arts Support
Chapter: Organize and Display Data Multi-Part Lesson 2
Not a single one has fleas. Three are orange with white Two are gray with black pa
bellies
ws.
How can I surely Keep track of them all? I’m sure a graph With its bars and lines By nearly a half Can shorten my time. Find the mode, or, the “m
ost”
And the median too.
Examining Math Have students get into groups of four, and then distribute graph paper to each group. Have ".&3*$"/4 0/5)& students turn to the table on page 8 in Americans on the Move. Tell them that they will be creating a line graph using informationn from the table. The x-axis will show the years 1860 through 1900 in one-decade increments. s. The y-axis will show the ton-miles shipped in billions up to 150 in increments of 10. Have students ignore the digits after the decimals in the right-hand column of the table. Wh When groups are finished, have them display their line graphs at the front of the class. Discuss which graphs are done correctly, and ask students for suggestions to correct the graphs that are not correct. MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2M AG?J2R
SBGCQ
.07&
#?R? L?JWQGQ
Just think what graphs Can do for you!
Extending Our Learning Read the poem aloud with students. Then ask them how they know this is a poem and not another form of literature. It has meter and there are rhyming lines. Then discuss with students which type of graph would work best to display the data about cats. Have students defend their choices. If there is time, create a graph or plot based on the information in the poem.
Reading and Language Arts Support
A29
Reading and Language Arts Support
USE WITH
Chapter: Organize and Display Data Multi-Part Lesson 3
Reading GLE 4.1.08.b.6 The student will check for understanding after reading by stating reasonable generalizations in reference to two pieces of text on a similar topic.
Literature Activity Reread with students pages 22–27 of Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Cindy Bickel. Ask students to compare this book to other books they have read this year. If necessary, prompt students by having them explain similarities and differences between Tiger Math and other nonfiction books. Next, have students get into pairs and return to the bar graph on page 24. Distribute graph paper and crayons or colored pencils to each pair. On the board, write the following data about T.J.’s weight: at 6 months = 125 pounds; at 12 months = 200 pounds; at 18 months = 275 pounds; at 24 months = 300 pounds Tell students to create a bar graph similar to the one in the book using the data written on the board. Afterward, have students explain how they decided on which increments to use in the y-axis. The weights could all be divided by 25, so we made each square on the graph paper equal to 25 pounds.
Reading GLE 4.1.09.g The student will retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
Reading GLE 4.1.06.a The student will build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Extending Our Learning Revisit Riding the Mail Trail, and then ask students to describe any historical places they have visited or read about. Then have them get into groups of four, and distribute graph paper and crayons or colored pencils to each group. Refer to the bar graph on page 16 in the reader. Tell students that they will be making a graph that shows how many Pony Express stations there were alongg the trail then compared to how many still stand today as historic landmarks or museums. Ask students to identify which kind of graph they could use to show both of these pieces of information. a double bar graph Have each group decide how many stations they think are left standing today in each state, and then create a double bar graph showing the number of stations then versus now. Afterward, display students’ graphs at the front of the class. Real-World Problem
Solving
s Math and Social Studie
Math and Science
Math and Social Studies
Number and Operations
8/2/07 2:24:02 PM
ii Cover_B9_G04LEV_106234x.indd
A30
Examining Math Distribute an index card to each student. On one side of their cards, have students describe two key learnings about displaying and organizing data that they feel they understand well. On the other side, have them describe two key learnings that they find confusing. Collect the cards, and then randomly choose several of them to read aloud. Review the key learnings that students find confusing.
Reading and Language Arts Support
Financial Literacy On the board, create a bar graph showing the amount of money spent each month on various expenses. Ask students to come up with categories for the bar graph. entertainment, snacks, school supplies, clothes, and so on Be sure to include Savings as one of the categories. Then make up amounts from $0 to $20 for each category and enter the data into the bar graph. Next, discuss with students the importance of savings. Ask them to identify any expenses they might adjust in order to increase the amount they save each month. I can spend less on candy and entertainment. Finally, discuss how these changes affect the bar graph.
USE WITH
Reading GLE 4.1.08.a.6 The student will derive meaning while reading by making inferences.
Reading GLE 4.1.02.a The student will use parts of text (e.g., title, title page, table of contents, chapter title, glossary, and index).
Literature Activity Reread with students Hottest Coldest Highest Deepest by Steve Jenkins. As you read, ask students whether the chance is good or not that something will occur on a given day. For example, on the page describing the hottest spot on Earth, you might ask whether there is a good chance that it will be 136°F here tomorrow. not a good chance For the page describing the wettest place on Earth, ask students whether there is a good chance that it is raining on Mount Wai-ale-ale today. a good chance
Math in Our World Revisit with students A Force to Reckon With. Have them refer to the table of contents on the reader’s first page. Ask how the table of contents help them find more information about the Richter Scale. Looking at the table of contents, I would see that Chapter 3 is titled The Richter Scale, so I would know to skip ahead to that chapter. Ask students what otherr resources they might use to find out about thee Richter Scale. an index, the library, the Internett
Next, distribute to each student a 4-part spinner from page 122 of Hands-On Activity Tools and Resources. Explain that probability describes the chance that one outcome will occur out of several possible outcomes. Have students imagine that the arrow is spun. Have them explain how many possible outcomes there are of which number the arrow will stop on. 4 Explain that this means there is a probability of 1 in 4 that the arrow will land on a chosen number.
Understanding Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 of Hands-On Activity Tools and Resources. Write probability in the center rectangle, and work as a class to complete the surrounding squares. Then have each student spend several minutes writing a short description of a probable event that might happen to them, followed by a short description of an improbable event. Afterward, have several students share what they wrote, and discuss as a class the probability or improbability of the events.
Real-World Problem
Solving
Math and Scienc e
A FORCE TO RECKON WITH
Number and Operations
Reading and Language Arts Support
Chapter: Organize and Display Data Multi-Part Lesson 4
Next, have students turn to the table on page 16 in the reader. Discuss the probability of each level of earthquake occurring in their area. Which rating of earthquake has the highest probability of being felt by the most people in a given year? 4.0–4.9 Which has the lowest? 9.0 or greater
Reading GLE 4.1.01.a The student will listen attentively by facing the speaker, asking questions, and paraphrasing what is said.
Math in Action Have students get into groups of four, and distribute two number cubes and crayons or colored pencils to each group. Ask them if the sides were numbered 1–6, how many possible outcomes there would be. 6 Have students tell what the probability is of rolling a 4. 1 in 6 Next, challenge groups to color one cube so that there is a 1 in 2 chance of rolling a certain color, and the other cube so that there is a 1 in 3 chance of rolling a certain color.
Reading and Language Arts Support
A31
Reading and Language Arts Support
USE WITH
Chapter: Decimals and Fractions Multi-Part Lesson 1
Reading GLE 4.1.06.b The student will build vocabulary through frequent read alouds.
Reading GLE 4.1.06.c The student will infer word meanings using roots, prefixes, and suffixes.
Literature Activity Read aloud with students Follow the Money by Loreen Leedy. Then distribute to each student a random assortment of coins and bills from pages 78–79 in Hands-On Activity Tools and Resources. Have students count their money, write the amount on a slip of paper, and circle the digit in the hundredths place. Then have students group themselves in the front of the classroom, according to the number that was circled.
Using Math Vocabulary Write the word decimal on the whiteboard. Underline the root dec-, and discuss its meaning (“ten”), pointing out to students other words that share this root, such as decade and decathlon.
Record the number of the group with the fewest students and have that group sit down. The remaining students will exchange some of their bills and coins and write down their new totals. Repeat until the numbers 0–10 have been recorded. Evaluate with students how they thought this activity demonstrated place value through hundredths.
Reading GLE 4.1.12.j The student will explore the concept of theme.
A Dillar, A D ollar
Poem
Author Unkno
wn Four quarters m ake a dollar. Twenty nickels, ten thin dimes. If you have a hu ndred pennies, that’s a dollar ev ery time.
It would take tw o half-a-dollars if you want the same amount, and, of course, th e silver dollar’s worth a dollar w hen you count!
Then have students brainstorm a list of places where they have seen decimal numbers. prices, scientific measurements, gas pumps, and so on Have volunteers explain what decimals have to do with understanding place value.
Reading GLE 4.1.09.f The student will skim materials to develop a general overview of content or to locate specific information.
Math in Our World Divide the class into left and right halves. Tell students on the right that they are the tenths, and those on the left are the hundredths. As a class, browse Life in the United States in search of decimal numbers showing place values through hundredths. When a decimal number is found, point to the tenths side of the room, and have them call out the number in the tenths place. Then point to the hundredths side of the room and have them call out the number in the hundredths place, and on which page they found it. Repeat the process for each decimal number in the reader. Real-World Problem
Solving
s Math and Socia l Studie
Math and Science
Math and Social Studies
Number and Operations
8/6/07 12:01:42 PM
2951.indd ii COVER_B13_G04LEV_SE_106
Extending Our Learning Read the poem aloud with students. Ask students to identify the author’s theme and details from the poem that demonstrate it. Then create coins using the Coins manipulative found on page 108 in Hands-On Activity Tools and Resources, and randomly distribute one coin to each student. Have students form two lines. The students at the front of the lines will work together to find the total of their two coins and write it on the whiteboard as a decimal number. Sample answer: 1 nickel + 1 penny = 0.06 Have them identify which number is in the tenths place and which is in the hundredths. (Alternatively, you could provide students with a decimal amount and encourage them to show a configuration of coins that equals the amount provided.)
A32
Reading and Language Arts Support
Reading Graphic Novels Have students reread “Flying Feat.” Ask them what visuals show clues about the problem in the story. There are illustrations of students measuring the distance their paper airplane flies. Ask students if these visuals help characters solve the problem. Encourage students to justify their opinion using examples from the graphic novel.
USE WITH
Reading GLE 4.1.01.f The student will summarize orally what has been learned or accomplished after completing an activity or assignment.
Literature Activity Read aloud with students Fraction Fun by David A. Adler. Then distribute to each student an index card with a fraction written on one side. Have students draw a pictorial representation of their fractions on the back of the card. Then tell them that everyone has at least one equivalent fraction match somewhere in the class. Have students find the matches that are equivalent to their own. Encourage students to explain how they chose to represent their fractions. Are the representations similar? different?
Reading GLE 4.1.02.b The student will use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Math in Action Refer to pages 22 and 23 in Strange but True. Ask students how text features such as headers and captions can be used to quickly determine the main idea of these pages. Then divide students into groups of four, and distribute to each group a piece of paper. Have students begin by locating the two fractions on the page and writing three equivalent fractions for each one.
1 2
=
2 4
= 48 ;
1 4
=
2 8
= 123
MJTGLE
1C?J 6MPJB/PM@JCK2
Reading GLE 4.1.05.b The student will read with fluency and confidence from a variety of texts (e.g., poetry, drama, current events, novels).
Poem
The Great Equivilato r
by Dan Greenberg Find equivalent fractions? I’ll get right down to it Just tell me again: How on earth do you do it? Oh wait, don’t say it. How could I forget? You put this one over that one... What? Incorrect? Okay, how about that one over this one That okay with you? Now carry the seven, and borrow the two. Or something like that. Whatever. Who knows. Still incorrect? It’s possible, I suppose. You want equivalent? This I guarantee: I’m liable To be highly unreliable So don’t come to me.
Reading and Language Arts Support
Chapter: Decimals and Fractions Multi-Part Lesson 2
,?RF? LB2AG CLAC
Then have the students in each group work together as a team to find the fraction that answers the question on page 23. The group that finishes first will present their answer and describe the process they used to find it. Be sure students use complete sentences. Using Math Vocabulary Display a copyy of the Vocabulary graphic organizer foundd on page 28 in Hands-On Activity Tools and Resources. Write the phrase mixed numbers in the center rectangle, and then work as a class to complete the surrounding squares. Complete a second Vocabulary graphic organizer for the phrase simplest form. Discuss nonmathematical uses of equivalent and form to aid in students’ understanding of math vocabulary.
Extending Our Learning Read the poem aloud with students, and then divide them into four groups. Explain that the class will reread the poem aloud, but this time groups will take turns reading 1 of the poem at a time. Tell students that the poem is 20 lines 4 long, and then work as a class to find the fraction equivalent to 14 that shows the number of lines each group reads. 14 = 205 , so each group reads 5 lines Have groups reread the poem.
JEC@P?
Discuss with students that people often get confused and forget how to do something. In pairs, have students come up with various ways they might remember how to make equivalent fractions.
Reading and Language Arts Support
A33
Reading and Language Arts Support
USE WITH
Chapter: Decimals and Fractions Multi-Part Lesson 3
Literature Activity Before reading, ask students to keep track of the different amounts of money that Henry earns on his trip. Then read aloud with students Henry Hikes to Fitchburg by D. B. Johnson. Ask students to write each amount of money that Henry earned as both a decimal and a fraction. Then have them add up the total amount of money Henry earned and write it as both a decimal and a mixed number. Was it easier for students to represent the numbers as decimals or as mixed numbers? Encourage volunteers to explain the difference. Ask students why money is expressed using a decimal. Have them consider whether an amount would ever be expressed to more than the hundredths place. Why or why not?
Using Math Vocabulary Display a copy of the Venn Diagram graphic organizer found on page in Hands-On Activity Tools and Resources. Label one side of the diagram Improper Fraction and the other side Mixed Number. Then work as a class to complete the diagram with similarities and differences between the terms’ meanings.
Reading GLE 4.1.08.b.7 The student will check for understanding after reading by locating information to support opinions, predictions, and conclusions.
Reading GLE 4.1.01.d The student will formulate and respond to questions from teachers and other group members.
Math Investigations Divide students into pairs, and then have them browse Solving the Pyramid Puzzle and find one mixed fraction and one decimal number for this exercise. Students will write each number as a mixed fraction, an equivalent improper fraction, and an equivalent decimal number. Each pair will also choose one of the equivalencies to write in words. From page 8:
Problem Solving in Math Read the following story once, and repeat it. Direct students to complete the Four-Step ProblemSolving graphic organizer found on page 20 of Hands-On Activity Tools and Resources as you read. (You might also display for students key words and phrases to help them.)
449.5 = 449 12 =
899 , 2
four-hundred forty-nine and five-tenths Have
one student from each pair share their equivalencies with the class. Ask students if they used the same strategies each time to convert the numbers. Have students write paragraphs explaining when each type of number is appropriate to use, and when it is not. Encourage them to justify their reasoning using examples from the reader. Have students trade papers to check for spelling errors, using a dictionary if necessary.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
&CMKCRPW
A34
Reading and Language Arts Support
The Johnson Convention Center buzzed with activity. Superheroes strolled the halls. Big-eyed anime characters stared down from giant posters. And here and there an alien, orc, or space commander could be seen among the crowds of people. The 20th Annual Comics Jamboree was well underway. The first event was a welcoming breakfast at 9 A.M. that lasted 0.75 hours. Then there was a 0.25 hour break before the next event. The rest of the day’s events were, in order: Basic Cartooning Tips, 1.25 hours; Writing for Excitement, .75 hours; Meet Your Heroes Luncheon! 1.0 hours; Anime for Beginners, 1.0 hours; Costume Contest, 1.25 hours; Grand Finale, 0.5 hours. If there is a 0.25 hour break between each event, what time does the convention end? List the events and their lengths in decimal numbers on the whiteboard. Work as a class to rewrite each decimal number as a fraction. Then use the Analog Clock manipulative, found on page 106 in Hands-On Activity Tools and Resources, to show the passing of time as each event occurs and answer the question. The convention ends at 5 P.M.
USE WITH
Reading GLE 4.1.08.b.4 The student will check for understanding after reading by discussing similarities and differences in events and characters using evidence cited in two or three text(s).
Reading GLE 4.1.09.a The student will use and discern appropriate reference sources in various format (e.g., interviews with family and community; encyclopedias, card/electronic catalogs, almanacs, magazines, and newspapers).
Literature Activity Read aloud with students Each Orange Had 8 Slices by Paul Giganti, Jr. Than ask them to recall the three books read in the previous chapter (Follow the Money, Fraction Fun, and Henry Hike to Fitchburg). Have students identify a common theme or topic shared by those books, and then have them debate whether Each Orange Had 8 Slices shares the topic or theme as well.
Math in Our World Have students get into pairs, and distribute a cooking magazine or food section from a newspaper to each pair. Tell students to browse the recipes for six different fractions and record them on a sheet of paper. Next, have each pair use their fractions to practice adding and subtracting like and unlike fractions (for a total of at least four examples). Have pairs exchange papers and check each others answers. Finally, have each student choose a recipe that he or she thinks is both healthy and tasty. Ask students to spend several minutes writing and explanation of why they chose the recipes they did. If there is time, have volunteers share what they wrote.
Then have students get into groups of four, and distribute magazines, scissors, tape, and chart paper to each group. Tell students to cut out pictures from magazines to create sets, and then write fractions that describe their sets. Students cut out pictures of 9 4 7 __ __ 20 people, 4 are children: __ 20 ; 9 are women: 20 ; 7 are men: 20 Finally, have students use the fractions to create addition sentences 9 16 7 __ __ that describe combinations of their subsets. __ 20 + 20 = 20 of the people are adults Have groups describe their sets and fractions.
Reading and Language Arts Support
Chapter: Add and Subtract Fractions and Decimals Multi-Part Lesson 1
Math in Action Have students imagine that they will be tutoring younger math learners. On the whiteboard, write _23 – _16 = x. Ask students to write what they would tell a third grader about how to solve the equation.
Reading GLE 4.1.01.c The student will understand, follow, and give oral multi-step directions which may include illustrations.
Examining Math Distribute to each student a copy of the Four-Step Problem Solving Plan from page 20 of Hands-On 9 Activity Tools and Resources. On the board, write the fraction __ 36 . Have students complete the graphic organizer to show how they would rewrite this fraction in its simplest form. Math at Play Divide the class into two teams. For this activity, use the cards from the Fractions Made Equal game on page 66 of Hands-On Activity Tools and Resources. Have a student from each team come to the front and draw two cards. Each student will add his or her pair of fractions together by first simplifying them, then finding common denominators, and finally simplifying the 5 3 5 8 _3 _1 _1 __ __ __ answer if necessary. __ 25 + 9 = 5 + 3 = 15 + 15 = 15 The students who finds the correct answer first scores a point for his or her team. The first team to score 5 points wins.
Reading and Language Arts Support
A35
Reading and Language Arts Support
USE WITH
Chapter: Add and Subtract Fractions and Decimals Multi-Part Lesson 2
Reading GLE 4.1.03.a The student will develop awareness of the sounds of language through repeated exposure to a variety of auditory experiences (e.g., poetry, music lyrics, books on tape, sound effects, read alouds).
Literature Activity Before beginning this activity, write money amounts on enough index cards for 10 per student. Then read aloud If You Made a Million by David M. Schwartz. Briefly discuss with students why the illustrations are important in helping readers understand the text. Then divide students into groups of four, and distribute 40 index cards to each group. Tell students that they are going to play “Decimal Round Up.” Students take turns drawing cards from the deck and rounding the amounts to the nearest dollar. They write the rounded amount on the back of the card. Once all 40 cards have been rounded, have groups exchange cards to check their answers.
Reading GLE 4.1.09.h The student will develop an awareness of the effects of media (e.g., television, print materials, radio, internet, magazines) on daily life.
Reading GLE 4.1.02.b The student will use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Math in Our World Distribute to students copies of a newspaper’s Sports section. Have them browse the lists of statistics for decimal numbers, most likely where averages are shown. Discuss strategies for rounding these decimals to make them easier to use for mental math. Then list some of the decimal numbers on the board, and practice rounding them to different place values.
Extending Our Learning Refer to page 19 in the reader. Work as a class to calculate the distance from the bottom of the Ocean Abyss to the top of the Andes Mountains, rounded to the nearest kilometer. 11 km Ask students to describe the steps they need to take to find the answer using mental math. Then find the distances between the bottom of the abyss and the top of Mount Elbrus, as well as from Mount Elbrus to the top of the Andes. Finally, repeat the exercise, rounding each distance to the nearest tenth of a kilometer.
Finally, have students talk about which sports are featured in the paper and which ones are not. Ask them why they think certain sports are missing from the coverage. Are they not as popular? Are they out of season? Ask students why numbers are important in sports. Have volunteers tell some of the sports numbers they most commonly hear. scores from basketball, baseball, or football
A36
Using Math Vocabulary Have students form two lines. On the whiteboard, write a multi-digit number without using a decimal point, and then announce the place value for one of the numbers. For example, if you wrote 6759, you could say, The 7 is in the tenths place. The student at the front of one of the lines approaches the board and places the decimal point in the appropriate place. in this case, 6.759 Write a new number for the student at the front of the other line. Continue until all students have had a turn.
Reading and Language Arts Support
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
JEC@P?
USE WITH
Reading GLE 4.1.07.a The student will set a purpose for reading (e.g., to understand, to enjoy, to solve problems, to locate specific information/facts).
Literature Activity Before reading, ask students to record the amounts of money Henry earns on his trip. Then read aloud with them Henry Hikes to Fitchburg by D. B. Johnson. Have students convert each monetary amount into decimal form, and then have them add the amounts together to get the total Henry earned on his trip. Next, tell students that they went with Henry on the trip, but that they earned double what he did. Ask them to figure the new total. Finally, have students spend a few minutes discussing hikes they have taken.
Reading GLE 4.1.06.a The student will build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Using Math Vocabulary Divide the class into two teams, and have them line up. Tell students that they are having a Definition Bee. They will be defining math vocabulary words covered this year. You will name a letter of the alphabet. Then the person at the front of the line will name a math word that begins with that letter and define it. Decide which team will go first, and then begin with the letter A and work through the alphabet in order. for example, area, billion, circumference, decimal, estimate, fact family, greater than, half, and so on Students may show their understanding by either using the word in a complete sentence or writing an example on the whiteboard. Reading GLE 4.1.09.a The student will use and discern appropriate reference sources in various format (e.g., interviews with family and community; encyclopedias, card/electronic catalogs, almanacs, magazines, and newspapers).
Math in Our World Divide the class into groups of four, and then distribute to each group a copy of a newspaper’s Financial section. Tell students that each group has $100 to spend on stocks. They will search through stock prices to create lists of 3, 4, 5, and 6 stocks. (Show students which columns they should use to identify price.) Each list’s total price must come as close to $100 as possible without going over. Be sure students include the company abbreviations next to each stock in their groups. Have one student from each group present his or her group’s four lists. Declare a winning group for each category of list—3, 4, 5, or 6 stocks listed—based on who got closest to $100 without going over.
Math In the Content Areas Refer to pages 11 and 19 in A Force to Reckon With. Work as a class to add together the decimal numbers in the table on page 11 showing magnitude. Add only two numbers together at a time as you work through the list. 9.2 + 8.7 = 17.9; 17.9 + 8.6 = 26.5; 26.5 + 8.2 = 34.7; and so on Next have students use subtraction to find the differences in magnitude between various earthquakes.
Real-World Problem
Solving
Math and Scienc e
A FORCE TO RECKON WITH
Number and Operations
Reading and Language Arts Support
Chapter: Add and Subtract Fractions and Decimals Multi-Part Lesson 3
Then have students pair up and repeat the exercise using the magnitudes shown in the table on page 19. Ask pairs to exchange papers to check their answers. Then have each student spend a few minutes writing a description of what it would be like to experience an earthquake. Encourage students to include sensory details in their descriptions. Reading GLE 4.1.12.d The student will identify and describe the main and minor characters, considering the importance of their actions, motives, and appearances.
Reading Graphic Novels Review “Ride Riddle” with students. Discuss with students whether they have been to an amusement park or theme park. Encourage them to share stories about whether they rode the different rides. Ask students to explain who looks sick in the first frame. Dad Ask students which of the three characters converts units in this graphic novel. Candace and her dad Have a volunteer explain why it is important in this story for the characters to understand how to convert units. They need to know whether Candace is tall enough to ride theme-park rides. Challenge students to determine why the stand-up roller coaster might have different height requirements than other types of rides. Have the class write a brief description of each character based on what they learned from reading this graphic novel. Remind students to use not just the dialogue but also the artist’s details in writing their descriptions.
Reading and Language Arts Support
A37
Reading and Language Arts Support
USE WITH
Chapter: Identify and Describe Geometric Figures Multi-Part Lesson 1
Reading GLE 4.1.08.b.2 The student will check for understanding after reading by selecting main idea and supporting details from text.
Reading GLE 4.1.10.c The student will apply comprehension skills and strategies to informational text (e.g., prereading and active comprehension).
Literature Activity Read aloud with students Shape Up! by David A. Adler. Afterward, have them summarize the main ideas from the book. Then have students get into groups of four, and distribute to each group magazines, scissors, tape, and a large sheet of paper. Challenge them to search the magazines for examples of each shape mentioned in the book. They will cut out the shapes, tape them to the paper, and label them correctly. Afterward, have groups display their papers at the front of the class. Discuss which shapes were easiest to find and which were more difficult.
Examining Math Have students turn to the timeline on pages 2–3 of Solving the Pyramid Puzzle. Have students describe how the events are arranged on a timeline. Explain that some of the events are listed in a vertical list instead of being placed side-by-side. Have students consider why that might be, and how they can tell which event occurred first. These events happened close to each other in time. The events at top happened earlier than the ones below.
2MJTGLE
1C?J 6MPJB/PM@JCK
,?RF ?LB2 AGCLAC
&CMKCRPW
Next, have students browse the reader for photos of pyramids. Tell them to choose two pyramids and write a short paragraph comparing them. Students will include face, edge, and vertex in their comparisons. Afterward, have students exchange paragraphs to correct them for punctuation and spelling.
Reading GLE 4.1.01.d The student will formulate and respond to questions from teachers and other group members.
Math in Action On separate sheets of paper, write the names of the following shapes: cone, cube, cylinder, pyramid, rectangular prism, sphere, triangular prism. Then have seven volunteers come to the front of the class. Tape or otherwise attach one of the cards to the back of each student. Be sure they do not see which card they are wearing. The volunteers will stand facing the front of the class so that the remaining students can see which shapes they have been assigned. One by one, the students at front will ask questions about the number of faces, edges, and vertices they have in order to identify which shape they are wearing. As students guess their shapes, they can sit down. Continue until all volunteers are seated. If there is time, invite a second group of students to the front.
A38
Reading and Language Arts Support
Extending Our Learning Using the three-dimensional figures patterns found on pages 130–139 of Hands-On Activity Tools and Resources, distribute patterns to students. Have them examine the patterns to see the relationship between twodimensional figures and three-dimensional figures. On the board, create a list of two-dimensional figures. Then ask students to identify which three-dimensional figures have faces that are the shapes listed on the board. Ask whether there are any the threedimensional shapes made up of only one kind of two-dimensional shape. cube, triangular pyramid Have students identify any shapes that were not covered in this chapter. The cone has a half-circle.
USE WITH
Reading GLE 4.1.06.i The student will build vocabulary by reading from a wide variety of text and literary genres.
Reading GLE 4.1.06.f The student will foster word consciousness (e.g., word play, word walls and word sorts).
Literature Activity Reread aloud with students Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells. Afterward, have students come up with their own examples of measurements using unusual objects. For example, they might estimate how many students it would take to fill the classroom, the number of paper clips that would fit in the box of a semi truck, and so on.
Understanding Math Vocabulary Display a copy of the Venn Diagram graphic organizer found on page 27 of Hands-On Activity Tools and Resources. Write acute angle above the left oval and obtuse angle above the right oval. Work as a class to compare the definitions of these two terms and draw examples. Then have students pair up. Challenge them to come up with creative ways to remember the meanings of acute angle, obtuse angle, and right angle. Afterward, have pairs share their ideas and decide as a class which ones work best.
Next, review with students the meanings of acute angle, obtuse angle, and right angle. Then have students look for examples in the classroom, and list them on the whiteboard. Finally, discuss with students how the shape of the classroom would change if the walls formed acute or obtuse angles instead of right angles.
Reading GLE 4.1.12.a The student will read, view, and recognize various literary (e.g., poetry, novels, historical fiction, nonfiction) and media (e.g. photographs, the arts, films, video) genres.
Reading Graphic Novels Have students revisit “Tricky Turns,” or distribute copies from page 10 of Hands-On Activity Tools and Resources. Ask students refer to the fifth panel, and ask what the stars circling Andrew’s head indicate about Andrew. He bumped his head and he feels dizzy. Have students describe cartoons or comics where they have seen this visual shorthand for a bumped head used before. Have students brainstorm other common visual devices that they have seen. a light bulb is an idea, zzzz’s are snoring, pictures or words inside a cloud-shape are thoughts, lines can mean something is moving quickly
Reading and Language Arts Support
Chapter: Identify and Describe Geometric Figures Multi-Part Lesson 2
Extending Our Learning Have students pair up, and distribute magazines, scissors, tape, and three sheets of paper to each pair. Also, use the Protractors manipulative found on page 110 of Hands-On Activity Tools and Resources to give each pair a protractor. Have students label each sheet as acute, obtuse, or right. Then have them browse the magazines for several examples of each type of angle, cut out the examples, and tape them to the appropriate sheet. Tell them to use the protractor to measure the angles and write the measurement below each example. Finally, have pairs exchange papers to check their examples.
Next, ask students how they know that Andrew did not do “a 360.” A 360-degree turn is to turn around all the way. Andrew turned around only half way. Draw a circle on the whiteboard, and demonstrate 90, 180, 270, and 360 degrees.
Reading and Language Arts Support
A39
Reading and Language Arts Support
USE WITH
Chapter: Identify and Describe Geometric Figures Multi-Part Lesson 3
Reading GLE 4.1.12.h The student will summarize selected passages.
Literature Activity Revisit with students Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Cindy Bickel. Ask students to summarize the book’s content. Then ask them to explain the role of a caption in a book. It is text that explains or clarifies a photo or illustration. Choose several photos from the book, and have students write their own captions. Next, explain that a quadrilateral is a polygon with four sides. Have students browse the book for examples of quadrilaterals, and then ask which familiar shapes are quadrilaterals. rectangles and squares Then model other quadrilaterals on the whiteboard, such as parallelograms, diamonds, and trapezoids.
Reading GLE 4.1.02.a The student will use parts of text (e.g., title, title page, table of contents, chapter title, glossary, and index).
Math in Our World Revisit with students A Force to Reckon With. Have students turn to the lists on pages 21–23 in the reader. Ask how a list is different from other kinds of text. each line contains one item or idea, they are not always complete sentences, there is a title or header telling what is being listed
Real-World Problem
Solving
Math and Scienc e
A FORCE TO RECKON WITH
Next, tell students that they will be makingg lists of the pages in the reader that have quadrilaterals and triangles. On the whiteboard, write square, rectangle, trapezoid, parallelogram, and triangle. Then work as a class to list the pages on which these shapes can be found, either in the photos or the page layout. Finally, have students choose one shape and write a description of its unique characteristics. Number and Operations
Extending Our Learning Have students get into groups of four, and distribute a large sheet of paper to each group. Explain that they will be making “shape family trees.” Have students begin by listing the names of all shapes they have studied in this chapter. Then, on the whiteboard, model for students the first “branches,” with polygon at the base, and then triangle and quadrilateral above it. Have groups continue by adding parallelogram and trapezoid above quadrilateral and so on. If necessary, this activity can also be done collectively as class.
Reading GLE 4.1.10.a The student will develop and maintain vocabulary specific to content and to current events.
Reading GLE 4.1.01.b The student will use established rules for conversation (e.g., do not interrupt, ask questions, provide appropriate feedback).
Understanding Math Vocabulary Discuss what students know about triangles and quadrilaterals in this chapter. Ask students to draw an oval in the center of a blank piece of paper. Have them write triangle in the center oval. Next, have them add surrounding wedges with words and drawings that refer to triangles. Ask several students to share their work with the class.
Examining Math Distribute an index card to each student. On one side of their cards, have students describe two key learnings about geometric figures that they feel they understand well. On the other side, have them describe two key learnings that they find confusing. Collect the cards, and then randomly choose several of them to read aloud. Discuss the key learnings that students find confusing.
Repeat the activity, using quadrilateral in the center oval. Afterward, ask students how this activity helped them understand the vocabulary. Encourage them to tell whether drawing examples helped them understand these geometry words.
A40
Reading and Language Arts Support
USE WITH
Reading GLE 4.1.06.i The student will build vocabulary by reading from a wide variety of text and literary genres.
Literature Activity Revisit with students Hottest Coldest Highest Deepest by Steve Jenkins. As you read, pause on each spread to have students identify examples of parallel and intersecting lines. Then have students use the map at the end of the book to describe different places using superlatives and comparatives. Mauna Kea is taller than Mount Everest. Angel Falls is the highest waterfall on Earth. and so on
Examining Math Distribute to each student two copies of the _5 -Inch Grid Paper: 10 by 10 manipulative found on page 123 in 8 Hands-On Activity Tools and Resources. Starting on the far left edge, have students label the vertical grid lines along the bottom as 0–10. Then have them label the horizontal grid lines as 0–10, from the bottom line up. Next say, Place a dot at the coordinate 3,0. Place another dot at 5,8. Draw a line from the first dot to the second one. Continue reading the following coordinates, having students connect the dots as they place them: 7,0; 1,5; 9,5; 3,0 Then ask, What do you see on your grid? a star Next, have students pair up. One student will create a shape with dots on his or her grid paper and then read the coordinates to the other student. The other student will mark the coordinates and reveal the shape.
Reading and Language Arts Support
Chapter: Spatial Reasoning Multi-Part Lesson 1
Math in Action Write six math vocabulary words students learned earlier this year on the sides of a blank number cube. Then have students work in groups of four. Students will take turns rolling the cube and defining or giving an example of the word that appears. Continue until all students have had a turn.
Reading GLE 4.1.06.d The student will determine the meaning of unfamiliar words using context clues, dictionaries, glossaries, and other resources.
Reading GLE 4.1.09.g The student will retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
Understanding Math Vocabulary Divide the class into six groups, and then randomly distribute one of any Visual Vocabulary Cards 21, 33, 36, 48, 52, or 59 to each group. Also distribute to each group a large sheet of paper and crayons or colored pencils. Tell students that they will be making posters defining and describing their vocabulary words. The poster should define the term, present a visual example, and include a creative way to remember the meaning of the term. Afterward, have groups display their posters at the front to the class.
Math in Our World Display a map of the city in which students live. Find their school on the map, and then demonstrate to students how to find the coordinates of its location. Ask students for several other landmarks or popular sites, locate them on the map, and find their coordinates. Have students take turns describing streets and intersections on the map using the terms parallel, intersecting, and perpendicular.
Copyright © by The McGraw-Hill All rights reserved.
Companies, Inc.
ISBN: 978-0-02-101741-6 MHID: 0-02-101741-7
Reading and Language Arts Support
A41
Reading and Language Arts Support
USE WITH
Chapter: Spatial Reasoning Multi-Part Lesson 2
Reading GLE 4.1.06.b The student will build vocabulary through frequent read alouds.
Reading GLE 4.1.01.i The student will use different voice levels and speech patterns for small groups, informal discussions, and reports.
Literature Activity Read aloud with students pages 42–43 in Geometry by Lucille Caron and Philip M. St. Jacques, and then define translation, reflection, and rotation. Divide the class into groups of three, and distribute to each student an index card containing a pattern. Each student will create either a translation, reflection, or rotation of the pattern on his or her card. Then have students exchange cards within their group and repeat the exercise. Continue until each student has created a translation, reflection, and rotation for each of his or her group’s patterns.
Math in My Life Lead a discussion about puzzles. Ask students which kinds of puzzles they like complete, which ones they are best at, which ones are the hardest, and so on.
Using Math Vocabulary Distribute to students pieces of paper and pairs of scissors. Have each student trace his or her open hand on the paper and cut out the shape. Then have students trace the paper hands and cut them out in order to have two copies. Write the following words on the whiteboard: translation, rotation, reflection. Ask students to lay their paper hands next to each other, with the thumbs pointing the same direction, to demonstrate translation. Then have them rotate one of the hands 90 degrees to demonstrate rotation. Finally, have them flip one of the hands over so the thumbs point in opposite directions to demonstrate reflection. Reading GLE 4.1.12.b The student will determine the problem of a story, discover its solution, and consider alternate solutions.
Reading Graphic Novels Have students revisit “Tessellation Creation.” Ask them what choice is presented to the students in the story. which kind of tessellation to draw Survey students to learn whether they have had a dilemma like Olivia’s— that is, have they ever been presented with an option without having enough background information to arrive at an informed conclusion? Encourage students to share these experiences. Have the class closely examine the tessellations in frame 3. Have volunteers share which tessellation they think Olivia should choose. Be sure they justify their reasoning.
A42
Reading and Language Arts Support
Then divide the class into groups of four, and tell them that they are going to create their own jigsaw puzzles. (If you prefer, you might provide some early childhood puzzles for students to use for this activity.) Distribute to each group a piece of white poster board, colored pencils, and scissors. Have students draw and color a picture on one side of the board. Then have them flip the board over and use a pencil to divide the board into eight puzzle pieces. If necessary, draw a few interlocking puzzle pieces on the whiteboard as an example. Next, have students cut their boards into eight puzzle pieces. Groups will trade puzzles with each other and then reconstruct the pictures. Finally, have each group choose one puzzle piece and trace its shape on a new piece of paper. They will turn the puzzle piece as needed to trace one translation, one reflection, and one rotation of their pieces. Return each puzzle to its original group, along with the tracings, so groups can check each other’s work.
USE WITH
Reading GLE 4.1.02.b The student will use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Literature Activity Reread with students Shape Up! by David A. Adler. Afterward, have them describe how the author used illustrations to help clarify the information covered in the book. Next, have students trace onto sheets of paper several of the figures from the book and then cut them out. Each student will choose one figure to create a pattern. Have them flip and rotate their figures as they trace them onto paper in order to create the patterns. Finally, explain that congruent figures have the same size and shape, even if they are rotated or flipped in different directions. Have students count the congruent shapes used in their patterns, and ask them to write the number somewhere on the paper. Ask several volunteers to share the patterns they created, and have the class count the congruent figures they contain.
Using Math Vocabulary Display a copy of the Vocabulary graphic organizer from page 28 of Hands-On Activity Tools and Resources. Write congruent in the center rectangle, and then work as a class to fill in the surrounding squares. Then have students search the room for examples of congruent shapes. cabinet doors, tiles on the floor or ceiling, pattern on a shirt, and so on
Examining Math Have students get into pairs, and distribute to each pair a copy of the Square and Triangular Pyramid Patterns manipulative from page 137 of Hands-On Activity Tools and Resources, along with crayons or colored pencils. Tell students that they will be hunting for congruent figures within the two patterns on the page. Have each pair create a list of the unique figures in the two patterns and the number of times each one appears. large square: 1; large equilateral triangle: 4; small square: 8; small trapezoid: 8; small equilateral triangle: 4; small right triangle: 8 Then have students color the patterns, using a different color for each group of congruent figures.
Reading and Language Arts Support
Chapter: Spatial Reasoning Multi-Part Lesson 3
Reading GLE 4.1.09.a The student will use and discern appropriate reference sources in various format (e.g., interviews with family and community; encyclopedias, card/electronic catalogs, almanacs, magazines, and newspapers).
Math in Our World Have students get into pairs, and distribute to each pair magazines containing many photographs or illustrations. Briefly discuss with students the similarities and differences between magazines, newspapers, and Web sites, including the timeliness of the information each presents. Then have pairs browse the magazines for several examples of congruent shapes appearing in photographs or illustrations. Finally, have students write a brief paragraph describing the shapes and what makes them congruent. Ask several pairs to share what they wrote with the class.
Reading and Language Arts Support
A43
Reading and Language Arts Support
USE WITH
Chapter: Spatial Reasoning Multi-Part Lesson 4
Reading GLE 4.1.07.c The student will explore significant words to be encountered in selected/assigned text.
Literature Activity Before reading, introduce the vocabulary words symmetry and line of symmetry. Then read aloud with students Round Trip by Ann Jonas. Tell them that they are going to create their own symmetrical pieces of art. Distribute to each student a piece of paper, colored pencils, and scissors. Have students fold the paper and cut both sides at one time. Next, students will cut in half on the line of symmetry. Collect all the halves, shuffle them together, and then redistribute them randomly. Finally, students must search for the missing halves of the artworks they were given.
Extending Our Learning Have students browse Riding the Mail Trail to find several different kinds of shapes. Work as a class to locate the following: a curved shape with rotational symmetry, a curved shape with one line of symmetry, a polygon with rotational symmetry, a polygon with one line of symmetry, and a polygon with no symmetry. If students are having difficulty finding some of these shapes, direct their attention to the circle graph on page 4 and the map on pages 12 and 13. Afterward, ask students why it is important to understand symmetry and lines of symmetry. Ask students when in their lives they might use this concept. Math and Science
Real-World Problem
Solving
s Math and Socia l Studie
The Lost Point
Author Unknown Point P seemed hopelessly lost So she hailed a nearby Ra y. She said to Mr. R, “I think I’ve gone too far, “Can you help me find my way?” Mr. R explained his position In a voice that was calm an d slow. He said, “When all’s said an d done, “There’s really only one “Direction in which you can go!” “Not true!” cried a nearby Line “You’ve mistaken, I must pro test! “If your path’s true and str aight “There should be no deba te: “TWO directions are always best. Now R and the L began to quarrel: Was it one direction or tw o? Then Triangle appeared, And though it sounds weird She presented yet a third po int of view. “Stop fighting,” said Ms. T, “Calm down and don’t be bitter. “When folks disagree “It’s completely clear to me “There are always three sid es to consider.” “Three sides!” cried an ou traged Rectangle And her blockheaded chums , Cube and Square “This much is right; “To settle such a fight “You need FOUR sides to be fair.”
Math and Social Studies
Number and Operations 8/2/07 2:24:02 PM
d ii
Cover_B9_G04LEV_106234x.ind
A44
Poem
Reading and Language Arts Support
Math in Action Read the poem from page 51 in Hands-On Activity Tools and Resources aloud with students, and then discuss each shape and the basis for its argument. Then have students work in pairs to find the lines of symmetry for each shape mentioned in the poem.
USE WITH
Reading GLE 4.1.06.g The student will continue to use context clues to determine the correct meaning/usage of multiple meaning words.
Reading GLE 4.1.10.c The student will apply comprehension skills and strategies to informational text (e.g., prereading and active comprehension).
Literature Activity Reread with students Hottest Coldest Highest Deepest by Steve Jenkins. As you read, record on the whiteboard each measurement of length as it is mentioned. Afterward, explain that the measurements of length in the book are given in customary units. Explain to students that the customary units of length are inch, foot, yard, and mile. Work as a class to rewrite the list of measurements on the board from shortest to greatest length. Have a volunteer tell identify the greatest length listed in the book and its location. 4,145 miles, which is the length of the Nile River; The Nile River is located in Africa.
Math in Action Have students refer to the time line on pages 2–3 in Solving the Pyramid Puzzle. Ask students what they notice about how the events are listed. Why? Some events happened very close to each other in time. Have volunteers explain why the author might have arranged information in this format. They are listed vertically to save space. Then have students explain how they know which event happened first. The events are dated, but also they arranged with the earliest event at top.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
Reading and Language Arts Support
Chapter: Measure Length Multi-Part Lesson 1
&CMKCRPW
Next, have students get into groups of four and browse the reader for lengths measured in feet. Tell them to list six measurements and then convert them into inches. 1,475 feet × 12 = 17,700 inches, and so on Then have them choose six more measurements in feet to convert into yards, rounded to the nearest whole yard. 217 feet ÷ 3 = 72 yards Finally, have groups exchange papers to check their conversions.
Math in Our World Have students pair up, and distribute a copy of the Two-Column Chart graphic organizer found on page 24 in Hands-On Activity Tools and Resources to each pair. Have pairs count off to assign them numbers. Tell them that even numbered pairs will write Inches above one column and Yards above the other. Have odd numbered pairs write Feet above one column and Miles above the other. Have students list things that would be measured in each unit shown in their chart. Come together again as a class, and compile students’ suggestions into a master list on the whiteboard. If necessary, have students defend their choices.
Understanding Math Vocabulary Distribute to each student a copy of the Four-Step Problem Solving Plan graphic organizer from page 20 of Hands-On Activity Tools and Resources. Tell them that they will be creating and solving their own measurement problem. Ask students to consider an object in the classroom or something at home. Explain that this object will be measured in customary units of length. Have them decide on a realistic length for the item they chose. Next they should complete the problem-solving plan to show how they would convert the measurement to a different customary unit. Afterward, have students exchange papers and follow the problem-solving plans to see if they are reasonable.
Reading and Language Arts Support
A45
Reading and Language Arts Support
USE WITH
Chapter: Measure Length Multi-Part Lesson 2
Reading GLE 4.1.09.a The student will use and discern appropriate reference sources in various format (e.g., interviews with family and community; encyclopedias, card/electronic catalogs, almanacs, magazines, and newspapers).
Literature Activity Reread with students On Beyond a Million by David M. Schwartz. Afterward, have students recall the main ideas of the book. Then ask them where they might look for further information on exponents. Have students discuss places where they might go to do research about this topic. the library, a math teacher, a student who has already studied exponents, an encyclopedia, the Internet Next, review with students metric units of length and their equivalent values. Have them list the values as you discuss them. 1 km = 1000 m; 1 m = 100 cm; and so on Finally, have students rewrite the equivalencies using exponents. 1 km = 103 m = 105 cm = 106 mm; 1 m = 102 cm = 103, and so on
Reading GLE 4.1.06.i The student will build vocabulary by reading from a wide variety of text and literary genres.
Understanding Math Vocabulary Display a copy of the Venn Diagram graphic organizer found on page 27 of Hands-On Activity Tools and Resources. Use it to compare centimeters and meters, including things that might be measured in one unit versus the other, the number of millimeters each contains, the amount of each contained in a kilometer, and so on. Display a second Venn Diagram and repeat the exercise with a different pair of metric units of length. Examining Math Have students pair up, and distribute metric rulers to them. Then have them turn to the map on pages 20–21 in Ancient Giants of the Forest. Draw students’ attention to the key on the bottom left showing the map’s scale. Ask students what this shows. It is a scale showing how the map compares to the real distances between places.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
,C?QSPCKCLR
Next, have students measure how long 200 kilometers is in the key. about 1 cm Then tell pairs to use their rulers to measure from the West Coast to the East Coast, challenging them to find the farthest distance possible, rounded to the nearest whole centimeter. from the central coast of California to the easternmost point of Maine is 20 cm Finally, have students use the key to find the real distance in kilometers. 20 × 200 km = 4000 km
A46
Reading and Language Arts Support
Reading GLE 4.1.01.b The student will use established rules for conversation (e.g., do not interrupt, ask questions, provide appropriate feedback).
Math in Action Display a copy of the _14-Inch Grid manipulative from page 124 of Hands-On Activity Tools and Resources. Tell students that they will be creating a map of the classroom. Begin by having students use a measuring tape to find the length and width of the classroom in feet, yards, and meters. Have students round the lengths to the nearest whole unit. Then lead a discussion about what the map’s scale should be. Ask what length each square in the grid should be equal to. For example, 1 meter or 1 yard per square would most likely make the map too small to be useful, but 1 foot per square might make it too big to fit within the grid paper. 2 feet per square might be a good scale, depending on classroom size. Next, draw the dimension of the classroom in the grid using the scale determined by students. Finally, have the class decide what the major “landmarks” are within the room, measure them, and add them to the map according to scale. Have students suggest other common labels that should be added to the map. directions, labels, titles
USE WITH
Reading GLE 4.1.12.j The student will explore the concept of theme.
Literature Activity Read aloud with students Spaghetti and Meatballs for All by Marilyn Burns and Gordon Silveria. Have students identify the story’s main theme and several examples of how the authors developed the theme. Then ask them why changing the arrangement of the tables allows for more seating space. Next, give each student two 1-inch squares, and have them experiment with different arrangements to see how many people could be seated. Have students draw each configuration and label the lengths of the sides. Remind students that they will need to account for the space needed between chairs and the surrounding tables. Finally, ask them which configurations seated the most people and why. Which configuration seated the least?
Understanding Math Vocabulary Display a copy of the Vocabulary graphic organizer found on page 28 of Hands-On Activity Tools and Resources. Write perimeter in the center rectangle, and then work as a class to fill in the surrounding squares. Have students use rulers to find the perimeters of various objects in the room.
Reading GLE 4.1.12.h The student will summarize selected passages.
Reading Graphic Novels Have students revisit “Conversion Confusion.” Ask them to summarize the story in the graphic novel. Tai and his dad are measuring the perimeter of the yard to find out how much material they need to build a fence. Ask, Why does Rufus have a question mark above his head in the final panel? Tai is showing Rufus the plans for the fence, but a dog cannot read. The question mark shows that Rufus does not understand. Finally, have students give examples of other times when it is important to know the perimeter of something.
Reading GLE 4.1.05.c The student will participate in guided oral reading.
Poem
Out and About
by Chandler Tyrrell I walked 4 blocks north; the n I had to stop. With her hand held high, the re stood a cop. So I took a right turn and continued on, But 2 blocks later came to a pond. I went left this time to get around the park, But 3 blocks later I saw it wa s getting dark. So I made a right turn and started heading home, When 3 blocks later I hit a construction zone. It looked clear to my right, so I went that way, And for at least 4 blocks, I wasn’t delayed, But then once more, as yo u probably guessed, I hit a detour and had to tur n left. I walked up 1 block, turne d right, and went 3. Another right, 6 blocks, an d I’m home—finally!
Reading and Language Arts Support
Chapter: Measure Length Multi-Part Lesson 3
Math in Our World Read the poem aloud with students. Then have them get into groups of four, and distribute to each group a copy of the _58-Inch Grid Paper, 10 by 10 manipulative found on page 123 in Hands-On Activity Tools and Resources. Have students reread the poem carefully and trace the narrator’s route on the grid paper, starting at the bottom left corner of the grid and counting each square as one block. Ask students how many blocks total the narrator walked. 26 Then have students determine what the perimeter of the area the narrator walked around is, if each city block is 311 feet long. 311 × 26 = 8,086 feet Finally, have students write simple instructions explaining how to get from the classroom to another part of the school building. Have them include landmarks, cardinal directions, and other necessary information, as well as a simple map.
Reading and Language Arts Support
A47
Reading and Language Arts Support
USE WITH
Chapter: Measure Length Multi-Part Lesson 4
Reading GLE 4.1.08.b.4 The student will check for understanding after reading by discussing similarities and differences in events and characters using evidence cited in two or three text(s).
Literature Activity Read aloud Bigger, Better, Best by Stuart J. Murphy. Then lead a discussion about the book, focusing on the concept of area. What other books have students read that were about area? Have students work in pairs, and then distribute to each pair a variety of polygon shapes and grid paper and then count the squares to determine area. Finally, have students draw polygons for a given area. Afterward, discuss with students when it might be important to know the area of something.
Reading GLE 4.1.02.c The student will recognize different forms of text (e.g., poems, plays, drama, letters, ads, biographies).
Reflective Writing Refer to pages 7–16 in Solving the Pyramid Puzzle. Divide the class into groups of four, and have them compare the Great Pyramid of Giza with the Great Pyramid of Cholula. Ask each group to find the differences in heights, lengths of sides, and square footage of the bases.
MJTGLE
1C?J 6MPJB/PM@JCK2
,?RF? LB2AG CLAC
Come together as a class to discuss which pyramid was bigger in each category and by how much. 481 - 217 = Giza is 264 feet et taller; 1,476 - 756 = Cholula is 720 feet longer; 2,119,936 571,536 = Cholula is 1,548,400 square feet bigger Finally, use rounding to estimate the number of Giza-sized pyramids that could sit in the same area as a Cholula-sized pyramid. 1,500 × 1,500 = 2,250,000; 750 × 750 = 562,500; 560,000 × 4 = 2,240,000 &CMKCRPW
Have students discuss the significance of these pyramids, considering they were built without access to modern technology. Ask students to write a short persuasive paper in which they defend their thinking. Explain that they must choose one of the following persuasive techniques to use in the essay: word choice, repetition, or emotional appeal. Reading GLE 4.1.09.f The student will skim materials to develop a general overview of content or to locate specific information.
Math in Our World Refer to a newspaper’s Real Estate listings to students, as well as sheets of grid paper. Have them search for and circle any references to room dimensions, such as 20 × 15 living room. Use the whiteboard to list the dimension of several rooms, and have students draw the rooms on grid paper. Then work as a class to calculate the square footage for each room. Lead a discussion comparing the rooms by size and shape, especially rooms that are similar in square footage but different in shape. Then estimate the size of the classroom, and add it to the list. Ask how the classroom compares to the rooms listed in the newspaper. As a class, discuss what possible configurations of furniture could be created in your classroom space. Explain that finding area can be critical in planning space and how to fill it with furniture.
A48
Reading and Language Arts Support
Extending Our Learning Tell students that today they are working for a billboard company. Each billboard the company owns is 14 feet tall by 48 feet long and costs $1 per square foot each month to rent. Have students write a description of how they would calculate the cost of renting 1 billboard for 6 months. 14 feet × 48 feet × $1 × 6 = $4,032 Then have them trade papers to check for correct verb tenses, noun/pronoun agreement, and conjunctions.
USE WITH
Reading GLE 4.1.08.b.10 The student will check for understanding after reading by identifying and interpreting figurative language (e.g., idioms, similes, metaphors, personification).
Literature Activity Read aloud with students Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells. Afterward, discuss how the author uses similes and metaphors in his comparison. Have students spend a few minutes writing their own similes and metaphors comparing two objects of vastly different sizes. (Encourage them to use objects they might be studying in another subject area.) Return to the pages of the book describing whales in jars. Work with students to find the total capacities on each page, if each jar holds 1 pint. The first page has 1 jar, which is 1 pint. The second page has 2 jars, or 2 pints, which is equal to 1 quart. The third page has 20 jars, or 20 pints, which is equal to 10 quarts or 2 gallons and 2 quarts. Challenge students to repeat the exercise with the crate of 100 oranges if 1 orange equals 1 cup. 100 cups = 50 pints = 25 quarts = 6 gallons and 1 quart
Reading GLE 4.1.01.f The student will summarize orally what has been learned or accomplished after completing an activity or assignment.
Understanding Math Vocabulary Have students get into groups of four and create vocabulary books using the instructions found on the Foldables page on page 18 of Hands-On Activity Tools and Resources. Have them cut the front page into five separate flaps, and write one of following vocabulary words on each flap: ounce, cup, pint, quart, gallon. Have students create conversion equations for each unit of capacity and write them below the corresponding flap. For example: Below the gallon flap students would write gallons × 4 = quarts; gallons × 8 = pints; gallons × 16 = cups; gallons × 128 = ounces
Reading GLE 4.1.12.d The student will identify and describe the main and minor characters, considering the importance of their actions, motives, and appearances.
Reading Graphic Novels Have students revisit “Ice Cream Conversion.” Tell them to describe how Ethan feels in the third panel and how they know. The expression on his face is a frown, so I know he is feeling sad. Then ask why Ethan might be feeling sad if he is thinking about a cake. He thinks his mother has forgotten to get a cake for his birthday party because they are walking past the cake displays without stopping. Ask students to explain why, in the final panel, Ethan says, “Well I guess we’ll need a lot of pints then!” A pint is a small unit of capacity. 1 pint of ice cream would not be enough for a birthday party with several guests.
Reading and Language Arts Support
Chapter: Measure Capacity, Weight, and Mass Multi-Part Lesson 1
On the whiteboard, write the following units of capacity: cup, pint, quart, and gallon. Then have students brainstorm grocery items that they think are sold in each capacity.
Extending Our Learning Distribute to each student a copy of the Two-Column Chart found on page 24 of Hands-On Activity Tools and Resources. Ask them to list key learnings about customary units of capacity in the left-hand column and key learnings about metric units of capacity in the right-hand column. Have students share what they wrote, and compile a master list on the whiteboard. Review any key learnings that students did not include.
Afterward, have each group explain how they found one of their conversion equations.
Reading and Language Arts Support
A49
Reading and Language Arts Support
USE WITH
Chapter: Measure Capacity, Weight, and Mass Multi-Part Lesson 2
Reading GLE 4.1.08.b.1 The student will check for understanding after reading by indicating sequence of events in fiction and nonfiction selections.
Reading GLE 4.1.01.a The student will listen attentively by facing the speaker, asking questions, and paraphrasing what is said.
Literature Activity Revisit Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Cindy Bickel. Browse the book with students, and create a list of four or five main ideas from the book in the order that they are presented. Then, work as a class to come up with creative chapter titles for each main idea.
Financial Literacy Have students imagine that they have gone to the store to buy mixed nuts for a party. Explain that when they encounter the shelves filled with cans of nuts, they notice the cans are available in different sizes. Tell students that a 12-ounce can costs $2.64 and a 2-pound can costs $5.76. Ask them to explain which one is the better deal.
Next, have students turn to the graph on page 12 in the book. On the whiteboard, rewrite the chart so that it shows the weight in ounces instead of pounds (16, 32, 48, and so on) Survey students to learn which graph they think is easier to use—the one showing pounds or the one showing ounces—and have them defend their choice. Example: The graph showing pounds is easier to use because the numbers are smaller, and there is not as big a difference between them.
Next, have students spend several minutes writing a description of how they would find the price per ounce of both containers in order to tell which size is the best deal. 264 ÷ 12 = 22; 576 ÷ 32 = 18; The 2-pound can costs 4¢ less per ounce than the 12-ounce can. Then discuss why someone might still buy the smaller, more expensive can. The bigger can might be too many nuts for someone, and they would just go to waste.
Then have students turn to the graph on page 24. On the 5 __ 10 __ 15 4 __ whiteboard, rewrite this graph in pounds (__ 16 , 16 , 16 , 1 and 16 9 pounds, 1 and __ 16 pounds) Have students discuss which graph is easier to use in this instance—the one showing pounds or the one showing ounces—and have them defend their choice. The graph showing ounces is easier to use because it shows whole numbers, not fractions. It is easier to compare whole numbers than fractions. Finally, lead a discussion about choosing the appropriate unit of measurement.
Reading GLE 4.1.01.c The student will understand, follow, and give oral multi-step directions which may include illustrations.
Understanding Math Vocabulary Display a copy of the Venn Diagram graphic organizer found on page 27 of Hands-On Activity Tools and Resources. Write weight above the left oval and mass above the right oval. Work as a class to compare the two vocabulary words. Afterward, have students spend several minutes writing a descriptive paragraph about visiting a planet with gravity different from Earth’s. They should decide whether the planet has stronger or weaker gravity than Earth, and then include vivid descriptions and sensory details about how it feels to move about the new planet.
A50
Reading and Language Arts Support
Math in Action Have students imagine that they will be tutoring younger math learners. Write 3.25 kilograms on the whiteboard. Ask students to write what they would tell a third grader about how to convert this mass from kilograms to grams.
USE WITH
Reading GLE 4.1.01.e The student will participate in creative responses to text (e.g., choral reading, discussion, dramatization, and oral presentations).
Literature Activity Before reading, explain to students that elapsed time is the amount of time that passes from the beginning to the end of an activity or event. Then reread How Much Is a Million? by David M. Schwartz, emphasizing the amounts of elapsed time mentioned in the book. Afterward, have students spend several minutes discussing the longest events or activities they have experienced. Create a list on the board of students’ suggestions and the amount of time they think elapsed. Then work as a class to put the events in order from the most elapsed time to the least.
Math in Action Have students line up as two teams. Hand two Analog Clockfaces from page 106 in Hands-On Activity Tools and Resources. to the student at the front of one line. He or she will set the clocks to show 2 different times. The student at the front of the other line will calculate the difference between the times. If he or she is correct, the team scores a point, and the student goes to the back of the line. The student who had set the clocks now gets a turn calculating the elapsed time set by the next student in line on the other team. Continue until all students have had a turn finding elapsed times, or until a predetermined point total is reached.
Reading GLE 4.1.06.a The student will build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Reading GLE 4.1.01.f The student will summarize orally what has been learned or accomplished after completing an activity or assignment.
Math in Action Distribute to students copies of the Analog Clockface manipulative found on A ORCE TO page 106 in Hands-On Activity Tools ECKON ITH and Resources. Then have them turn to page 15 in A Force to Reckon With. Ask them to what time they would set a clock to show the time, rounded to the nearest 5 minutes, of the San Francisco earthquake. 5:10 Then ask at what time an aftershock occurred if it occurred 2 hours and 35 minutes later. 7:45 Explainn that yet another aftershock occurred at 12:35. Have students determine how much time had elapsed since the first quake. 7 hours and 25 minutes Ask them how much time had elapsed between the first and second aftershocks. 4 hours and 50 minutes Ask students how they arrived at their responses.
Examining Math Divide the class into groups of four. Ask each group to discuss their favorite lesson from the past year, as well as the lesson with which they had the most trouble. One student from each group will write down the main points of the discussion and share them with the class. Ask students which math concept they are ready to learn more about and why.
Real-World Problem
R
F
Solving
Math and Scienc e
W
Reading and Language Arts Support
Chapter: Measure Capacity, Weight, and Mass Multi-Part Lesson 3
Number and Operations
Discuss various strategies for telling elapsed time. use a stopwatch, use an analog clockface, count backward Have students explain when each method would be appropriate to use, and why. Using Math Vocabulary On the whiteboard, create a 3-square by 3-square grid. In each space, write a different vocabulary word students have learned in this chapter. Divide the class into two teams, and assign one team to be X’s and the other to be O’s. Have teams take turns defining vocabulary words by either using them in complete sentences or demonstrating their meanings on the whiteboard. When a team defines a word correctly, an X or an O is placed on that space. The rules of tic-tac-toe are used to determine the winning team.
Reading and Language Arts Support
A51
Reading and Language Arts Support
Tennessee Reading Standards, Grade 4 Benchmark Code
Benchmark
Chapter(s)/Lesson(s)
Page Number(s)
1.01 Continue to develop oral language and listening skills. 4.1.01.a
Listen attentively by facing the speaker, asking questions, and paraphrasing what is said.
Apply Multiplication and Division Facts, 1 Multiply by One-Digit Numbers, 2 Organize and Display Data, 4 Measure Capacity, Weight, and Mass, 2
A9 A18 A31 A50
4.1.01.b
Use established rules for conversation (e.g., do not interrupt, ask questions, provide appropriate feedback).
Apply Multiplication and Division Facts, 4 Multiply by One-Digit Numbers, 4 Identify and Describe Geometric Figures, 3 Measure Length, 2
A12 A20 A40 A46
4.1.01.c
Understand, follow, and give oral multi-step directions which may include illustrations.
Apply Multiplication and Division Facts, 2 Multiply Multi-Digit Numbers, 3 Add and Subtract Fractions and Decimals, 1 Measure Capacity, Weight, and Mass, 2
A10 A23 A35 A50
4.1.01.d
Formulate and respond to questions from teachers and other group members.
Algebraic Patterns, 3 Understand Division, 2 Decimals and Fractions, 3 Identify and Describe Geometric Figures, 1
A15 A26 A34 A38
4.1.01.e
Participate in creative responses to text (e.g., choral reading, discussion, dramatization, and oral presentations).
Measure Capacity, Weight, and Mass, 3
A51
4.1.01.f
Summarize orally what has been learned or accomplished after completing an activity or assignment.
Multiply by One-Digit Numbers, 1 Multiply Multi-Digit Numbers, 1 Decimals and Fractions, 2 Measure Capacity, Weight, and Mass, 1 Measure Capacity, Weight, and Mass, 3
A17 A21 A33 A49 A51
4.1.01.g
Create and deliver an oral presentation on an assigned topic (e.g., book reports, demonstrations, science projects).
4.1.01.h
Present and/or perform original or published literary work with a group and/ or individually.
4.1.01.i
Use different voice levels and speech patterns for small groups, informal discussions, and reports.
Understand Division, 3 Spatial Reasoning, 2
A27 A42
4.1.01.j
Interpret and use a variety of non-verbal communication techniques (e.g., gestures, facial expression, posture).
4.1.01.k
Participate in recitations of assigned/self-selected passages.
1.02 Demonstrate knowledge of concepts of print.
A52
4.1.02.a
Use parts of text (e.g., title, title page, table of contents, chapter title, glossary, and index).
Organize and Display Data, 4 Identify and Describe Geometric Figures, 3 Spatial Reasoning, 3
A31 A40 A43
4.1.02.b
Use common text features to enhance understanding (e.g., headings, key words, graphics, captions, side bars).
Place Value, Addition, and Subtraction, 3 Multiply Multi-Digit Numbers, 3 Decimals and Fractions, 2 Add and Subtract Fractions and Decimals, 2
A8 A23 A33 A36
4.1.02.c
Recognize different forms of text (e.g., poems, plays, drama, letters, ads, biographies).
Apply Multiplication and Division Facts, 2 Understand Division, 3 Measure Length, 4
A10 A27 A48
Reading and Language Arts Correlations
1.03
Benchmark
Chapter(s)/Lesson(s)
Page Number(s)
Expand reading skills through phonemic awareness.
4.1.03.a
Develop awareness of the sounds of language through repeated exposure to a variety of auditory experiences (e.g., poetry, music lyrics, books on tape, sound effects, read alouds).
Place Value, Addition, and Subtraction, 1 Add and Subtract Fractions and Decimals, 2
A6 A36
4.1.03.b
Understand rhyming patterns in printed materials.
Multiply Multi-Digit Numbers, 4
A24
4.1.03.c
Respond and analyze the effects of the sounds of language (e.g., alliteration, onomatopoeia, rhythm, beat).
Multiply Multi-Digit Numbers, 1
A21
1.04
Use decoding strategies to read unfamiliar words.
4.1.04.a
Continue to use knowledge of letter-sound correspondence and structural analysis to decode words.
4.1.04.b
Expand understanding and use of root words, prefixes, and suffixes to decode words.
4.1.04.c
Use syllabication to decode words.
4.1.04.d
Understand, recognize, and use spelling patterns and word families to decode words.
4.1.04.e
Decode unknown grade level words by utilizing learned strategies (e.g., reading ahead, drawing upon prior knowledge) to verify word meanings within the context.
1.05
Read to develop fluency, expression, accuracy, and confidence.
4.1.05.a
Increase confidence and poise in reading aloud (e.g., paired reading, shared reading, choral reading, recorded reading, echo reading).
Organize and Display Data, 2
A29
4.1.05.b
Read with fluency and confidence from a variety of texts (e.g., poetry, drama, current events, novels).
Decimals and Fractions, 2
A33
4.1.05.c
Participate in guided oral reading.
Multiply by One-Digit Numbers, 3 Measure Length, 3
A19 A47
4.1.05.d
Read orally using appropriate pronunciation, expression, and rate.
4.1.05.e
Adjust speed based on the purpose for reading and reading level.
4.1.05.f
Read independently daily.
1.06
Reading and Language Arts Support
Benchmark Code
Expand reading vocabulary.
4.1.06.a
Build vocabulary by listening to literature, participating in discussions, and reading self-selected and assigned texts.
Place Value, Addition, and Subtraction, 1 Apply Multiplication and Division Facts, 3 Organize and Display Data, 3 Add and Subtract Fractions and Decimals, 3 Measure Capacity, Weight, and Mass, 3
A6 A11 A30 A37 A51
4.1.06.b
Build vocabulary through frequent read alouds.
Decimals and Fractions, 1 Spatial Reasoning, 2
A32 A42
4.1.06.c
Infer word meanings using roots, prefixes, and suffixes.
Decimals and Fractions, 1
A32
4.1.06.d
Determine the meaning of unfamiliar words using context clues, dictionaries, glossaries, and other resources.
Algebraic Patterns, 4 Spatial Reasoning, 1
A16 A41
4.1.06.e
Use appropriate synonyms, antonyms, and homonyms.
4.1.06.f
Foster word consciousness (e.g., word play, word walls and word sorts).
Place Value, Addition, and Subtraction, 1 Multiply Multi-Digit Numbers, 2 Identify and Describe Geometric Figures, 2
A6 A22 A39
4.1.06.g
Continue to use context clues to determine the correct meaning/usage of multiple meaning words.
Algebraic Patterns, 2 Multiply by One-Digit Numbers, 1 Organize and Display Data, 1 Measure Length, 1
A14 A17 A28 A45
Reading and Language Arts Correlations
A53
Reading and Language Arts Support
Benchmark Code 4.1.06.h
Select the correct word to complete an analogy.
4.1.06.i
Build vocabulary by reading from a wide variety of text and literary genres.
1.07
Chapter(s)/Lesson(s)
Page Number(s)
Multiply by One-Digit Numbers, 2 Identify and Describe Geometric Figures, 2 Spatial Reasoning, 1 Measure Length, 2
A18 A39 A41 A46
Employ pre-reading strategies to facilitate comprehension.
4.1.07.a
Set a purpose for reading (e.g., to understand, to enjoy, to solve problems, to locate specific information/facts).
Place Value, Addition, and Subtraction, 2 Algebraic Patterns, 2 Multiply Multi-Digit Numbers, 4 Add and Subtract Fractions and Decimals, 3
A7 A14 A24 A37
4.1.07.b
Organize prior knowledge using a variety of strategies (e.g., webbing, mapping, brainstorming, listing).
Apply Multiplication and Division Facts, 1
A9
4.1.07.c
Explore significant words to be encountered in selected/assigned text.
Spatial Reasoning, 4
A44
4.1.07.d
Preview text using text features (e.g., illustrations/pictures, graphs, diagrams, and headings).
4.1.07.e
Make predictions about text using text features (e.g., title, author, illustrations, and text format).
4.1.07.f
Relate text to prior personal and historical experiences, current events, as well as previously read print and non-print media.
Algebraic Patterns, 4 Multiply Multi-Digit Numbers, 4
A16 A24
Apply Multiplication and Division Facts, 3 Multiply Multi-Digit Numbers, 3 Organize and Display Data, 4
A11 A23 A31
Apply Multiplication and Division Facts, 1 Multiply Multi-Digit Numbers, 2
A9 A22
1.08.a
Use active comprehension strategies to derive meaning while reading.
4.1.08.a.1
Derive meaning while reading by formulating clarifying questions.
4.1.08.a.2
Derive meaning while reading by predicting outcomes based upon prior knowledge and adjusting appropriately.
4.1.08.a.3
Derive meaning while reading by using metacognitive and self-monitoring reading strategies to improve comprehension (e.g., rereading, identifying miscues, reading ahead, asking for help, and drawing on earlier reading).
4.1.08.a.4
Derive meaning while reading by creating mental images.
4.1.08.a.5
Derive meaning while reading by expressing reactions and personal opinions to a selection.
4.1.08.a.6
Derive meaning while reading by making inferences.
4.1.08.a.7
Derive meaning while reading by verifying or modifying the pre-reading purpose.
4.1.08.a.8
Derive meaning while reading by drawing conclusions based on evidence gained.
1.08.b
A54
Benchmark
Use active comprehension strategies to check for understanding after reading.
4.1.08.b.1
Check for understanding after reading by indicating sequence of events in fiction and nonfiction selections.
Understand Division, 1 Measure Capacity, Weight, and Mass, 2
A25 A50
4.1.08.b.2
Check for understanding after reading by selecting main idea and supporting details from text.
Multiply by One-Digit Numbers, 1 Multiply Multi-Digit Numbers, 1 Identify and Describe Geometric Figures, 1
A17 A21 A38
4.1.08.b.3
Check for understanding after reading by identifying the author’s purpose (e.g., to entertain, to inform, to explain).
Multiply by One-Digit Numbers, 4 Understand Division, 3
A20 A27
4.1.08.b.4
Check for understanding after reading by discussing similarities and differences in events and characters using evidence cited in two or three text(s).
Add and Subtract Fractions and Decimals, 1 Measure Length, 4
A35 A48
4.1.08.b.5
Check for understanding after reading by selecting information to meet a specific purpose.
4.1.08.b.6
Check for understanding after reading by stating reasonable generalizations in reference to two pieces of text on a similar topic.
Organize and Display Data, 3
A30
Reading and Language Arts Correlations
Benchmark Code
Benchmark
Chapter(s)/Lesson(s)
Page Number(s)
4.1.08.b.7
Check for understanding after reading by locating information to support opinions, predictions, and conclusions.
Multiply by One-Digit Numbers, 3 Understand Division, 2 Decimals and Fractions, 3
A19 A26 A34
4.1.08.b.8
Check for understanding after reading by identifying cause and effect relationships.
Algebraic Patterns, 1
A13
4.1.08.b.9
Check for understanding after reading by distinguishing between fact/opinion and reality/fantasy.
Organize and Display Data, 2
A29
4.1.08.b.10
Check for understanding after reading by identifying and interpreting figurative language (e.g., idioms, similes, metaphors, personification).
Measure Capacity, Weight, and Mass, 1
A49
4.1.08.b.11
Check for understanding after reading by recognizing the theme of a single passage.
4.1.08.b.12
Check for understanding after reading by reflecting upon comprehension strategies utilized to make meaning from text.
Algebraic Patterns, 2
A14
Add and Subtract Fractions and Decimals, 1 Add and Subtract Fractions and Decimals, 3 Spatial Reasoning, 3 Measure Length, 2
A35 A37 A43 A46
Algebraic Patterns, 3 Organize and Display Data, 1
A15 A28
1.09
Develop appropriate information skills and study skills to facilitate learning.
4.1.09.a
Use and discern appropriate reference sources in various format (e.g., interviews with family and community; encyclopedias, card/electronic catalogs, almanacs, magazines, and newspapers).
4.1.09.b
Use media (e.g., photographs, films, videos, the arts, on-line catalogs, nonfiction books, encyclopedias, CD-ROM references, internet) to view, read, and represent information.
4.1.09.c
Use current technology as a research and communication tool for personal interest, research, and clarification.
4.1.09.d
Understand a variety of informational texts, which include primary sources (e.g., autobiographical sketches, letters, and diaries; and internet sites).
4.1.09.e
Utilize the dictionary, glossary, thesaurus, and other word-referenced materials.
4.1.09.f
Skim materials to develop a general overview of content or to locate specific information.
Algebraic Patterns, 4 Multiply by One-Digit Numbers, 3 Multiply Multi-Digit Numbers, 3 Decimals and Fractions, 1 Measure Length, 4
A16 A19 A23 A32 A48
4.1.09.g
Retrieve, organize, and represent information (e.g., charts, maps, graphs, forms, tables, timelines).
Place Value, Addition, and Subtraction, 2 Apply Multiplication and Division Facts, 2 Multiply by One-Digit Numbers, 4 Organize and Display Data, 3 Spatial Reasoning, 1
A7 A10 A20 A30 A41
4.1.09.h
Develop an awareness of the effects of media (e.g., television, print materials, radio, internet, magazines) on daily life.
Apply Multiplication and Division Facts, 1 Add and Subtract Fractions and Decimals, 2
A9 A36
4.1.09.i
Gather and record information on a research topic using two different sources.
Multiply Multi-Digit Numbers, 2
A22
1.10
Develop skills to facilitate reading to learn in a variety of content areas.
4.1.10.a
Develop and maintain vocabulary specific to content and to current events.
Place Value, Addition, and Subtraction, 3 Algebraic Patterns, 1 Multiply by One-Digit Numbers, 2 Understand Division, 1 Identify and Describe Geometric Figures, 3
A8 A13 A18 A25 A40
4.1.10.b
Locate information using available text features (e.g., maps, charts, graphics, appendices, and tables of contents).
Place Value, Addition, and Subtraction, 1 Algebraic Patterns, 1 Multiply by One-Digit Numbers, 1 Multiply Multi-Digit Numbers, 1
A6 A13 A17 A21
4.1.10.c
Apply comprehension skills and strategies to informational text (e.g., prereading and active comprehension).
Identify and Describe Geometric Figures, 1 Measure Length, 1
A38 A45
Reading and Language Arts Correlations
A55
Benchmark Code 4.1.10.d
Use self-correction strategies while reading (e.g., pausing, rereading, consulting other sources, asking for help).
4.1.10.e
Determine the reliability of sources on a given topic (e.g., editorials, newspapers, magazines, biographies).
1.11
Chapter(s)/Lesson(s)
Page Number(s)
Read independently for a variety of purposes.
4.1.11.a
Read for literary experience.
4.1.11.b
Read to gain information.
4.1.11.c
Read to perform a task.
4.1.11.d
Read for enjoyment.
4.1.11.e
Read to expand vocabulary.
4.1.11.f
Read to build fluency.
1.12
Experience various literary and media genres.
4.1.12.a
Read, view, and recognize various literary (e.g., poetry, novels, historical fiction, nonfiction) and media (e.g. photographs, the arts, films, video) genres.
Place Value, Addition, and Subtraction, 3 Apply Multiplication and Division Facts, 4 Multiply by One-Digit Numbers, 4 Identify and Describe Geometric Figures, 2
A8 A12 A20 A39
4.1.12.b
Determine the problem of a story, discover its solution, and consider alternate solutions.
Apply Multiplication and Division Facts, 4 Algebraic Patterns, 3 Spatial Reasoning, 2
A12 A15 A42
4.1.12.c
Sequence the events of a selection from beginning to end, determining how the incidents are connected and lead to a solution/conclusion.
4.1.12.d
Identify and describe the main and minor characters, considering the importance of their actions, motives, and appearances.
Add and Subtract Fractions and Decimals, 3 Measure Capacity, Weight, and Mass, 1
A37 A49
4.1.12.e
Make inferences about print and non-print text.
4.1.12.f
Compare and contrast events and characters using evidence cited from print and non-print text(s).
Organize and Display Data, 1
A28
4.1.12.g
Compare and contrast different versions/representations of the same stories/ events that reflect different cultures.
4.1.12.h
Summarize selected passages.
Identify and Describe Geometric Figures, 3 Measure Length, 3
A40 A47
4.1.12.i
Distinguish between first and third person points of view.
4.1.12.j
Explore the concept of theme.
Algebraic Patterns, 4 Decimals and Fractions, 1 Measure Length, 3
A16 A32 A47
4.1.12.k
Recognize and understand basic literary devices (e.g., imagery, simile, metaphor, personification).
Understand Division, 1
A25
Multiply by One-Digit Numbers, 2 Understand Division, 2
A18 A26
1.13
A56
Benchmark
Develop and sustain a motivation to read.
4.1.13.a
Visit libraries/media centers and book fairs to explore books.
4.1.13.b
Use personal criteria to select reading material (e.g., personal interest, knowledge of authors, text difficulty, text, genres, recommendation of others).
4.1.13.c
Read daily from self-selected materials.
4.1.13.d
Relate literary experiences (e.g., book discussions, literacy circles, writing, oral presentations, artistic expressions).
4.1.13.e
Begin a personal reading list or reading log/journal to reflect reading progress and accomplishments.
4.1.13.f
Experience and develop an awareness of literature that reflects a diverse society.
4.1.13.g
Choose to read as a leisure activity.
Reading and Language Arts Correlations
EP0–EP1
EP00_EP01_EM_SH_103030.indd 682
Quick Reference. . . Inside Back Cover
Index . . . . . . . . . . . . . . . . . . . . . . . . . R27
English-Spanish Glossary . . . . . . . . R3
Photo Credits . . . . . . . . . . . . . . . . . . . R1
Reference
Extra Practice . . . . . . . . . . . . EP2
3/12/10EP00_EP01_EM_SH_103030.indd 1:41 PM EP1
What If I Forget a Multiplication/ Division Fact or Formula?
What If I Need to Find Something Quickly?
What If I Forget a Vocabulary Word?
What If I Need More Practice?
Inside the back cover of your math book is a Quick Reference of a multiplication table and formulas that are used in the book.
The Index alphabetically lists the subjects covered throughout the entire textbook and the pages on which each subject can be found.
The English-Spanish Glossary provides a list of important, or difficult, words used throughout the textbook. It provides a definition in English and Spanish.
You, or your teacher, may decide that working through some additional exercises would be helpful. The Extra Practice section provides these exercises for each lesson so you have ample opportunity to practice new skills.
3/12/10 1:42 PM
The Student Handbook is the additional skill and reference material found at the end of this textbook. The Student Handbook can help answer these questions.
Extra Practice
Student Handbook
EP2–EP3
Extra Practice
B
thousands; 1,000
11. 509,909
10. 27,621
8. 9,604,138 9,064,946 >
7. 7,863,403 7,863,304 >
846,465; 361,259; 361,084; 61,999
6. 42,204; ten thousands 40,000 8. 83,756; tens 83,760
5. 36,801; hundreds 36,800
7. 70,988; thousands 71,000
Extra Practice
EP02_EP40_EM_EP_103030.indd EP2
EP2
11. 849,604; thousands 850,000
12. 934,567; hundred thousands 900,000
10. 455,877; tens 455,880
4. 20,368; thousands 20,000
3. 4,965; thousands 5,000
9. 437,947; ten thousands 440,000
2. 949; hundreds 900
PAGES 28–31
1. 451; hundreds 500
Round each number to the given place-value position.
PART D
16. 361,259; 361,084; 61,999; 846,465
286,344; 275,391; 258,983
15. 275,391; 286,344; 258,983
94,846; 84,694; 49,846; 46,948
14. 94,846; 49,846; 84,694; 46,948
52,951; 52,865; 51,954; 49,384
12. 52,951; 49,384; 51,954; 52,865
PAGES 24–27
85,625; 85,611; 85,610; 85,185
13. 85,610; 85,185; 85,611; 85,625
19,400; 19,004; 10,440; 9,400
11. 19,400; 9,400; 19,004; 10,440
1,444; 1,443; 1,434; 1,344
9. 1,443; 1,434; 1,444; 1,344
6,600; 6,519; 4,872; 3,941
6. 758,438 758,438 =
5. 325,614 235,614 >
10. 6,519; 6,600; 3,941; 4,872
4. 89,629 89,635 <
3. 34,925 34,952 <
12. 250,345
9. 81,306
hundred thousands; 400,000
6. 427,055
2. 3,780 3,080 >
Order the numbers from greatest to least.
PAGES 19–23
hundreds; 0
3. 3,000
1. 9,719 9,791 <
Compare. Use >, <, or =.
PART C
7–12. See Extra Practice Answer Appendix.
8. 14,523
7. 8,954
Write each number in expanded form and word form.
5. 351,089
ones; 3
4. 67,023
ten thousands; 80,000
2. 80,761
tens; 20
1. 4,322
Write the place of the underlined digit. Then write its value.
PART A
Multi-Part Lesson 1-1 Place Value
Extra Practice
3/12/10 1:43 PM
PAGES 36–39
EP02_EP40_EM_EP_103030.indd EP3
estimate; about 100 comic books
3. Kim has 23 comic books. Adrienne has 41 comic books and Michelle has 37. About how many comic books do the girls have in all?
1. The fourth grade students are going to watch a ballet. There are 4 classes of 22 students. How many seats will the students fill? exact; 88 seats
3/12/10 1:45 PM
Extra Practice EP3
4. Haley spends 2 hours each night working on a puzzle. It takes her two weeks to complete it. How many hours does it take Haley to complete the puzzle? exact; 28 hours
estimate; about $20
2. Torrence bought a shirt for $12 and a pair of pants for $20. He paid with a $50-bill. About how much change should he get back?
PAGES 40–41
50,000 + 30,000 = 80,000
46,000 + 45,000 = 91,000
10. 54,879 + 26,348; ten thousands
8. 46,321 + 44,961; thousands
Tell whether an estimate or exact answer is needed. Then solve.
PART C
$37,000 + $6,000 = $43,000
80,000 + 10,000 = 90,000
9. $36,518 + $6,499; thousands
7. 83,592 + 14,648; ten thousands
$5,700 + $2,200 = $7,900
6. $5,655 + $2,163; hundreds
5. 41,623 + 3,692; thousands
42,000 + 4,000 = 46,000
4. 2,467 + 3,184; hundreds
2,500 + 3,200 = 5,700
2. 472 + 56; tens 470 + 60 = 530
541; Subtraction Rule
44; Commutative Property (+)
8. 863 + 44 = + 863
9; Commutative Property (+)
197; Identity Property 6. 72 + 9 = + 72
3. 495 + 321; hundreds
500 + 300 = 800
1. $87 + $33; tens $90 + $30 = $120
PAGES 32–35
37; Commutative Property (+)
4. 197 + 0 =
2. 14 + 37 = + 14
10. 541 - = 0
Estimate. Round to the indicated place value.
PART B
17; Associative Property (+)
9. 21 + ( + 9) = (21 + 17) + 9
8; Associative Property (+)
7. (14 + 3) + 8 = 14 + (3 + )
0; Subtraction Rule
5. 233 - = 233
8; Associative Property (+)
3. 7 + (4 + 8) = (7 + 4) +
20; Subtraction Rule
1. 20 - = 0
Copy and complete each number sentence. Identify the property or rule used.
PART A
Multi-Part Lesson 1-2 Addition and Subtraction
Extra Practice
Extra Practice
Extra Practice
EP4–EP5
$691,414
$1,766 $ 819 ________
$24,509 $ 7,625 _________
4.
7.
8.
5.
2.
21,565
Extra Practice
EP02_EP40_EM_EP_103030.indd EP4
Extra Practice
4. Casey has $6. He buys a sandwich for $2, a salad for $2, and milk for $1. How much money will he have left? $1
3. The cats in the animal shelter eat 18 pounds of food each day. How many pounds of food do the cats eat each week? 126 lb
EP4
2. Tia is hanging lights around her window. The window is a square with sides that are 28 inches. How many inches of lights will Tia need? 112 in.
PAGES 54–55
1. Mr. Lee spent about $23 on paintbrushes, $50 on paint, and $15 on colored chalk. How much did he spend on art supplies? $88
22,197
71,864 49,667 ________
55,788 34,223 ________ 9.
$2,758
4,462
$6,741 $3,983 ________
6.
9,663 5,201 _______
926 644 ______
282
3.
PAGES 48–53
$1,628,922
$479
$807 $328 _______
Use any strategy to solve each problem.
PART D
$16,884
947
158
721 563 ______
1.
Subtract. Use addition or estimation to check.
C
451,218
$983,107 + $645,815_ ___________
9.
$572,938 + $118,476_ ___________
357,816 + 93,402 _________ 8.
$100,194
158,701
$45,150
$32,819 + $67,375 __________
6.
60,483 + 98,218 _________
5.
$38,406 + $ 6,744 __________
PART B
7.
4.
8,109
$4,227
5,678 + 2,431 ________
689
3.
3/12/10 1:45 PM
3,319
569,228
37,000 –−−−−−− 18,256
18,744
1,915
8. 604,009 – 34,781 −−−−−−
4,889
9.
B
24 ÷ 3 = 8
24 ÷ = 3 8
72 ÷ 9 = 8
2. 9 × = 72 8
5. 32 ÷ 8 4
4. 18 ÷ 6 3
6. 24 ÷ 3 8
3. 10 ÷ 2 5
2. 0 ÷ 15 = 0
3. 3 × (4 × 5) = (3 × 4) × 5
EP02_EP40_EM_EP_103030.indd EP5
3/12/10 1:45 PM
Extra Practice EP5
5; Commutative Property (×)
7. × 8 = 8 × 5
14; Ones in Division
6. 14 ÷ = 1
0; Zero Property (×)
5. 16 × = 0
6; Ones in Division
4. 6 ÷ = 1
the property or rule used.
Comm. Prop. (×) Zeros in Division Assoc. Prop. (×) Algebra Copy and complete each number sentence. Identify
1. 7 × 4 = 4 × 7
PAGES 80–83
PAGES 78–79
10; 5 × 10 = 50
8. 50 ÷ 5 =
6; 6 × 6 = 36
PAGES 73–77
PAGES 56–59
5. 36 ÷ 6 =
72 ÷ 8 = 9
8 × = 72 9
Identify the property or rule shown by each number sentence.
PART D
2. 12 ÷ 3 4
1. 21 ÷ 7 3
4; 8 × 4 = 32
7. 32 ÷ 8 =
6; 9 × 6 = 54
4. 54 ÷ 9 =
Use repeated subtraction to solve.
PART C
8; 11 × 8 = 88
6. 88 ÷ 11 =
9; 3 × 9 = 27
3. 27 ÷ 3 =
Algebra Divide. Use a related multiplication fact.
8 × = 24 3
1. 3 × 8 = 24
Algebra Copy and complete each fact family.
PART A
26,195
203,050 – 176,855 −−−−−−−
14,910
4,091
6,025 – 1,934 −−−−− 6. 20,400 – 5,490 −−−−−
3.
Multi-Part Lesson 2-1 Relate Multiplication and Division
7.
5. 3,300 –______ 1,385
4. 8,006 –______ 3,117
269
2. 4,000 – 681 −−−−
508 –−−−− 239
1.
Subtract. Use addition to check.
PART E
Find each sum. Check your work by estimating. 1. 456 2. $3,879 + 233 + $ 348 ________ ______
Multi-Part Lesson 1-3 (continued)
PART A
Extra Practice
PAGES 44–47
Multi-Part Lesson 1-3 Add and Subtract Whole Numbers
Extra Practice
EP6–EP7
Extra Practice 3 18 ×6 ____
4 28 ×7 ____
15. 24 ÷ 4 6
11. 30 ÷ 5 6
7.
3.
10. 48 ÷ 6 8 14. 81 ÷ 9 9
9. 42 ÷ 6 7
13. 35 ÷ 5 7
Extra Practice
EP02_EP40_EM_EP_103030.indd EP6
Extra Practice
6. 9 × 5 45
5. 5 × 8 40
EP6
2. 6 × 8 48
1. 9 × 6 54
15. 36 ÷ 6 6
11. 90 ÷ 9 10
7. 6 × 10 60
3. 7 × 7 49
Multiply or divide. Use arrays or area models if needed.
PART C
14. 28 ÷ 4 7
13. 45 ÷ 5 9
2 14 ×7 ____
10. 32 ÷ 4 8
6.
9 36 ×4 ____
5.
5 25 ×5 ____
9. 27 ÷ 3 9
2.
3 24 ×8 ____
1.
Multiply or divide. Use arrays or area models if needed.
PART B
12 36 ×3 ____
2 18 ×9 ____
16. 72 ÷ 8 9
12. 56 ÷ 7 8
8. 7 × 9 63
4. 8 × 10 80
PAGES 90–92
16. 45 ÷ 3 15
12. 15 ÷ 3 5
8.
4.
PAGES 86–89
4. A basketball game has 4 quarters. If 5 players each score 2 points during each quarter, how many total points are scored? 40 points
3. Tom watched 45 movies this year. Each movie was two hours long. How many hours did he spend watching movies this year? 90 hours
30 pictures
2. Carisa can draw 3 pictures in the morning and 3 pictures in the afternoon. If she draws for 5 days, how many pictures can she make?
1. Mrs. Beal’s students earned a class party. An extra-large pizza costs $28. If she bought 3 pizzas, how much did she spend? $84
Choose an operation to solve each problem.
3/12/10 1:45 PM
14. 10 60 6
3 30 × 10 _____
15. 10 90 9
11. 80 ÷ 10 8
7.
3. 10 × 5 50
11 66 ×6 ____
PAGES 100–102
16. 10 20 2
12. 96 ÷ 12 8
9. 12 48 4
6. 4 × 12 48
3.
9 90 × 10 _____ 12. 70 ÷ 10 7
8.
4. 10 × 7 70
4. bag; 15 individual oranges cost $30, which is more than $20. PAGES 104–105
11. 99 ÷ 11 9
8. 3 × 3 × 12 108
7. 8 × 4 × 3 96
EP02_EP40_EM_EP_103030.indd EP7
11. 9 × 4 × 2 72
5. 3 × 4 × 5 60
4. 9 × 3 × 2 54 10. 6 × 11 × 1 66
2. 5 × 7 × 2 70
1. 6 × 3 × 4 72
Multiply.
3/12/10 1:46 PM
Extra Practice EP7
12. 12 × 2 × 4 96
9. 10 × 3 × 5 150
6. 9 × 1 × 4 36
3. 8 × 2 × 5 80
PAGES 106–109
4. A bag of 15 oranges costs $20. Oranges that are sold individually cost $2. Is it cheaper to buy 15 oranges in a bag or 15 oranges sold individually? Explain.
3. Aaron bought a shirt that cost $27 and a hat that cost $3. How much change will he receive if he pays with two $20 bills? $10
PART D
2. A chicken runs 5 miles an hour. An ostrich runs 40 miles an hour. How many hours would it take a chicken to run the same distance it took an ostrich to run in two hours? 16 h
1. Lisa lives 7 miles from school. She bikes to school and back every day. If there are 5 days in 1 school week, how many miles does she bike in 1 school week? 70 miles
Use any strategy to solve each problem.
PART C
10. 120 ÷ 12 10
8. 11 110 10
4 48 × 12 _____
7. 11 88 8
2.
5. 7 × 11 77
3 33 × 11 _____
4. 8 × 12 96
1.
Multiply or divide. Use arrays or area models if needed.
PART B
13. 10 40 4
10. 30 ÷ 10 3
6. 10 20 × 2 ___
5. 10 40 × 4 ___ 9. 50 ÷ 10 5
2. 8 × 10 80
1. 6 × 10 60
Multiply or divide.
PART A
PAGES 96–99
Multi-Part Lesson 2-3 Multiplication and Division Facts Greater Than 9
PART A PAGES 84–85
Multi-Part Lesson 2-2 Multiplication and Division Facts Through 9
Extra Practice
Extra Practice
Extra Practice
EP8–EP9
1–12. See Extra Practice Answer Appendix.
6. 24
5. 11
4. 35
2.
4.
1.
3.
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP8
EP8
Laps
1 8
2 16
3 24
4 32
5 40
1 45
2 3 4 5 90 135 180 225
Time Spent Practicing Minutes
Day
6. Trevor practices the guitar every day. What is the rule for the pattern shown in the table? + 45
5. Sareeta jogs on a track five days a week. What is the rule for the pattern shown in the table? + 8
Distance Jogged
4. 5, 1, 7, 3, 9, - 4 then + 6; 5
Day
2. 27, 22, 17, 12, 7, - 5; 2
1. 3, 7, 11, 15, 19, + 4; 23
PAGES 130–133
PAGES 127–129
3. 2, 5, 3, 6, 4, + 3 then - 2; 7
Identify, describe, and extend each pattern.
PART B
41, 43, and 47
1–4. See Extra Practice Answer Appendix.
Copy and extend each pattern.
PART A
Multi-Part Lesson 3-1 Patterns
6. 57 composite
3. 21 composite
PAGES 114–115
PAGES 110–113
8. What three prime numbers are greater than 40 and less than 50?
5. 53 prime
4. 33 composite
7. What prime number is greater than 30 and less than 35? 31
2. 14 composite
1. 1 neither
Tell whether each number is prime, composite, or neither.
PART B
9. 6 12. 9
8. 7 11. 8
7. 4
10. 12
Identify the first five multiples for each number.
3. 16
2. 18
1. 36
Find the factors of each number.
PART A
3/12/10 1:46 PM
Carol, Jorge, Steph, Jordan
guitar
8. 16 - (c + 5) 4
5. c - 2 5
2. x - 3 3
6. q + 14 = 22 8
5. 9 - x = 2 7
7. 8 + d = 18 10
3. p - 8 = 6 14
8. 7 + 6 = f 13
4. 18 - 13 = y 5
PAGES 140–144
EP02_EP40_EM_EP_103030.indd EP9
9 + b = 28; 19
11. The sum of nine and a number is twenty-eight. Find the number.
y – 12 = 16; 28
q + 11 = 25; 14
3/12/10 1:46 PM
Extra Practice EP9
12. A number plus eleven equals twenty-five. What is the number?
n - 8 = 13; 21
Write and solve an equation for each situation. 9. Twelve less than a number is sixteen. 10. Eight subtracted from a number What is the number? equals thirteen. What is the number?
2. 7 + m = 18 11
1. 4 + b = 12 8
Solve each equation.
C
13. fifty-one subtracted from f f - 51
12. d minus twenty-four d - 24
PART B
11. the sum of b and seventeen b + 17
9. 5 + (6 + x) 17
6. 14 - x 8
3. c + 9 16
10. five less than y y - 5
Write an expression for each situation.
7. (x - 2) + 9 13
4. 7 + x 13
1. c + 5 12
PAGES 136–139
4. Mr. Davis noticed a pattern in a parking lot. In the first parking space was a white car. In the second space was a red car. The next space had a white car and the fourth space had a red car. If the pattern continues, what color car will be parked in the tenth space? a red car
Find the value of each expression if x = 6 and c = 7.
PART A
PAGES 134–135
2. Jonah takes piano and guitar lessons. Over the summer he has piano lessons every three days. He has guitar lessons every four days. If Jonah has piano and guitar lessons on Monday, what lesson will he have the following Tuesday?
Multi-Part Lesson 3-2 Addition and Subtraction Relationships
3. Lashonda is doing a project on rocks. She collected 3 rocks the first day of the project. Each day she collected 2 more rocks than the day before. How many rocks did Lashonda collect on the seventh day of the project? 15 rocks
1. Four students are waiting in line. Jordan is last. Steph is not next to Carol. Carol is ahead of Jorge. What is the order of the students?
Solve. Use the draw a picture strategy.
PART C
Multi-Part Lesson 3-1 (continued)
Extra Practice
Multi-Part Lesson 2-4 Factors and Multiples
Extra Practice
EP10–EP11
Extra Practice 5. x × 7 56 8. 32 ÷ (x ÷ v) 16
4. v ÷ v 1
7. (v × 4) ÷ x 2
5. c × 3 = 24 8 8. 50 ÷ k = 5 10 11. w ÷ 6 = 8 48
4. a × 6 = 54 9
7. 18 ÷ h = 6 3
10. 18 ÷ n = 9 2
Extra Practice
EP02_EP40_EM_EP_103030.indd EP10
Extra Practice
4. Angelina is placing photos in an album. Each page in the album can hold 4 photos. There are 32 pages in the album. How many photos can Angelina place in the album? 128 photos
3. A vine in the park grows 2 inches every week. The vine is 13 inches tall now. How many inches tall will the vine be in 2 weeks? 4 weeks? 8 weeks? 17 in.; 21 in.; 29 in.
EP10
2. Ian is eating pizza with 5 friends. They ordered 3 pizzas. If each pizza is cut into 6 slices, how many slices can each person have? 3 slices
PAGES 158–159
12. y ÷ 8 = 8 64
9. 28 ÷ p = 4 7
6. d × 7 = 35 5
3. 11 × f = 44 4
PAGES 152–157
1. Ty wants to buy posters that cost $7 each. He has $50. How many posters can he buy? 7 posters
Use any strategy to solve each problem.
PART D
2. 7 × r = 21 3
1. 5 × m = 30 6
Solve each equation.
C
13. 9 times a number 9 × n
12. a number divided by 10 n ÷ 10
PART B
11. the product of 3 and a number 3 × n
9. (x ÷ 2) × 9 36
6. 5 × v 20
10. a number divided by 5 n ÷ 5
Write an expression for each situation.
2. 6 × v 24
1. x ÷ 4 2
3. x ÷ v 2
3/23/10 11:42 AM
13 15 19
Output (x)
10 14 20 24
$16 $24 $32
Output (q)
f – 8 = q ; $40, $48, $56
$24 $32 $40 $48 $56 $64
Input (f )
Rule:
b + 9 = x ; 23, 29, 33
6
4
Rule: Input (b)
4.
2.
28 35
24 36
4 6
49 56
12
D
EP02_EP40_EM_EP_103030.indd EP11
1.
16 20 24
1 2 3 4
Output (y)
Input (x)
(3 + x) × 4 = y
28
Complete each function table.
C
5
4
3
Output (v)
25 19
2 3
16
3/12/10 1:46 PM
Extra Practice EP11
43
1
4
Output (y)
Input (x)
(36 ÷ x) + 7 = y
PAGES 168–173
Divide by 7; g ÷ 7 = v ; 6, 7, 8
42
8 10
2.
21
Input (g)
12 2
2. Output (q)
PAGES 164–167
m + 11 = p ; $36, $39, $42
$27 $30 $33
Output ( p)
Rule:
$16 $19 $22 $25 $28 $31 Input (m)
Input (a)
Multiply by 6; a × 6 = q ; 48, 60, 72 PART
1.
12
y – 7 = c ; 16, 20, 24
8
4 Output (c)
Rule:
11 15 19 23 27 31
PAGES 160–163
Input (y)
Write an equation that describes each pattern. Then use the equation to find the next three numbers.
PART B
3.
1.
Write an equation that describes each pattern. Then use the equation to find the next three numbers.
PART A
Find the value of each expression if v = 4 and x = 8.
Multi-Part Lesson 3-4 Function Tables
PART A PAGES 148–150
Multi-Part Lesson 3-3 Multiplication and Division Relationships
Extra Practice
Extra Practice
Extra Practice
EP12–EP13
5. 5 × 6 5 × 60 5 × 600 5 × 6,000
27 270 2,700 27,000
4. 3 × 9 3 × 90 3 × 900 3 × 9,000
11. 9 × 400 3,600
10. 500 × 7 3,500
2. 484 500 × 5 = 2,500; × 5 greater −−−
12. 8 × 3,755
3. 723 700 × 8 = × 8 5,600, less −−−
PAGES 190–193
12. 8,000 × 5 40,000
11. 6 × $9,810
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP12
EP12
yes; 600 × 7 = 4,200
3. The chickens on a farm produce about 4,200 eggs per week. Is it reasonable to say that the chickens produce 600 eggs each day?
1. Bianca practices the guitar 30 minutes every day. Is it reasonable to say that she practices the guitar 300 minutes each week?
no; 24 × 200 = 4,800
4. An album can hold 24 stamps on each page. There are 200 pages. Is it reasonable to say that the album can hold 48,000 stamps?
= 1,560
2. The soccer fields in a park are each 130 yards long. Is it reasonable to say that 4 soccer fields are a total of 1,560 feet long? yes; (4 × 130) × 3
PAGES 194–195
8 × 4,000 = 32,000; greater
Decide whether each answer is reasonable. Explain your reasoning.
6 × $10,000 = $60,000; 3 × $500 = $1,500; greater greater 1. no; Bianca practices for 210 minutes each PART D week, so 300 is not reasonable.
10. 3 × $478
6. 9 × $460 9 × $500 greater $3,000; greater = $4,500; greater 7. 7 × 1,986 7 × 2,000 = 8. 8 × $5,420 8 × $5,000 = 9. 5 × 6,752 5 × 7,000 $40,000; less = 35,000; greater 14,000; greater
4. 3 × 692 3 × 700 = 2,100; 5. 6 × $472 6 × $500 =
1. 584 600 × 3 = 1,800; × 3 greater −−−
28 280 2,800 28,000
48 480 4,800 48,000
9. 90 × 3 270
6. 7 × 4 7 × 40 7 × 400 7 × 4,000
3. 8 × 6 8 × 60 8 × 600 8 × 6,000
Estimate each product. Then tell if the estimate is greater than or less than the actual product.
PART C
8. 60 × 6 360
30 300 3,000 30,000
21 210 2,100 21,000
7. 7 × 80 560
Multiply. Use mental math.
2. 3 × 7 3 × 70 3 × 700 3 × 7,000
20 200 2,000 20,000
1. 4 × 5 4 × 50 4 × 500 4 × 5,000
Multiply. Use basic facts and patterns.
3/12/10 1:47 PM
14. 201 804 × 4 ____
13. 132 396 × 3 ____
15. 310 620 × 2 ____
11. 41 82 × 2 ___
7. 41 × 2 82
3. 4 × 22 88
B
C
42 3(40 + 2) = 126 × 3 −−−
14 6(10 + 4) = 84 × 6 −−−
56 4(50 + 6) = 224 × 4 −−−
23 5(20 + 3) = 115 × 5 −−−
8. 33 × 4 4(30 + 3) = 132
5.
2.
72 5(70 + 2) = × 5 360 −−−
18 4(10 + 8) = 72 × 4 −−−
9. 51 × 7 7(50 + 1) = 357
6.
3.
PAGES 206–213
16. 102 306 × 3 ____
12. 21 84 × 4 ___
8. 2 × 340 680
4. 3 × 20 60
PAGES 196–203
EP02_EP40_EM_EP_103030.indd EP13
3/16/10 1:05 PM
Extra Practice EP13
right: cheetahs, jaguars, tigers, lions
4. At the zoo, the big cats are in a row. The lions are last. The jaguars are to the left of the tigers. The cheetahs are to the left of the jaguars. In what order are the big cats? from left to
3. Rita is making muffins. There are 36 muffins in each batch. How many muffins will be in 3 batches? How many muffins will be in 7 batches?
108 muffins; 252 muffins
2. Movie tickets are $7 for adults and $4 for children. What is the total cost if three adults and five children go to the theater? $41
PAGES 214–215
1. Javier bikes 224 miles each month. He bikes the same number of miles each week. How many miles does Javier bike each week? 56 miles
Use any strategy to solve each problem.
PART D
10. 17 × 9 9(10 + 7) = 153 11. 42 × 8 8(40 + 2) = 336 12. 34 × 6 6(30 + 4) = 204
7. 21 × 6 6(20 + 1) = 126
4.
1.
Use models and the Distributive Property to solve.
PART A
Multi-Part Lesson 4-3 Multiply with Regrouping
10. 33 66 × 2 ___
6. 121 × 4 484
5. 213 × 2 426 9. 23 69 × 3 ___
2. 14 × 2 28
1. 32 × 3 96
Multiply. Check for reasonableness.
C
PART A
B
Multi-Part Lesson 4-2 Multiply Without Regrouping PAGES 185–189
PART A
Extra Practice
B
Multi-Part Lesson 4-1 Multiples
Extra Practice
EP14–EP15
Extra Practice 28 140 × 5 −−− 5. 6 × 25 150 8. 4 × $86 $344
7. 5 × 73 365
9. 5 × 2,845 14,225
B
8. 6 × 4,090 24,540
11.
$28 $840 × 30 −−−−
10.
Extra Practice
EP02_EP40_EM_EP_103030.indd EP14
EP14
Extra Practice
8.
64 1,920 × 30 −−−−
7. 92 6,440 × 70 −−−−
$49 $2,940 × 60 −−−−
24 1,200 × 50 −−−− 75 3,000 5. × 40 −−−− 2.
1.
18 540 × 30 −−−− 47 2,820 4. × 60 −−−−
Multiply.
PART A
Multi-Part Lesson 5-1 Multiplication with Tens
11. 8 × 9,502 76,016
7. 3 × $8,702 $26,106
10. 4 × 7,084 28,336
5. 7 × $3,408 $23,856
2. 507 4,056 × 8 −−−
4. 2 × 6,009 12,018
1. 408 1,632 × 4 −−−
Multiply. Check for reasonableness.
PART A
Multi-Part Lesson 4-4 Multiplication with Zeros
12.
9.
63 5,670 × 90 −−−−
85 5,950 × 70 −−−−
48 4,320 × 90 −−−− 56 5,040 6. × 90 −−−− 3.
PAGES 241–243
12. 5 × 5,047 25,235
9. 9 × $6,205 $55,845
6. 5 × 9,206 46,030
3. 906 6,342 × 7 ____
PAGES 226–230
12. 9 × 5,670 51,030
8. 6 × $8,562 $51,372
10. 4 × 3,488 13,952
11. 8 × 2,376 19,008
5. $493 $2,958 × 6 _____
4. 734 5,138 × 7 −−−
7. 6 × 5,630 33,780
6. $724 $2,896 × 4 −−−−
2. 392 2,352 × 6 −−−
3. $256 $2,048 × 8 −−−−
PAGES 220–223
12. 7 × $56 $392
9. 9 × 39 351
6. 7 × $43 $301
3. $17 $153 × 9 −−−
1. 538 1,614 × 3 −−−
Multiply. Check for reasonableness.
PART F
10. 3 × $92 $276
11. 8 × 78 624
2.
18 108 × 6 −−− 4. 2 × 99 198
1.
3/12/10 1:47 PM
38 × 26 −−−−
$98 × 57 −−−−
63 × 44 −−−−
43 × 82 −−−−
EP02_EP40_EM_EP_103030.indd EP15
$44 $3,652 × 83 −−−−
10.
6.
74 6,882 × 93 −−−− 5.
9.
2.
17 425 × 25 −−−−
B 1.
Multiply.
PART A
64 6,080 × 95 −−−−
$65 $3,120 × 48 −−−−
56 1,848 × 33 −−−−
$67 × 38 −−−−
PAGES 248–249
800 × 90 = 72,000; greater
12. 799 × 87
9. 982 × 34
1,000 × 30 = 30,000; less
$70 × 40 = $2,800; greater
6.
11.
7.
3.
$58 $986 × 17 −−−−
36 2,016 × 56 −−−−
$84 $3,528 × 42 −−−−
75 5,475 × 73 −−−−
49 3,773 × 77 −−−−
62 3,410 × 55 −−−−
3/12/10 1:47 PM
Extra Practice EP15
12.
8.
4.
PAGES 250–254
4. Roger earns $3,600 a year delivering newspapers. How much does he earn in one month? $300
2. Sherri jogged 9 miles last week, which is 3 times as many miles as her sister and half as much as her brother. How many miles did her sister and brother each jog?
Multi-Part Lesson 5-2 Two-Digit Multiplication
3. There are 6 rows of desks in a classroom. There are 7 desks in each row. How many desks are in the classroom? 42 desks
1. Sanjay and 3 of his teammates together scored 52 points in a basketball game. They each scored the same number of points. How many points did each teammate score? 13 points
59 × 37 −−−−
PAGES 244–247
60 × 40 = 2,400; greater
3.
3 miles; 18 miles
900 × 60 = 54,000; greater
11. 877 × 59
700 × 30; 21,000 greater
8. 668 × 27
40 × 80 = 3,200; less
5.
60 × 40 = 2,400; less
2.
Make a table to solve each problem.
PART C
400 × 30 = 12,000; less
10. 441 × 33
300 × 60 = 18,000; less
7. 322 × 64
$100 × 60 = $6,000; greater
4.
40 × 30 = 1,200; greater
1.
Estimate. Tell whether the estimate is greater than or less than the actual product.
PART B
Multiply. Check for reasonableness.
Multi-Part Lesson 5-1 (continued)
PART E PAGES 216–219
Multi-Part Lesson 4-3 (continued)
Extra Practice
Extra Practice
Extra Practice
EP16–EP17
6.
10.
377 19,981 × 53 −−−−
588 22,932 × 39 −−−−
5.
9.
542 34,688 × 64 −−−−
309 25,029 × 81 −−−−
186 5,952 × 32 −−−−
11.
7.
3.
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP16
EP16
3. Kim wants to buy a snowboard that costs $160. She has $88 in the bank. If she earns $6 an hour babysitting, how many hours will Kim have to work to earn enough money to buy the snowboard? 12 h
$12; $16
1. Tyree earns $4 for every 3 dozen cookies he sells. How much will Tyree earn if he sells 9 dozen cookies? 12 dozen cookies?
Use any strategy to solve each problem.
PAGES 264–266
41,328
738 × 56 −−−−
11,826
438 × 27 −−−−
17,600
275 × 64 −−−−
PAGES 268–269
9. 17,455 1,605,860 × 92 −−−−−
6. 7,708 655,180 × 85 −−−−
4. An art gallery has paintings on display in 7 rooms. There are 12 paintings in each room. How many paintings are on display in the art gallery? 84 paintings
2. Larisa has 24 jazz CDs and 7 country CDs. She has 2 times as many pop CDs as country CDs. How many CDs does she have in all?
45 CDs
8. 12,304 799,760 × 65 −−−−−
7. 8,544 324,672 × 38 −−−−
PART B
5. 6,504 624,384 × 96 −−−−
2. 2,345 145,390 × 62 −−−−
4. 5,792 278,016 × 48 −−−−
Multiply. 1. 1,877 45,048 × 24 −−−−
PART A
12.
8.
4.
3. 3,906 230,454 × 59 −−−−
663 30,498 × 46 −−−−
452 16,724 × 37 −−−−
207 10,143 × 49 −−−−
Multi-Part Lesson 5-4 Multi-Digit Multiplication
2.
104 1,872 × 18 −−−−
1.
Multiply.
3/12/10 1:47 PM
PART A
12
1 3 36 - −−− 6 −−−−
14
7 98 - −−− 8 −−−− 5. 79 ÷ 3 26 R1
2.
16 R2
1 R 4 66 - −−− 6 −−−−
87 adventure novels
chickens: 39 pounds
2.
5.
48 ÷ 6 = 8 480 ÷ 6 = 80 4,800 ÷ 6 = 800 72 ÷ 9 = 8 720 ÷ 9 = 80 7,200 ÷ 9 = 800
14. 1,600 ÷ 4 400
13. 8,100 ÷ 9 900
EP02_EP40_EM_EP_103030.indd EP17
8. 300 ÷ 5 60 11. 5,600 ÷ 7 800
35 ÷ 7 = 5 350 ÷ 7 = 50 3,500 ÷ 7 = 500
$40 ÷ 8 = $5 $400 ÷ 8 = $50 $4,000 ÷ 8 = $500
PAGES 288–291
3/23/10 3:52 PM
Extra Practice EP17
15. 3,000 ÷ 6 500
12. 7,200 ÷ 8 900
9. $280 ÷ 7 $40
6.
$27 ÷ 3 = $9 $270 ÷ 3 = $90 $2,700 ÷ 3 = $900 7. 420 ÷ 6 70
3.
63 ÷ 9 = 7 630 ÷ 9 = 70 6,300 ÷ 9 = 700
10. $210 ÷ 3 $70
Divide. Use patterns.
4.
1.
Copy and complete each set of patterns.
PART A
Multi-Part Lesson 6-2 Use Mental Math to Divide
Sample answer: 11 tricycles and 14 wagons
4. A toy store has at least 10 wagons and at least 10 tricycles on sale. There are a total of 89 wheels. How many tricycles and how many wagons are on sale?
3. The chickens on a farm eat 3 times as much grain as the turkeys do per week. The chickens and turkeys eat a total of 52 pounds of grain every week. How much grain do the chickens and turkeys each eat every week? turkeys: 13 pounds,
and 1 of them cost $15.
2. Maria has 49 more mystery novels than adventure novels. She has 223 novels in all. How many mystery novels and adventure novels does Maria have? 136 mystery novels and
PAGES 286–287
6. 95 ÷ 7 13 R4
3.
PAGES 281–285
1. Ren bought 5 CDs for $55. One of the CDs cost $5 more than the others. How much did each CD cost? 4 of the CDs each cost $10,
Solve. Use the guess, check, and revise strategy.
PART C
4. 60 ÷ 5 12
1.
Divide. Copy and complete each exercise. Check each answer.
B
Multi-Part Lesson 6-1 Model Division PAGES 256–261
PART A
Extra Practice
B
Multi-Part Lesson 5-3 Three-Digit Multiplication
Extra Practice
EP18–EP19
Extra Practice $540 ÷ 6 = $90
$250 ÷ 5 = $50
$6,300 ÷ 9 = $700
320 ÷ 8 = 40
2,400 ÷ 3 = 800
11. $6,580 ÷ 9
3. 5 71
7. 169 ÷ 8
2. 3 32
6. 814 ÷ 9
5. 422 ÷ 6
C
6. 6 2,558 426 R2
5. 3 1,677 559
7. 5 3,697 739 R2
3. 7 875 125 8. 9 2,93 8 326 R4
4. 4 936 234
PAGES 300–303
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP18
EP18
807 R1
13. 1,615 ÷ 2
$105 R2 1,090 R3
14. 4,363 ÷ 4
207 R4 $203 R2
15. $611 ÷ 3
$907
309
16. 1,236 ÷ 4
1,051
12. 9 9,459
11. 3 $2,721
10. 5 1,039
9. 3 $317
108
109 R2
208 R1
8. 7 756
108 R4
4. 9 976
PAGES 304–307
207
7. 2 414
6. 4 438
625 5. 3
3. 4 $432
$108
2. 4 837
209 R1
105
315 1. 3
Divide. Use estimation to check.
PART D
9. 1,539 ÷ 2 769 R1 10. 7,564 ÷ 8 945 R411. 4,255 ÷ 7 607 R6 12. 2,687 ÷ 4 671 R3
2. 2 764 382
1. 3 693 231
Divide. Use estimation to check.
PART B
70 R2; 420 ÷ 6 = 70 90 R4; 810 ÷ 9 = 90 21 R1; 160 ÷ 8 = 20 98 R2; 500 ÷ 5 = 100
8. 492 ÷ 5
4. 3 65
21 R2; 66 ÷ 3 = 22
PAGES 296–299
8,100 ÷ 9 = 900
12. 8,256 ÷ 9
1,200 ÷ 6 = 200
9. 1,244 ÷ 6
280 ÷ 4 = 70
6. 298 ÷ 4
430 ÷ 5 = 86
3. 433 ÷ 5
11 R3; 44 ÷ 4 = 11 10 R2; 30 ÷ 3 = 10 14 R1; 70 ÷ 5 = 14
47 1. 4
Divide. Use estimation to check.
PART A
Multi-Part Lesson 6-3 Divide Whole Numbers
10. 2,240 ÷ 3
8. $259 ÷ 5
5. $537 ÷ 6
480 ÷ 8 = 60
7. 337 ÷ 8
4. 476 ÷ 8
490 ÷ 7 = 70
2. 510 ÷ 7
200 ÷ 4 = 50
1. 241 ÷ 4
3/12/10 1:48 PM
11,902
14. 59,510 ÷ 5
1,557 6. 8 9,872 1,234 10. 9 33,786 3,754
2. 3 4,671
EP02_EP40_EM_EP_103030.indd EP19
3,946 R2
PAGES 312–313
19,157
16. 95,785 ÷ 5
football soccer
football basketball
tennis
basketball
football
football
fish
bird
lizard
dog
PAGES 327–329
3/12/10 1:48 PM
Extra Practice EP19
baseball basketball
soccer
Favorite Sports
dog
fish
dog
cat
Pets
soccer
bird
dog
cat
cat
Organize each set of data in a tally chart and a frequency table.
2. Tina conducted a survey to find out the favorite sports of the children in the park. Her recordings are shown at the right.
9,648
12. 6 23,678
4. Mei hiked for 20 minutes every morning from her campsite to the lake. She hiked back to the campsite every afternoon. Mei hiked for a total of 8 hours to and from the lake. How many days was Mei at camp? 12 days
PART A 1, 2. See Extra Practice Answer Appendix. 1. George recorded the types of pets that his classmates have. His recordings are shown at the right.
1,208
8. 6 57,888
4. 6 7,248
PAGES 308–310
2. A plant produces about 45 new flowers every 2 weeks. After 8 weeks, how many flowers will the plant have produced? 180 flowers
7,516 R7
15. 67,651 ÷ 9
1,169 R2 7. 7 9,256 1,322 R2 11. 7 25,984 3,712
3. 5 5,847
Multi-Part Lesson 7-1 Collect and Organize Data
3. There are 9 seals at a zoo. Altogether, the seals eat about 750 fish each day. About how many fish does each seal eat every day? 80 fish
1. At the drugstore, pencils are on sale for 10 for $1. Pens are on sale for 4 for $2. How much do 20 pencils and 12 pens cost? $8
Use any strategy to solve each problem.
PART F
1,204 R2
13. 9,634 ÷ 8
1,832 5. 4 6,184 1,546 9. 8 18,816 2,352
1. 2 3,664
Divide. Use estimation to check.
PART E
Estimate. Check your estimate. 1–12. Sample answers are given.
Multi-Part Lesson 6-3 (continued)
PART B PAGES 292–294
Multi-Part Lesson 6-2 (continued)
Extra Practice
Extra Practice
Extra Practice
EP20–EP21
Number of Students
2 22
3 27
4 24
5 22
1 46
Roller Coaster
Number of Riders
2 38
3 41
4 17
5 45
7
Extra Practice
9 11 10 9 6 9
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Extra Practice
6
Week 1
EP02_EP40_EM_EP_103030.indd EP20
EP20
Seeds
Week
Seeds That Sprouted
1. Number of seeds that sprouted
Organize each set of data in a line plot.
PART B
5 7 6 4 5 4 3
Tuesday Wednesday Thursday Friday Saturday Sunday
Miles Hiked
Monday
Day
Miles Hiked per Day
2. Miles hiked by campers
1, 2. See Extra Practice Answer Appendix.
PAGES 336–339
4. Maria bought some six-packs of soda. She bought 48 cans of soda in all. How many six-packs of soda did she buy? 8 six-packs
3. Nick earns $7 an hour walking dogs. He works the same number of hours each week. Nick earns $252 in 1 month. How many hours does he work each week if there are 4 weeks in a month? 9 h
PAGES 334–335
2. During the soccer season, for every 3 penalty kicks he took, Jamil scored on 2 of them. If he scored on 12 penalty kicks, how many penalty kicks did he take? 18 kicks
36
1. Akira mailed invitations to his birthday party. The postage to mail each invitation was 42¢. Akira paid 252¢ in all for postage. How many invitations did he send? 6 invitations
Solve. Use the make a table strategy.
PART A
6 39
no mode; 39; 29; outlier: 17
22; 24; 5; no outliers
Roller Coaster Riders at an Amusement Park
1 26
Grade
Students in Each Grade
Multi-Part Lesson 7-2 Line Plots and Line Graphs
2.
1.
Find the mode, median, and range of the set of data. Identify any outliers.
PAGES 330–333
3/12/10 1:49 PM
55 58
57 49
59
60
55
56
48
59
2.
EP02_EP40_EM_EP_103030.indd EP21
4. How many years would three generations of humans last? 225 years
whale
3. Which animal has a life span that is 45 years longer than a gorilla’s life span? blue
African elephant
2. Which animal has a life span of 70 years?
killer whale
1. Which animal has the longest life span?
Use the graph shown.
PART A
Multi-Part Lesson 7-3 Bar Graphs
2 P.M. the number of skiers has dropped.
5. Predict whether there will be more or fewer skiers at 5 P.M. than at 3 P.M. Explain. Sample answer: fewer; Since
100 more skiers
4. How many more skiers were there at 2 P.M. than at 12 P.M.?
3. How many skiers were there at 4 P.M.? 50 skiers
1 P.M. and 3 P.M.
2. At which two times were there the same number of skiers?
1. At what time were there the most skiers? 2 P.M.
Use the line graph to answer the questions.
E
54
Heights of Ms. Jenkins’ Students (in.) 48
PART D
1.
PAGES 340–341
200 175 150 125 100 75 50 25 0
120
115
120
80
130 118
124 95
95
PAGES 342–346
125
128
110
0
10
20
30
40
50
60
70
80
90
100
PAGES 348–351
an t ric an Af ph e El
Animal
la ril Go
H
um
an
r lle Ki hale W
3/23/10 11:45 AM
Extra Practice EP21
ue Bl ale h W
Average Life Spans of Mammals
Time
12 P.M. 1 P.M. 2 P.M. 3 P.M. 4 P.M.
88 100
48 125
Number of Minutes Reading
1, 2. See Extra Practice Answer Appendix.
Organize each set of data in a stem-and-leaf plot.
PART C
Multi-Part Lesson 7-2 (continued)
Life Span (years)
PART B
Extra Practice
Multi-Part Lesson 7-1 (continued)
Extra Practice
Pounds Produced 0
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP22
EP22
4. Draw a tree diagram to find the number of possible outcomes if a spinner with three equal sections labeled 1, 2, and 3 is spun twice.
PAGES 362–367
3. Draw a tree diagram to find the number of possible outcomes if a coin is tossed and a spinner with four equal sections labeled 1, 2, 3, and 4 is spun.
1–4. See Extra Practice Answer Appendix.
A model home has 8 windows on the first floor and 7 windows on the second floor. There are 180 windows altogether. How many model homes are there? 12 model homes
2. Draw a grid to find the number of possible outcomes if a coin is tossed and a 0–5 number cube is rolled.
B
PAGES 358–359
1. Draw a grid to find the number of possible outcomes if two counters are tossed once. Each counter is red on one side and yellow on the other.
PART A
Multi-Part Lesson 7-4 Probability
Type of Fruit
Franny’s Farm Fred’s Farm
PAGES 352–356
2. Radio station ABC plays songs that are 3 minutes long. How many songs can the station play in 50 minutes? 16 songs
3. Emilio’s sister is twice his age. In 4. 6 years, his sister will be 3 times his age right now. How old are Emilio and his sister? Emilio is 6. His sister is 12.
1. Leila bought a hat for $5, mittens for $7, and a scarf for $11. The cashier gave her $7 in change. How much did Leila give the cashier? $30
Use any strategy to solve each problem.
PART D
4. How many pounds of fruit are produced in all? 1,825 lb
3. How many more pounds of strawberries and plums were produced on Fred’s Farm than on Franny’s Farm? 150 lb
500 400 300 200 100
P
s he
ea c
2. Of which fruit did Fred’s farm produce the least? peaches
es
Fruits Produced
pl Ap
1. Of which fruit did Franny’s farm produce the most? apples
s
Use the graph shown.
um
C
Pl
PART B
w ra
Multi-Part Lesson 7-3 (continued)
3/12/10 1:49 PM
B
1. two out of ten
5. six-tenths
2. seven out of ten
0.16
2.
EP02_EP40_EM_EP_103030.indd EP23
4.
0.34
5.
0.82
0.72
Write a decimal for each part of a dollar shown.
1.
Write each decimal.
PART C
6.
3.
0.55
0.30
PAGES 388–391
3/12/10 1:50 PM
Extra Practice EP23
6. five-tenths
8. Zachary has ten state capitals to learn. He has learned 6 of them. What part of this assignment has he completed?
0.6 of the assignment
PAGES 383–387
5
4 3
PAGES 368–371
3. nine out of ten
7. Marisol has ten pages to read in her history book for homework tonight. She has read 7 pages. Write a decimal to show what part of the assignment she still has to read. 0.3 of the pages
4. one-tenth
impossible
4. a number greater than 6
likely
2. a number that is less than 5
1–6. See Extra Practice Answer Appendix.
Model and write each decimal.
PART A
Multi-Part Lesson 8-1 Decimals
likely
3. an even number equally
1. a number certain
The number cubes are rolled. What is the probability of each outcome? Write certain, likely, equally likely, unlikely, or impossible.
PART C
Multi-Part Lesson 7-4 (continued)
2
St
s rie
Extra Practice
1
EP22–EP23
5
be r
Extra Practice
Extra Practice
Extra Practice
EP24–EP25
1–6. See Extra Practice Answer Appendix.
5. 1.97
4. 3.06 6. 2.41
3. 2.14
PAGES 392–395
5. 13.80 13.8 =
B
6 3
_2 ; _1
2.
_3 ; _6
_
4 8
_
3.
5 10
_1 ; _2
PAGES 399–403
10. 0.78, 0.87, 0.08 0.87, 0.78, 0.08
8. 53.03, 53.33, 53.13
6. 4.91 4.9 >
_
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP24
EP24
3 6 10. _ 8 16
_
6 1 9. _ 18 3
_
_
_
6 2 11. _ 9 3
_
1 3 12. _ 2 6
13.
_1 20 5
4 _
_
Find an equivalent fraction for each fraction. 4–13. Sample answers given. 3 1 4 2 1 2 4 2 3 6 4. _ 5. _ 6. _ 7. _ 8. _ 4 8 6 3 12 4 10 5 7 14
1.
PAGES 396–398
3. 55.5 55.50 =
Write the fraction for the part that is shaded. Then find an equivalent fraction. 1–3. Sample equivalent fractions are given.
PART A
Multi-Part Lesson 8-2 Fractions
9. 65.02, 6.86, 6.5 65.02, 6.86, 6.5
7. 2.08, 2.98, 2.88 2.98, 2.88, 2.08
Order from greatest to least. 8. 53.33, 53.13, 53.03
2. 3.96 3.09 >
1. 6.7 0.67 >
4. 0.67 0.76 <
Compare. Use >, <, or =.
PART E
10. twenty-three and seven hundred six thousandths 23.706; 20 + 3 + 0.7 + 0.006
9. six and forty-five hundredths 6.45; 6 + 0.4 + 0.05
8. eighteen and seventy-two hundredths 18.72; 10 + 8 + 0.7 + 0.02
7. four and twelve-hundredths 4.12; 4 + 0.1 + 0.02
Write each decimal in standard and expanded form.
2. 0.53
1. 1.17
Model each decimal.
PART D
3/12/10 1:50 PM
5
4 _ 5
3 _ 5
12
>
9
5
5
5 4 8. _ _ >
10
9
6 _
3
2 _
form
6 5 5. _ _ >
2.
=
_
EP02_EP40_EM_EP_103030.indd EP25
4
form
3 simplest 11. _
_ 18 3 12. _ 24 4
20 4 7. _ 25 5
_ 16 2 6. _ 24 3
_
_
_ 11 1 13. _ 44 4
_ 30 5 8. _ 36 6
8
0
2
1 _ 3
_
_ 20 4 14. _ 45 9
_ 9 1 9. _ 27 3
9
<
1
15.
10.
_1 42 7
6 _
_3 20 5
12 _
3
_ 3 1 5. _ 9
PAGES 410–413
6
3 _
3/12/10 1:50 PM
Extra Practice EP25
12
3 9 9. _ _ <
3 1 6. _ _ <
3.
PAGES 406–409
history book, art book, novel
4. There are 4 books on display. The cookbook is next to the history book but not next to the art book or the novel. The art book is third. What is the order of the books? cookbook,
football. The rest are on the swings. How many children are on the swings? 5 children
3
1 are playing soccer. _ are playing
2
PAGES 404–405
1 2. There are 30 children at the park. _
Write each fraction in simplest form. If it is in simplest form, write simplest form. 3 1 8 1 4 1 1 1. _ 2. _ 3. _ simplest 4. _ 12 4 8 2 16 2 5
PART E
8
7 7 7. _ _ >
6
2 1 4. _ _ >
1.
Compare. Use >, <, or =.
PART D
the CDs are jazz. 5 are classical music, and 3 are blues. The rest are pop music. How many CDs are pop music? 4 CDs
4
1 3. There are 16 CDs on a shelf. _ of
poodle
1. Four dogs are standing in a row. The Great Dane is ahead of the poodle. The terrier is not next to the poodle. The collie is to the right of the terrier and is not first. What is the order of the dogs? terrier, collie, Great Dane,
Solve. Use the make a model strategy.
PART C
Multi-Part Lesson 8-2 (continued)
Extra Practice
Multi-Part Lesson 8-1 (continued)
Extra Practice
EP26–EP27
Extra Practice
B
0.88
100
88 _ ;
10
_7 ; 0.7 5.
2.
10
100
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP26
EP26
2. The first plant is 12 feet tall, the second is 4 feet tall, and the third is 6 feet tall.
4. Emily walked halfway home from school. She walked back 3 blocks to find a book. Then she walked home. She walked 20 blocks in all. How many blocks is it from Emily’s house to school? 14 blocks
3. Simon is hanging wallpaper on 3 walls of his room. Each wall is 10 feet wide and 8 feet tall. Each roll of wallpaper covers 40 square feet. How many rolls of wallpaper does Simon need? 6 rolls
PAGES 426–427
0.34
34 _ ;
0.5
_5 ;
PAGES 420–423
2. There are 3 plants in a garden. The first plant is 3 times taller than the second and 2 times taller than the third. The plants are a total of 22 feet tall. How tall is each plant?
100
7 _ ; 0.07 6.
10
_2 ; 0.2 3.
21 6. _ 4
3
1. Marcus has 20 coins. One fourth are dimes. One fifth are nickels. The rest are quarters. How much are Marcus’s coins worth? $3.45
Use any strategy to solve each problem.
PART C
4.
1.
Write a fraction and a decimal for each shaded part.
PART A
Multi-Part Lesson 8-3 Relate Fractions and Decimals
_ 5_1 4
_
Write each as an improper fraction or a mixed number. Use models if needed. 3 33 2 11 1 13 3. 3_ 4. 3_ 5. 3_ 3 3 4 4 10 10
_
3
1 _ 3_ ; 10
Write a mixed number and an improper fraction for each model. 21; 5 1. 2. 2 2
__
3/12/10 1:50 PM
_
4
_1 ; 0.25 5.
10
_3 ; 0.30
_
_
_
_
_ 13 8 1 11. _ - _ 15 15 3
_
9 4 5 8. _ - _ 12 12 12
2 2 2 5. _ + _ 6 6 3
_
_
_
EP02_EP40_EM_EP_103030.indd EP27
3 14 2 7. _ + _ 5 15 6
1 1 1 8. _ + _ 4 3 12
2 2 8 5. _ + _ 3 9 9
_
1 1 7 4. _ + _ 4 3 12
_
_
Add. Use fraction tiles if needed. Write in simplest form. 3 3 9 1 1 2 2. _ + _ 1. _ + _ 5 2 6 3 10 10
PART B
5 2 1 10. _ - _ 6 6 2
_
6 2 2 7. _ - _ _ 10 10 5
4 2 3 4. _ + _ 10 10 5
Find each sum or difference. Write in simplest form. 3 3 1 2 1 3 2. _ + _ 1. _ + _ 4 4 4 12 12 2
PART A
Multi-Part Lesson 9-1 Add and Subtract Fractions
4.
_
3/12/10 1:50 PM
Extra Practice EP27
3 2 7 9. _ + _ 4 8 8
_
3 1 3 6. _ + _ 4 4 6
_
_
PAGES 448–451
2 1 13 3. _ + _ 3 5 15
4 2 2 12. _ - _ 9 9 9
_
8 5 3 9. _ - _ 8 8 8
_
_
PAGES 445–447
2
_1 ; 0.50
5
_1 ; 0.20
PAGES 428–432
3 5 8 6. _ + _ 11 11 11
3 2 5 3. _ + _ 9 9 9
6.
Write a fraction and a decimal to describe the shaded part of each model. 3 2. 3. 1. 3 ; 0.60 ; 0.75 5 4
_
PART D
E
Multi-Part Lesson 8-3 (continued)
PART F PAGES 414–418
Multi-Part Lesson 8-2 (continued)
Extra Practice
Extra Practice
Extra Practice
EP28–EP29
_
_
6. 38.11 38
5. 55.79 56
14. 73.64 73.6
13. 29.28 29.3
15. 51.82 51.8
11. 47.11 47.1
7. 82.7 83
3. 73.81 74
26.2 -14.8 −−−−
7.
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP28
EP28
12. 59.5 - 23.12 60 - 23 = 37
26 - 15 = 11 10. 27.8 - 14.7 28 - 15 = 13
8.
9.
6.
3.
34.95 -18.50 −−−−−
13 - 7 = 6
13.3 7.2 −−−−
$15 + $23 = $38
$14.96 +$23.17 −−−−−−
PAGES 460–463
$12 .49
16. 85.83 85.8
12. 33.76 33.8
8. 25.5 26
4. 32.41 32
PAGES 456–459
13. $83.32 - $54.86 $83 - $55 = $28
35 - 19 = 16 11. $38.91 - $26.78 $39 - $27 = $12
$26 + $16 = $42
$25.85 +$16.27 −−−−−−
10 - 4 = 6
9.8 -3.7 −−−−
18 + 24 = 42
5+4=9
17.67 +23.78 −−−−− 5.
5+2=7
4.
5.3 +4.2 −−−−
4.7 +2.1 −−−−
1.
2.
Estimate. Round to the nearest whole number.
PART B
13 cm
18. The European mole is 12.7 centimeters long. What is this amount rounded to the nearest whole number?
17. A CD costs the amount shown. What is this amount rounded to the nearest whole number? $12
10. 93.39 93.4
9. 16.72 16.7
Round to the nearest tenth.
2. 46.21 46
1. 19.8 20
Round to the nearest whole number.
PART A
_
6 1 1 6. _ - _ 2 4 8
Multi-Part Lesson 9-2 Round and Estimate with Decimals
5 1 8 5. _ - _ 7 3 21
_
3 2 5 4. _ - _ 4 6 12
_
_
3/12/10 1:51 PM
B
2. 6.
0.5 1.2 +0.7 −−−− 7.65 17.03 +9.38 −−−−
4. Delmar surveyed 500 students to find out their favorite color. Blue was the favorite color of 7 out of 10 students. How many students’ favorite color is blue? 350 students
3. A number is multiplied by 3. The product is subtracted from 50. The result is 11. What is the number? 13
8.
4.
11.46 16.39 + 4.93 −−−−−
6.4 15.74 +9.34 −−−−
PAGES 468–473
3/12/10 1:51 PM
Extra Practice EP29
5 roses for $4
2. A flower shop is selling roses at the price shown below. How much would 12 roses cost? $9.60
PAGES 474–475
14. 6.6 + 4.7 + 9.9 21.2
11. 42.52 + 21.84 64.36
14.79 20.34 + 5.55 −−−−−
2.3 2.45 +0.15 −−−−
13. 5.2 + 8.3 + 7.4 20.9
1. There are two numbers whose product is 48 and difference is 8. What are the numbers? 12 and 4
EP02_EP40_EM_EP_103030.indd EP29
7.
3.
10. 17.99 + 12.99 30.98
$7.25 $13.74 +$6.49 −−−−−
0.8 1.5 +0.7 −−−−
Use any strategy to solve each problem.
PART C
12. 6.4 + 3.6 + 2.8 12.8
9. 22.48 + 18.67 41.15
5.
1.
Add. Use estimation to check for reasonableness.
PART A
Multi-Part Lesson 9-3 Add and Subtract Decimals
6 games
4. The Bears won 18 games. The Lions won one game for every three games the Bears won. The Sharks won 8 more games than the Lions. How many games did the Lions win?
3. A group of 3 adults and 7 students rode a ferry. The cost for the entire group was $36. If the cost for a student to ride was $3, what was the cost for an adult? $5
bank, school, museum
2. There are three buildings on a block. The bank is next to the school. The museum and school are not first. What is the order of the buildings?
PAGES 464–465
1. Mr. Myers is thinking of a number between 20 and 28. The number is not even, not a factor of 50, and not divisible by 3. What is the number? 23
Use logical reasoning to solve each problem.
PART C
Subtract. Use fraction tiles if needed. Write in simplest form. 5 3 1 1 1 7 2 1 5 2. _ - _ 3. _ - _ 1. _ - _ 5 10 3 6 2 3 10 9 9
Multi-Part Lesson 9-2 (continued)
PART C
Extra Practice
PAGES 452–455
Multi-Part Lesson 9-1 (continued)
Extra Practice
EP30–EP31 5.6
4.
Extra Practice 10.
6.
11.
7.
$9.79
$26.74 $16.95 −−−−−−
$7.39
$9.45 $2.06 −−−−−
20.91
48.03 27.12 −−−−−
4.17
8.55 4.38 −−−−−
2.4
hexagon 2.
yes 5.
no 6.
quadrilateral 3.
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP30
EP30
4.
1.
2.
5. 6 faces, 12 edges, 8 vertices; cube
0 faces, 0 edges, 0 vertices; sphere 3.
5 faces, 6. 8 edges, 5 vertices; square pyramid
2 faces, 0 edges, 0 vertices; cylinder
Tell the number of faces, edges, and vertices. Then identify each figure.
PART B
4.
Tell whether each figure is a polygon.
1.
1 face, 0 edges, 1 vertex; cone
5 faces, 9 edges, 6 vertices; triangular prism
PAGES 499–501
no
octagon
3/12/10 1:51 PM
4
_1 turn
90°;
2.
obtuse
5.
right
2
_1 turn
180°;
6.
3.
EP02_EP40_EM_EP_103030.indd EP31
4.
1.
5 ft
5 ft
4 cm
3 in.
5.
6 yd
right; scalene
2.
3 in.
11 yd
8 yd
acute; isosceles
4 in.
acute; equilateral obtuse; scalene
5 ft
5 cm
3 cm
2 ft
5 ft
acute
6 ft
8 in.
10 in.
6 in.
3/12/10 1:51 PM
Extra Practice EP31
right; scalene
6.
4
270°;
_3 turn
PAGES 510–513
obtuse; scalene
3.
Classify each triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene.
PART A
Multi-Part Lesson 10-3 Triangles and Quadrilaterals
4.
Classify each angle as right, acute, or obtuse.
1.
PAGES 504–508
Multiply by 7.
21 35 49 56
3 5 7 8
Write the measure of each angle in degrees and as a fraction.
Identify each polygon.
B
Multi-Part Lesson 10-2 Angles
Output
Input
PART A PAGES 495–498
15. 41.93 - 15.98 25.95
12.
8.
PART A
14. 38.04 - 23.60 14.44
$6.37
$19.23 $12.86 −−−−−−
3.13
7.56 4.43 −−−−−
3.6
PAGES 502–503
2. Copy and complete the table. What is the pattern?
Multi-Part Lesson 10-1 Two- and Three-Dimensional Figures
13. 54.50 - 46.72 7.78
3.86
9. 12.61 8.75 −−−−−
2.34
2.5
3.78 1.44 −−−−−
5.
1. A flowering plant produces 15 seeds on the first day of spring. On the second day, it produces 23 seeds. On the third day, it produces 31 seeds. Describe the pattern. How many seeds will the plant produce on the sixth day? Add 8; 55 seeds
3.
Solve. Use the look for a pattern strategy.
6.9 3.3 −−−−
2.
4.8 2.3 −−−−
1.
Subtract. Use estimation or addition to check. 5.2 2.8 −−−−
PART C
8.3 2.7 −−−−
Multi-Part Lesson 10-1 (continued) PAGES 476–481
PART D
E
Multi-Part Lesson 9-3 (continued)
Extra Practice
Extra Practice
Extra Practice
EP32–EP33
3. rectangle, parallelogram
6.
parallelogram
5.
trapezoid
C
A
B
Extra Practice
Extra Practice
−− ⎯⎯ FG || LM
L
F
EP02_EP40_EM_EP_103030.indd EP32
EP32
4.
M
G
Describe each figure.
1.
Identify each figure.
B
⎯⎯ AB
Q
R
−− RS
B
PAGES 518–519
trapezoid
PAGES 514–517
C
R
S
P
G
K
−− ⎯⎯ PQ intersects KL
6.
3.
L
H
Q
⎯ GH
PAGES 533–539
2. For every 30 minutes that Julia swims, she rests for 15 minutes. In 3 hours of swimming, how many minutes will she rest? 90 min
⎯ intersects ⎯⎯ BC QR
5.
2.
Multi-Part Lesson 11-1 Lines
1. What is the next number in the pattern 4, 14, 34, 64, 104? 154
PART A
3.
square, rectangle, parallelogram, rhombus
rhombus, parallelogram
2.
Use any strategy to solve. Tell what strategy you used.
PART C
4.
1.
Classify each quadrilateral in as many ways as possible.
PART B
3/12/10 1:51 PM
0
10 9 8 7 6 5 4 3 2 1
B
H
C
EP02_EP40_EM_EP_103030.indd EP33
3.
1.
reflection
translation
M
X
PAGES 544–545
2. Lee, Diego, Tara, and Irena will ride the Ferris wheel. Two people can sit in each car. What pairs are possible for the four friends to ride the Ferris wheel?
4.
2.
PAGES 546–551
3/12/10 1:52 PM
Extra Practice EP33
translation
rotation
Identify each transformation. Write rotation, reflection, or translation.
PART A
P
J
Q
1 2 3 4 5 6 7 8 9 10
A
K
PAGES 540–543
Lee/Diego and Tara/Irena; Lee/Tara and Diego/Irena; Lee/Irena and Diego/Tara
Multi-Part Lesson 11-2 Transformations
1. Jim has 1 blue jacket, 1 green jacket, and 1 brown jacket. He has 1 tan hat and 1 black hat. How many different combinations of a jacket and a hat can he wear? 6
Solve. Make an organized list.
PART E
9. (1, 1) A
8. (8, 8) X
7. (5, 7) Q
6. (4, 0) H
5. (3, 3) P
4. (8, 3) M
3. (7, 6) C
2. (3, 4) J
1. (1, 8) K
Identify the letter that is located at each ordered pair.
PART D
Multi-Part Lesson 11-1 (continued)
Extra Practice
Multi-Part Lesson 10-3 (continued)
Extra Practice
EP34–EP35
Extra Practice translation, reflection 2.
yes 4.
B
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP34
EP34
4.
1.
no
no 5.
2.
yes; 6. translation
yes; 3. reflection
PAGES 560–563
no
yes; rotation and translation
Tell whether the figures appear to be congruent. Write yes or no. If they are, describe the movements that show the congruence.
PART A
Multi-Part Lesson 11-3 Congruent Figures
boots: 3 pairs; mittens: 6 pairs
4. Mike makes $4 an hour babysitting. Omar makes $6 an hour gardening. How many hours will Mike have to work to make the same amount that Omar makes in 8 hours? 12 h
PAGES 556–557
no
3. Evan has twice as many pairs of mittens as boots. He has 6 times as many pairs of socks as boots. He has 18 pairs of socks. How many pairs of boots and mittens does he have?
5.
2. Suna wants to make 5 bracelets and 3 necklaces. She plans to use 3 shells for every bracelet and 4 shells for every necklace. How many shells does she need? 27 shells
yes
translation
1. Tyron is replacing the wheels on 6 bicycles. He is also replacing the wheels on 4 tricycles and 3 wagons. How many wheels is Tyron replacing in all? 36 wheels
Use any strategy to solve each problem.
PART D
3.
Determine whether the figure can be used alone to make a tessellation. Write yes or no.
1.
Identify the transformation(s) that could have been used to make each tessellation. Write rotation, reflection, or translation.
3/12/10 1:52 PM
PART A
yes; 1
yes; 1
yes; 1
8. no
5.
2.
no
9.
yes; 2 6.
3.
yes; 2
EP02_EP40_EM_EP_103030.indd EP35
4.
1.
yes
yes
5.
2.
no
no
6.
3.
3/12/10 1:52 PM
Extra Practice EP35
yes
yes
PAGES 572–574
yes; 2
PAGES 566–571
yes; 4
Tell whether each figure shows rotational symmetry. Write yes or no.
PART C
7.
4.
1.
Tell whether each figure has line symmetry. Write yes or no. If yes, then tell how many lines of symmetry the figure has.
B
Multi-Part Lesson 11-4 Symmetry
PART C PAGES 552–555
Multi-Part Lesson 11-2 (continued)
Extra Practice
Extra Practice
Extra Practice
EP36–EP37
1 1; 1; 1 _
2
4
2.
5. yd = 24 ft 8
4. ft = 48 in. 4
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP36
EP36
4. The price of oranges at Super Mart is 6 for $2. The price of oranges at Food Palace is 9 for $3. Which is the better value? How much does each orange cost at each store?
3. Tony’s house is 8 blocks from school. If Tony walks to and from school every day, how many blocks does he walk during two school weeks? 160 blocks
They are equal; about 33¢
2. Anita bought a sandwich for $3, a salad for $2, a glass of juice for $1, and a cookie for $1. How much did she spend for lunch? $7
PAGES 592–593
1. Mark painted a mural on each of the 4 walls of his room. It took him 6 hours and 25 minutes for each wall. How long did it take him to finish? 25 h and 40 min
20 feet and 20 ft > 17 ft
6. in. = 5 ft 60 8. A python at a zoo is 6 yards 2 feet long. A cobra at the same zoo is 17 feet long. Which snake is longer? Explain. python; 6 yard 2 feet =
Solve. Use the solve a simpler problem strategy.
PART D
yes
7. A sign at an amusement park says that a person must be 52 inches tall in order to ride a roller coaster. If Kwam is 4 feet 6 inches tall, is he tall enough to ride the roller coaster?
2. 3 ft = in. 36
1. 24 in. = ft 2
Complete.
PAGES 590–591
I. 14 yards F
H. 14 feet
2
3. 15 ft = yd 5
G. 140 inches
D. 2 yards B
PART C
F. 14 inches
C. 22 feet
B. 2 feet
4.
A . 2 inches
3.
Choose the best estimate for each length.
1.
4
1 _ 1; 1 _ ;11
4
3/12/10 1:52 PM
PART A
1 1 Estimate. Then measure each to the nearest inch, _ inch, and _ inch.
3 cm
D. 1 kilometer
C. 1 meter
C
40 cm; 38 cm
12 cm
7 cm
2.
9 mm
3.
3 mm
40 mm; 34 mm
8 mm
3 mm
20 units; 22 units
5.
EP02_EP40_EM_EP_103030.indd EP37
1. Sample answer: length: 8 units, width: 2 units
3. Each bunch of flowers has 12 tulips and 23 daisies. There are 6 bunches of flowers. How many flowers are there in all? 210 flowers
1. The perimeter of a rectangular yard is 20 meters. What are the possible lengths of the sides?
6.
13 ft
13 ft
13 ft
PAGES 606–607
3/12/10 1:52 PM
Extra Practice EP37
197 limes and 392 oranges
4. There are 324 apples. There are 68 fewer apples than oranges and 127 more apples than limes. How many limes and oranges are there?
2. Stella bought 5 pencils for 25¢. How much would she pay for 15 pencils? 75¢
10 units; 14 units Use any strategy to solve each problem.
PART B
4.
13 ft
13 ft
PAGES 602–604
20 units; 26 units
13 ft
13 ft
13 ft
80 ft; 104 ft
Estimate. Then find the perimeter of each rectangle in units.
1.
H. 26 meters
G
4 cm
PAGES 594–598
G. 26 centimeters I. 26 kilometers
F. 26 millimeters
4.
2.
Estimate the perimeter. Then find the exact perimeter.
PART A
Multi-Part Lesson 12-3 Perimeter
B. 1 centimeter
A . 1 millimeter
3.
Choose ose the best esti estimate.
1.
Measure each object to the nearest centimeter.
B
Multi-Part Lesson 12-2 Metric Measurement PAGES 585–589
PART A
Extra Practice
B
Multi-Part Lesson 12-1 Customary Measurement
Extra Practice
EP38–EP39
Extra Practice
21 square units
2. 3m
B
12 square meters
4m
3.
15 fluid ounces 15 pints 15 quarts 15 gallons A
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP38
EP38
10. 4 c 2 pt =
7. 3 qt 1 gal <
Compare. Use >, <, or =.
11. 2 qt 9 c <
8. 3 c 4 fl oz >
5. fl oz = 5 c 40
1 fluid ounce 1 cup 1 quart 1 gallon D
4. 2 gal = qt 8
A. B. C. D.
F. 2 fluid ounces G. 20 fluid ounces H. 2 quarts I. 2 gallons H
2. 32 fl oz = c 4
5.
2.
1. 6 c = pt 3
Complete.
PART C
F. 6 fluid ounces G. 60 fluid ounces H. 6 cups I. 6 pints F
4.
A. B. C. D.
1.
PAGES 627–631
6 fluid ounces 6 cups 6 pints 6 quarts B
6 in.
18 square inches
12. 10 pt 1 gallon >
9. 3 qt 5 pt >
6. 10 pt = c 20
PAGES 632–634
F. 1 fluid ounce G. 1 cup H. 1 pint I. 1 quart G
A. B. C. D.
3 in.
3. 8 qt = pt 16
6.
3.
Choose the most reasonable estimate for each capacity.
PART A
Multi-Part Lesson 13-1 Capacity
1.
Estimate the area. Then find the exact area of each square or rectangle.
3/12/10 1:53 PM
1 mL
11 mL
1L 1L
11 L 11 L 4.
2.
B
235 mL
710 mL
EP02_EP40_EM_EP_103030.indd EP39
3.
1.
F F. 1 ounce G. 10 ounces H. 1 pound I. 10 pounds 4.
B A . 8 ounces B. 8 pounds C. 80 pounds D. 8 tons
I
F. 70 ounces G. 7 pounds H. 700 pounds I. 7 tons
2.
3/12/10 1:53 PM
Extra Practice EP39
PAGES 642–647
235 L 235 mL
8 ounces 80 pounds 8 pounds 8 tons
A. B. C. D.
A
PAGES 638–640
710 L 710 mL
Choose the most reasonable estimate for the weight of each object.
PART A
Multi-Part Lesson 13-2 Weight and Mass
3.
1.
PAGES 636–637
2. Mrs. Hansen made some soup. She put one cup of soup in each bowl for her four children. There is enough soup left to put two cups of soup in each bowl below. How many pints of soup did she make? 4 pints
Choose the more reasonable estimate for each capacity.
PART E
1. Melinda uses 1 pint of paint to cover each table she makes. She has the paint shown below. Each can holds 1 gallon of paint. How many more gallons of paint are needed to cover 24 tables? 2 gallons
Solve. Use the work backward strategy.
PART D
PAGES 608–615
Multi-Part Lesson 13-1 (continued)
C
PART A
B
Multi-Part Lesson 12-4 Area
Extra Practice
Extra Practice
18
4g
4 kg 4 kg 2.
350 g
PAGES 658–661
350 kg 350 g
PAGES 654–657
7 6 5
Extra Practice
Extra Practice
EP02_EP40_EM_EP_103030.indd EP40
EP40
$0.95
$2.45
milk
$1.60
taco
Cost
salad
Item
Pedro’s Lunch
Use any strategy to solve. 1. Pedro has $3.75 left from lunch. He bought the items shown in the table below. How much money did he have before lunch? $8.75
PART B
8
9
2 3 7 6 5
2 3
Mow Grass
Pull Weeds
Rake leaves
Chore
45
15
30
Time to Complete (minutes)
Allison’s Chores
7:00
PAGES 662–663
2. Allison completed the chores shown in the table below. If she finished her chores at 8:30, what time did she start?
8
9
10
11 12 1
10
11 12 1
2 hours 30 minutes
4. The clock shows when Helki’s hockey practice started. It is 6:30 when it stops. 1 hour 45 minutes
2. Start Time: 10:15 End Time: 12:45
3. The clock shows when Lydia started ice skating. It is 12:45 when she stops. 1 hour 15 minutes
Find each elapsed time.
1. Start Time: 2:30 End Time: 4:45 2 hours 15 minutes
The following are times of tennis matches. Find the length of each match.
PART A
Multi-Part Lesson 13-3 Elapsed Time
1.
Choose the more reasonable estimate for the mass of each object.
PART D
5. 1 lb and 2 oz = oz 6. 3 T and 400 lb = lb 6,400
4. 2 T = lb 4,000
3. 64 oz = lb 4
2. 8,000 lb = T 4
PAGES 648–651
1. 2 lb = oz 32
Complete.
PART C
Multi-Part Lesson 13-2 (continued)
3/12/10 1:54 PM
Extra Practice
Extra Practice
EP40
B
1-1 PAGE XX
Extra Practice Answer Appendix
2-4
EP40a Extra Practice Answer Appendix
12. 0, 9, 18, 27, 36
baseball tennis
baseball tennis
football
soccer
Sport
basketball
Tally
basketball
football
Sport
2
1
2
4
3
Frequency
Pets
PAGE XX
PAGE XX
1
1
3
4
3
Frequency
Favorite Sports
fish Favorite Sports
lizard fish
lizard
soccer
2.
bird
cat
Pet
bird
Tally
dog
Pets
7-1
3-1
dog
cat
Pet
11. 0, 8, 16, 24, 32
PAGE XX
1.
10. 0, 12, 24, 36, 48
9. 0, 6, 12, 18, 24
8. 0, 7, 14, 21, 28
7. 0, 4, 8, 12, 16
6. 1, 2, 3, 4, 6, 8, 12, 24
5. 1, 11
4. 1, 5, 7, 35
3. 1, 2, 4, 8, 16
2. 1, 2, 3, 6, 9, 18
1. 1, 2, 3, 4, 6, 9, 12, 18, 36
PART A
Multi-Part Lesson
PART A
Multi-Part Lesson
4.
11. 500,000 + 9,000 + 900 + 9; five hundred nine thousand, nine hundred nine
12. 200,000 + 50,000 + 300 + 40 + 5; two hundred fifty thousand, three hundred forty-five
3.
2.
1.
PART A
Multi-Part Lesson
10. 20,000 + 7,000 + 600 + 20 + 1; twenty-seven thousand, six hundred twenty-one
9. 80,000 + 1,000 + 300 + 6; eighty-one thousand, three hundred six
8. 10,000 + 4,000 + 500 + 20 + 3; fourteen thousand, five hundred twenty-three
7. 8,000 + 900 + 50 + 4; eight thousand, nine hundred fifty-four
PART A
Multi-Part Lesson
8
9
X X X
10
X
5
X X
6
X
8 = 48 minutes
58 04558
8 5
Leaf
8 0 5 0 0 0 0
8 = 48 inches
8 8 9 4 5 5 6 7 8 9 9 0
Leaf
4
X X
Miles Hiked per Day
7
4 8 9 10 11 12 13 4
7-2
Seeds That Sprouted
Stem
4
4 5 6
Stem
3
X
6
X X
4/30/10 10:05 AM EP40a-EP40d_EP_AA_101791.indd 3
2.
1.
PART C
2.
1.
PART B
Multi-Part Lesson
7
X
11
X
PAGE XX
PAGE XX
2.
1.
4.
3.
B
Red
3
2
1
tails
heads
1 2 3
1 2 3
1 2 3
Heads Heads, 0 Tails Tails, 0
0
Heads, 2 Tails, 2
2
5 Heads, 5 Tails, 5
tails, section 1 tails, section 2 tails, section 3 tails, section 4
Extra Practice Answer Appendix
3,1 3,2 3,3
2,1 2,2 2,3
1,1 1,2 1,3
section 1 section 2 section 3 section 4
4 Heads, 4 Tails, 4
PAGE XX
4/30/10 10:05 AM
EP40b
heads, section 1 heads, section 2 heads, section 3 heads, section 4
Heads, 3 Tails, 3
3
Number Cube
section 1 section 2 section 3 section 4
Heads, 1 Tails, 1
1
red, yellow yellow, yellow
Yellow
Counter 2
7-4
red, red Yellow yellow, red
Red
PART A
Multi-Part Lesson
Counter 1 Coin
EP40a–EP40b
EP40a-EP40d_EP_AA_101791.indd 2
Extra Practice Answer Appendix
Extra Practice Answer Appendix
Extra Practice Answer Appendix
Extra Practice Answer Appendix
EP40c–EP40d
0.9
0.6
3.
5.
6.
4.
2.
Extra Practice Answer Appendix
EP40a-EP40d_EP_AA_101791.indd 4
EP40c Extra Practice Answer Appendix
0.2
B
1.
PART A
8-1
0.5
0.1
0.7
PAGE XX
3.
2.
1.
Part
D
Multi-Part Lesson
Page XX
8-1
4/30/10 EP40a-EP40d_EP_AA_101791.indd 10:06 AM 5
6.
6.
5.
4.
Extra Practice Answer Appendix
4/30/10 10:06 AM
EP40d
Extra Practice Answer Appendix
Multi-Part Lesson
Extra Practice Answer Appendix
R1 Photo Credits R01_R02_EM_PC_103092_Workup.indd R1
iv Comstock Images/Getty Images; vi (tl tr)The McGraw-Hill Companies, (bl br)Doug Martin; x Eduardo Garcia/Photographer’s Choice/Getty Images; xi Perry Mastrovito/CORBIS; xii Tim Ridley/Getty Images; xiii G.K. & Vikki Hart/Getty Images; xiv (t)G.K. Vikki Hart/Getty Images, (b)C Squared Studios/ Getty Images; xv Don Farrall/Photodisc/Getty Images; xvi Thinkstock/ Wonderfile; xviii Martin Harvey/Digital Vision/Getty Images; xix Siede Preis/ Photodisc/Getty Images; xx (l)CORBIS, (r)Getty Images; xxi Getty Images; xxii Photolibrary/Index Stock Imagery; xxiii Design Pics/FotoSearch; 0–1 Laurie Rubin/Getty Images; 4 Kim Karpeles/Alamy Images; 6 GK Hart/Vikki Hart/ Getty Images; 8 Eduardo Garcia/Photographer’s Choice/Getty Images; 12 Martin Harvey/Getty Images; 13 Scott Camazine/Photo Researchers, Inc.; 14 Mark Steinmetz; 20 John Giustina/Iconica/Getty Images; 22 Digital Vision/ Getty Images; 24 Robert E Daemmrich/Stone/Getty Images; 28 Don Smith/ Photodisc/Getty Images; 30 Michael Kappeler/AFP/Getty Images; 36 (t)Image Source/Punchstock, (b)Index Stock Imagery; 38 Michele Falzone/ Photographer’s Choice/Getty Images; 40 Don Klumpp/Photographer’s Choice/Getty Images; 42 (t)Richard Hutchings/Digital Light Source (b)Ed-Imaging; 45 (t)Brand X Pictures/Alamy Images, (b)2006 Photos To Go/ Index Open/Index Stock Imagery NY; 48 Ed-Imaging; 51 CORBIS; 53 (l) Comstock Images/Alamy Images, (r)Mark Steinmetz; 54 Ed-Imaging; 55 (t)Photodisc/Getty Images, (b)Getty Images; 56 Comstock/PunchStock; 59 Perry Mastrovito/CORBIS; 60–61 (bkgd)Jeff Rotman/Photographer’s Choice/Getty Images; 75 The McGraw-Hill Companies; 77 Stockbyte/Getty Images; 78 S.T. Yiap/Alamy Images; 81 C Squared Studios/Getty Images; 82 BananaStock/Alamy Images; 83 Mark Steinmetz; 84 Paul Seheult/Eye Ubiquitous/CORBIS; 86 Lon C. Diehl/PhotoEdit; 89 Mark Steinmetz; 90 Getty Images; 93 (l)Mark Steinmetz, (c)Getty Images, (r)C Squared Studios/Getty Images; 94 (bl)John Van Hasselt/CORBIS Sygma, (bc)Bettmann/CORBIS, (br)Webster & Stevens Collection/Museum of History and Industry, Seattle/ CORBIS; 94–95 (bkgd)Tracy Hebden/Alamy Images; 95 (l)SuperStock, (r) Rachel Epstein/PhotoEdit; 96 Howard Shooter/Getty Images; 97 C Squared Studios/Getty Images; 98 (t)G.K. Vikki Hart/Getty Images, (bl)Brian Hagiwara/ PictureArts/CORBIS, (br)Stockdisc/PunchStock; 99 Mark Steinmetz; 100 Tetra Images/Alamy Images; 101 Nick White/Getty Images; 102 Kevin Schafer/ zefa/CORBIS; 103 (t)Richard Hutchings/Digital Light Source, (c)CORBIS, (b)Ed-Imaging; 104 106 Ed-Imaging; 107 Bluemoon Stock/Getty Images; 109 Tim Ridley/Getty Images; 110 Dennis Macdonald/PhotoEdit; 111 Mark Richards/PhotoEdit; 113 (l)C Squared Studios/Getty Images, (r)Getty Images; 115 MBC Design Studio/iStockphoto; 117 Getty Images; 128 (t)Getty Images, (b)Ingram Publishing/Alamy Images; 129 Mark Steinmetz; 134 (t)G.K. & Vikki Hart/Getty Images, (bl)CMCD/Getty Images, (br)Stockdisc/PunchStock; 135 (t)Mark Steinmetz, (b)Stockbyte/PunchStock; 136 Don Smetzer/ PhotoEdit; 139 Jacques Cornell/The McGraw-Hill Companies; 142 Stockdisc/ Jupiterimages/Getty Images; 146–147 (bkgd)Roine Magnusson/Getty Images 147 (inset)Joe McDonald/CORBIS; 148 Jim Cummins/CORBIS; 149 Photodisc/ Getty Images; 150 Stockdisc/PunchStock; 151 (t)CORBIS, (b)Ed-Imaging; 154 G.K. Vikki Hart/Getty Images; 155 Mark Steinmetz; 156 (l to r)Mark Steinmetz, (others)CORBIS; 157 Siede Preis/Getty Images; 158 altrendo images/Getty Images; 164 Ed Bock/Getty Images; 170 Philip Scalia/Alamy Images; 177 (l)Ken Karp/The McGraw-Hill Companies, (r)C Squared Studios/ Getty Images; 185 Hutchings Photography; 187 Jurgen Freund/JACANA/HOAQUI/ImageState; 188 George Hall/CORBIS; 189 CORBIS; 190 Ren Long/AP Images; 194 (t)G.K. Vikki Hart/Getty Images, (b)C Squared Studios/Getty Images; 200 CORBIS; 202 (t)Mark Steinmetz, (b)Photodisc Collection/Getty Images; 203 Mark Steinmetz; 204 (t)Richard Hutchings/Digital Light Source, (b)Ed-Imaging; 205 CORBIS; 210 Food Image Source/Frank Rogozienski/ StockFood; 211 INTERFOTO Pressebildagentur/Alamy Images; 214 Ed-Imaging; 215 The McGraw-Hill Companies; 218 (l)Mark Steinmetz, (r)Michael Houghton/StudiOhio; 220 Richard Hutchings/PhotoEdit; 224 (inset)Daniel A. Bedell/Animals Animals/Earth Scenes; 224–225 (bkgd)David Tipling/Lonely Planet Images; 228 Robin Lynne Gibson/Taxi/Getty Images; 229 age fotostock/SuperStock; 234 Natphotos/Getty Images; 237 238 Mark Steinmetz; 241 Cooperphoto/CORBIS; 243 Robert Lubeck/Animals Animals/Earth Scenes; 244 G.K. & Vikki Hart/Getty Images; 246 (l)Colin Keates/Dorling Kindersley/Getty Images, (r)Don Farrall/Photodisc/Getty Images; 252 Getty Images; 253 (l)Ryan McVay/Getty Images, (r)Michael Houghton/StudiOhio
Unless otherwise credited, all currency courtesy of the US Mint.
Photo Credits
4/23/10 11:14 AM
Photo Credits R1
258 Getty Images; 260 Photodisc/Getty Images; 261 CMCD/Getty Images; 262–263 (bkgd)CORBIS; 264 Mark Newman/Photo Researchers; 265 Christian Petersen/Getty Images Sport/Getty Images; 267 Ed-Imaging; 268 David Young-Wolff/PhotoEdit; 269 (l)C Squared Studios/Getty Images, (r) Michael Houghton/StudiOhio; 272 Ryan McVay/Getty Images; 275 (t)Michael Houghton/StudiOhio, (b)Siede Preis/Getty Images; 277 Mark Richards/ PhotoEdit; 281 Ed-Imaging; 283 Craig Lovell/Terra/CORBIS; 287 Ryan McVay/Getty Images; 293 Stockbyte/Getty Images; 294 Tami Chappell/ America 24-7/Getty Images; 295 Michael Houghton/StudiOhio; 296 CORBIS; 297 Tony Freeman/PhotoEdit; 298 Thinkstock/Wonderfile; 302 Brand X/ SuperStock; 304 CORBIS; 307 Michael Houghton/StudiOhio; 308 SuperStock; 309 Sergio Pitamitz/Robert Harding World Imagery/CORBIS; 311 (t to b) Richard Hutchings/Digital Light Source, CORBIS, Ed-Imaging; 312 Ed-imaging; 314–315 Mauritius/SuperStock; 320 blickwinkel/Alamy Images; 323 Mark Steinmetz; 328 G.K. Vikki Hart/Getty Images; 330 Creatas/SuperStock; 334 Barros & Barros/Stone/Getty Images; 335 (bl)Stockdisc/Getty Images, (br) PhotoLink/Getty Images; 340 Jeremy Woodhouse/Getty Images; 341 (t)C Squared Studios/Getty Images, (b)Siede Preis/Getty Images; 342 C Squared Studios/Getty Images; 343 Ingram Publishing/age fotostock; 345 352 Ed-Imaging; 357 (t)C Squared Studios/Getty Images, (b)Ed-Imaging; 358 Ed-Imaging; 359 Getty Images; 360–361 David R. Frazier Photolibrary, Inc./ Alamy Images; 364 Richard Lewisohn/Photodisc/Getty Images; 366 Getty Images; 374 CORBIS; 377 (r)Jupiterimages, (others)Stockdisc/PunchStock; 385 Stockbyte/PunchStock; 388 The McGraw-Hill Companies; 391 Mark Steinmetz; 393 Wim van den Heever/Getty Images; 394 Martin Harvey/ Digital Vision/Getty Images; 395 Alan Carey/CORBIS Yellow/CORBIS; 403 Purestock/PunchStock; 404 Stockdisc/PunchStock; 405 (tr)C Squared Studios/Getty Images, (others)Burke/Triolo Productions/Getty Images; 411 Digital Vision Ltd.; 413 Mark Steinmetz; 419 Stockdisc/PunchStock; 421 MedioImages/SuperStock; 424–425 (bkgd)Digital Vision/Getty Images; 426 Doug Menuez/Getty Images; 427 (tl)Joe Polillio/The McGraw-Hill Companies, (r)Brand X Pictures/PunchStock, (bl)The McGraw-Hill Companies; 430 Greg Probst/Encyclopedia/CORBIS; 433 (t)Richard Hutchings/Digital Light Source, (c)CORBIS, (b)Ed-Imaging; 445 Myrleen Ferguson Cate/PhotoEdit; 448 Tetra Images/Getty Images; 453 Glen Allison/Stockbyte/Getty Images; 456 Kaku Kurita/Time & Life Pictures/Getty Images; 460 David Madison/ CORBIS; 461 Michael Houghton/StudiOhio; 462 Mauritius/SuperStock; 463 Mark Steinmetz; 464 Brand X Pictures/PunchStock; 465 G.K. Vikki Hart/ Getty Images; 466 (t)Mark Steinmetz, (b)Ed-Imaging; 467 Gary Neil Corbett/ SuperStock; 468 Ed-Imaging; 470 BigStockPhoto.com; 471 Darryl Leniuk/ Lifesize/Getty Images; 474 Getty Images; 475 (l to r, t to b)Photodisc/Getty Images, 2006 Photos to Go/Photolibrary/Index Stock Imagery, CORBIS, Ken Karp/The McGraw-Hill Companies; 476 Ed-Imaging; 478 Bettmann/CORBIS; 479 John Cancalosi/Peter Arnold, Inc.; 482–483 (bkgd)Osports/NewSport/ CORBIS; 483 (l)AFP/Getty Images, (r)Getty Images; 494 Getty Images; 495 (l) Getty Images, (t)S. Wanke/PhotoLink/Getty Images, (cr)CORBIS, (b)Comstock Images/Alamy Images; 496 (l)Davies and Starr/Stone/Getty Images, (r)Siede Preis/Getty Images; 497 (l)C Squared Studios/Getty Images, (r)Ryan McVay/Getty Images; 498 McGraw-Hill Companies; 499 Thomas Northcut/Getty Images; 500 Ken Karp/The McGraw-Hill Companies; 501 (l)C Squared Studios/Getty Images, (c)Brand X Pictures/Getty Images, (r)Stockdisc/PunchStock; 505 (l)Mark Steinmetz, (r)Stockbyte/Getty Images; 509 Photos.com/Jupiterimages; 510 McGraw-Hill Companies; 511 Lawrence Manning/CORBIS; 514 Photodisc/Getty Images; 515 (t)Ryan McVay/Getty Images, (c)Stockbyte/Getty Images, (bl)Image Source/Alamy Images, (br)D. Hurst/Alamy Images, (frame)Creatas/SuperStock, (couple)Purestock/ Jupiterimages; 516 (tl)Jorg Greuel/Photographer’s Choice/Getty Images, (tr)Brand X Pictures/Getty Images, (bl)Thomas Northcut/Getty Images, (bc)Ken Karp/McGraw-Hill Companies, (br)Purestock/Alamy Images; 518 Ed-Imaging; 519 CORBIS; 520–521 (inset)Steve Gorton/Dorling Kindersley/Getty Images, (bkgd)Piotr Adamczyk shapencolour/Alamy Images; 522 (t)Richard Hutchings/Diital Light Source, (b)Ed-Imaging; 524 Mark Steinmetz; 533 (l c)Siede Preis/Getty Images, (r)Image Source/ Getty Images; 535 (l)Brand X Pictures/PunchStock, (c)Siede Preis/Getty Images, (r)Jupiterimages/Comstock Premium/Alamy Images; 536 L. Clarke/ CORBIS; 538 (t)Brand X/ImageState, (bl)C Squared Studios/Getty Images, (br)Getty Images; 550 Mark Steinmetz; 556 Ed-Imaging; 557 Ryan McVay/ Getty Images; 558 (t)Photos.com/Jupiterimages, (b)C Squared Studios/Getty
Photo Credits
R2–R3
Photo Credits
R01_R02_EM_PC_103092_Workup.indd R2
R2 Photo Credits
Images; 559 Ed-Imaging; 561 Photos.com/Jupiterimages; 562 (l)Gerry Ellis/ Getty Images, (r)Ryan McVay/Getty Images; 564–565 (inset)UpperCut Images/Getty Images, (bkgd)Denis Tangney Jr./Photodisc/Getty Images; 568 Darrell Gulin/CORBIS; 569 (t)Mark Steinmetz, (b)CMCD/Getty Images; 570 (l)Image Source/PunchStock, (c)C Squared Studios/Getty Images, (b)Martin Harvey/Gallo Images/Getty Images; 571 Mark Steinmetz; 572 Gerben Oppermans/Getty Images; 573 (t to b)Getty Images, Creatas/ Punchstock, Mark Steinmetz, Photodisc/Getty Images; 574 (l to r, t to b)Getty Images, Getty Images, Siede Preis/Getty Images, Kurt Scholz/SuperStock, image100/CORBIS; 584 (l)Design Pics Inc./Alamy Images, (r)Creatas Images/ Jupiterimages; 585 PhotoLink/Getty Images; 586 Photolibrary/Index Stock Imagery; 587 (tl)C Squared Studios/Getty Images, (tc)The McGraw-Hill Companies, (tr)Photos.com/Jupiterimages, (br)ilian animal/Alamy Images; 588 (l to r, t to b)The McGraw-Hill Companies, Siede Preis/Getty Images, C Squared Studios/Getty Images, C Squared Studios/Getty Images; 589 (l to r, t to b)Stockdisc/PunchStock, G.K. Vikki Hart/Getty Images, The McGraw-Hill Companies, Siede Preis/Getty Images, Image Ideas Inc./Index Stock; 590 Blue Line Pictures/The Image Bank/Getty Images; 592 C Squared Studios/Getty Images; 593 Getty Images; 595 (t)Jupiterimages, (others) Photos.com/Jupiterimages; 596 (l to r, t to b)Jupiterimages, Getty Images, D. Hurst/Alamy Images, Michael Grimm/Getty Images; 597 (l to r, t to b) Jeffrey Coolidge/CORBIS, Westend61 GmbH/Alamy Images, Ingram Publishing/Alamy Images, Jupiterimages/Comstock Images/Alamy Images, The McGraw-Hill Companies; 598 (l to r, t to b)The McGraw-Hill Companies, Jill Braaten/The McGraw-Hill Companies, Photodisc/Getty Images, Joseph Sohm-Visions of America/Getty Images, CORBIS; 599 (l to r, t to b)Getty Images, Ryan McVay/Getty Images, Jupiterimages, Ingram Publishing/ Alamy Images; 600 (inset)Sea World of California/CORBIS; 600–601 (bkgd) CORBIS; 601(inset)Robert Marien/CORBIS Yellow/CORBIS; 605 (t)PhotoLink/ Getty Images, (b)Ed-Imaging; 606 Ed-Imaging; 607 age fotostock/SuperStock; 609 The McGraw-Hill Companies; 613 (l)Siede Preis/Getty Images, (r)The McGraw-Hill Companies; 614 Ed-Imaging; 617 (tl)Stockbyte/PictureQuest/ Jupiterimages, (tr)Getty Images, (b)C Squared Studios/Getty Images; 618 (tl) Creatas/PunchStock, (r)Getty Images, (bl)CORBIS; 621 (t)C Squared Studios/ Getty Images, (c)USDA Natural Resources Conservation Service, (b)Joe Polillio/The McGraw-Hill Companies; 624 Mark Steinmetz; 626 Andy Crawford/Dorling Kindersley/Getty Images; 627 Ed-Imaging; 628 (l to r, t to b)Lawrence Manning/CORBIS, Ed-Imaging, Ed-Imaging, Ed-Imaging, Ed-Imaging, GK Hart/Vikki Hart/The Image Bank/Getty Images, Mark Steinmetz, Mark Steinmetz, Jill Braaten/The McGraw-Hill Companies; 629 (l to r, t to b)Burke/Triolo Productions/FoodPix/Getty Images, Ingram Publishing/Alamy Images, 2006 Photos to Go/Index Open, Photos.com/ Jupiterimages, CORBIS, Jacques Cornell/The McGraw-Hill Companies; 630 (l to r, t to b) John Foxx/Stockbyte/Getty Images, Jupiterimages, Jupiterimages/Brand X/Alamy Images, The McGraw-Hill Companies, PhotoSpin, Inc./Alamy Images, Burke/Triolo Productions/Brand X/CORBIS, CMCD/Photodisc/Getty Images; 631 Comstock Images/Alamy Images; 632 Ed-Imaging; 634 (l to r, t to b)Mark Steinmetz, Stockbyte/Getty Images, Mark Steinmetz, Mark Steinmetz, Mark Steinmetz; 635 (t)Mark Steinmetz, (b)Ed-Imaging; 636 Mark Steinmetz; 637 (l)Mark Steinmetz, (others)CORBIS; 638 (t)Getty Images, (bl)Roger Weber/Digital Vision/Getty Images, (br) Ed-Imaging; 639 (l to r, t to b)Comstock/Jupiterimages, Bob Scott/Photonica/ Getty Images, Dynamic Graphics Value/SuperStock, Jacques Cornell/The McGraw-Hill Companies, Inc., C Squared Studios/Getty Images; 640 (l to r, t to b)Ryan McVay/Stone/Getty Images, McGraw-Hill Companies, Lawrence Manning/Spirit/CORBIS, The McGraw-Hill Companies, Andy Crawford/Dorling Kindersley/Getty Images, The McGraw-Hill Companies; 641 (l to r, t to b) Michael Matisse/Getty Images, Photodisc/Getty Images, The McGraw-Hill Companies, Russell Illig/Photodisc/Getty Images; 642 (t)Lew Robertson/ Jupiterimages, (others)Ed-Imaging; 644 (l to r, t to b)CMCD/Getty Images, CMCD/Getty Images, Car Culture/Collection Mix: Subjects/Getty Images, The McGraw-Hill Companies, Caren Alpert/FoodPix/Getty Images, The McGrawHill Companies Inc.; 645 (l to r, t to b)C Squared Studios/Photodisc/Getty Images, C Squared Studios/Photodisc/Getty Images, Jupiterimages/ Thinkstock/Alamy Images, Stockdisc/Getty Images, CORBIS/Jupiterimages; 646 (l to r, t to b)Siede Preis/Photodisc/Getty Images, CORBIS, Siede Preis/ Photodisc/Getty Images, Pete Starman/Digital Vision/Getty Images, G.K. Vikki Hart/Photodisc/Getty Images, Jeffrey Coolidge/CORBIS, David R. Frazier Photolibrary, Inc./Alamy Images; 647 (l to r, t to b)Mark Steinmetz, Getty Images, Mark Steinmetz, Mark Steinmetz, Mark Steinmetz, Getty Images, Ingram Publishing/Alamy Images; 648 Ingram Publishing/Alamy Images; 650 Design Pics/FotoSearch; 651 (tl)C Squared Studios/Getty Images, (tr)G.K. Vikki Hart/Getty Images, (bl)Joe Polillio/The McGraw-Hill Companies, Unless otherwise credited, all currency courtesy of the US Mint. T1 (tl)Creatas Images/Jupiterimages, (tr)Andersen Ross/Getty Images, (bl)Getty Images, (bl)The McGraw-Hill Companies; T2 Comstock Images/ Getty Images; T4–T5 Richard Hutchings/Digital Light Source, Inc.; T5 (b)Jose Luis Pelaez/Getty Images, (others)Richard Hutchings/Digital Light Source, Inc.; T8 Getty Images; T13 Comstock/PictureQuest; T15 Huntstock/Getty Images; T18 Digital Vision/Getty Images; T19 BananaStock/PunchStock; T22 (tl tr)The McGraw-Hill Companies, (bl br)Doug Martin; T23 (br)The McGraw-Hill Companies, (others)Doug Martin (15)courtesy Dinah Zike; T25 The McGraw-Hill Companies; T26 Blend Images/Alamy Images; ii Eduardo Garcia/Photographer’s Choice/Getty Images; iii Perry Mastrovito/CORBIS Yellow/CORBIS; iv Tim Ridley/Dorling Kindersley/Getty Images; v G.K. & Vikki Hart/Getty Images; vi (t)G.K. Vikki Hart/Getty Images, (b)C Squared Studios/ Getty Images; vii Don Farrall/Photodisc/Getty Images; viii Thinkstock/ Wonderfile; x Martin Harvey/Digital Vision/Getty Images; xi Siede Preis/Getty Images; xii (bl)Getty Images, (br)Brand X Pictures/CORBIS; xiii Photodisc/ Getty Images; xiv Photolibrary/Index Stock Imagery; xv Design Pics/ FotoSearch; xvi–xvii Laurie Rubin/Stone/Getty Images; A2–A3 (bkgd)Vico Collective/Blend Images/Getty Images; A3 (r)Sue Z. Beers.
Teacher Edition Photo Credits
McGraw-Hill would like to acknowledge the artists and agencies who contributed to illustrating this program: Cover Jim Talbot represented by Mendola Artists; Kenny Kiernan represented by Mendola Artists; Argosy Publishing; AA Reps, Inc.; Gary Ciccarelli represented by AA Reps, Inc., Keith Batcheller, Jean-pascal Donnot, Shawn McKelvey, Garth Glazer represented by AA Reps, Inc.; Dick Gage represented by Deborah Wolfe Ltd., Mark Collins represented by Deborah Wolfe Ltd., Richard Carbajal represented by Deborah Wolfe Ltd.; Terri Chicko represented by Cornell & McCarthy, LLC; Bill Smith Studio; Monotype, LLC; Articulate Graphics; Peter Grosshauser, Garry Colby represented by Cliff Knecht Artist Representative; Fian Arroyo Illustration, Inc.; Precision Graphics; TSI Graphics.
(br)2006 Photos to Go/Index Open; 652 (bl)David Toase/Photodisc/Getty Images, (bc)Iconotec/Alamy Images, (br)Dianne Nelson; 652–653 (bkgd) Wayne Levin/Taxi/Getty Images; 654 Ed-Imaging; 655 (l to r, t to b)Big Cheese Photo/Jupiterimages, Ron Chapple/Jupiterimages, Photodisc/Getty Images, CORBIS; 656 (l to r, t to b)Monotype, LLC, McGraw-Hill Companies, C Squared Studios/Photodisc/Getty Images, ThinkStock LLC/Index Stock Imagery, Image Farm Inc./Alamy Images, Charlie Roy/Workbook Stock/Getty Images, C Squared Studios/Getty Images, C Squared Studios/Getty Images; 657 Photodisc/Getty Images; 658 2006 Photos to Go/Index Open; 661 G.K. Vikki Hart/Getty Images; 662 CORBIS; 663 (l to r, t to b)G.K. Vikki Hart/Getty Images, G.K. Vikki Hart/Getty Images, C Squared Studios/Photodisc/Getty Images; 665 (l to r, t to b) Peter Dazeley/Dorling Kindersley/Getty Images, McGraw-Hill Companies, Jupiterimages, Masterfile; 666 (l to r, t to b)Mark Steinmetz, Mark Steinmetz, Judith Collins/Alamy Images, Jan Tadeusz/Alamy Images, Purestock/Getty Images; 667 (l to r, t to b)Thomas Northcut/ Photodisc/Getty Images, Jeffrey Coolidge/Photodisc/Getty Images, PhotoLink/ Getty Images, Ann Cutting/Botanica/Getty Images, G.K. Vikki Hart/Getty Images; 668 (l)Siede Preis/Photodisc/Getty Images, (r)Photodisc/Getty Images; 669 (l to r, t to b)The McGraw-Hill Companies, The McGraw-Hill Companies, The McGraw-Hill Companies, Inc./Nature Picture Library/Alamy Images, Jupiterimages/Brand X/Alamy Images, H. Wiesenhofer/PhotoLink/ Getty Images; 672 (t)Getty Images, (c)Punchstock, (b)Bob Daemmrich/ PhotoEdit/Getty Images; 673 Tim Fuller; 674 (t)BananaStock/Alamy Images, (b)Comstock Images/Alamy; 676 (t)Food Image Source/O’Gara/Bissell/ StockFood, (bl)Stockdisc/PunchStock, (br)Creatas/PunchStock; 677 Comstock/Jupiterimages; 678 Sindre Ellingsen/Alamy Images; 679 Burke/Triolo/Brand X Pictures/Jupiterimages; 680 (t)Laurie Rubin/Getty Images, (b)Getty Images; 681 Brand X Pictures; EP0–EP1 Creatas/ PunchStock; EP28 EP29 Getty Images; EP32 (l)Photodisc/Getty Images, (c)Nancy R. Cohen/Getty Images, (r)Burke/Triolo Productions/Getty Images; EP36 (l)D. Hurst/Alamy Images, (r)C Squared Studios/Getty Images; EP37 (l to r, t to b)G.K. Vikki Hart/Getty Images, C Squared Studios/Getty Images, C Squared Studios/Getty Images, F. Schussler/PhotoLink/Getty Images; EP38 (l to r, t to b)The McGraw-Hill Companies, Ingram Publishing/ Superstock, C Squared Studios/Getty Images, Joe Polillio/The McGraw-Hill Companies, CORBIS, Mark Steinmetz; EP39 (l to r, t to b)Mark Steinmetz, Mark Steinmetz, Mark Steinmetz, Mark Steinmetz, Mark Steinmetz, Mark Steinmetz, Stockdisc/PunchStock, Jeremy Woodhouse/Getty Images, Ryan McVay/Getty Images, Image Source/Jupiterimages; EP40 (l)Getty Images, (r)G.K. & Vikki Hart/Getty Images.
4/23/10 11:14 AM R03_R26_EM_GL_103030.indd R3
álgebra Rama de las matemáticas en la que se usan símbolos, generalmente letras, para explorar relaciones entre cantidades. algebra A branch of mathematics that uses symbols, usually letters, to explore relationships between quantities.
3/12/10 1:57 PM
Glossary/Glosario R3
sumando Cualquier número que se suma a otro.
9 + 3 = 12
suma (sumar, adición) Operación de dos o más sumandos que resulta en una suma.
addend Any numbers being added together.
9 + 3 = 12
add (adding, addition) An operation on two or more addends that results in a sum.
triángulo acutángulo Un triángulo cuyos tres ángulos miden menos de 90°. acute triangle A triangle with all three angles less than 90°.
(Español)
Spanish
Vietnamese
Urdu
ángulo agudo Un ángulo que mide más de 0° y menos de 90°.
Tagalog
Spanish
acute angle An angle with a measure greater than 0° and less than 90°.
English
Haitian Creole
Brazilian Portuguese
Aa
Korean
English
Bengali Russian
Hmong
Cantonese
A bi Arabic
Click on the eGlossary link to find out more about these words in the following 13 languages. C
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
1
Glossary/Glosario
R03_R26_EM_GL_103030.indd R4
2 Week
Snowfall
R4 Glossary/Glosario R
0
2
4
6
8
3
bar graph A graph that compares data by using bars of different lengths or heights to show the values.
Bb
3 × (6 × 2) = (3 × 6) × 2
Associative Property of Multiplication The property that states that the grouping of the factors does not change the product.
(4 + 5) + 2 = 4 + (5 + 2)
Associative Property of Addition The property that states that the grouping of the addends does not change the sum.
area = 6 square units
area The number of square units needed to cover the inside of a region or plane figure without any overlap.
endpoint
angle A figure that is formed by two rays with the same endpoint.
angle/bar graph
Amount of Snow (in.)
R4–R5 Glossary/Glosario ángulo/gráfica de barras
0
2
4
6
8
1
2 Semana
Nevada
3
gráfica de barras Gráfica en la que se comparan los datos usando barras de distintas longitudes o alturas para mostrar los valores.
3 × (6 × 2) = (3 × 6) × 2
propiedad asociativa de la multiplicación Propiedad que establece que la agrupación de los factores no altera el producto.
(4 + 5) + 2 = 4 + (5 + 2)
propiedad asociativa de la suma Propiedad que establece que la agrupación de los sumandos no altera la suma.
área = 6 unidades cuadradas
área El número de unidades cuadradas necesarias para cubrir el interior de una región o figura plana sin traslapes.
extremo
ángulo Figura formada por dos rayos con el mismo extremo.
Cantidad de nieve (pulg)
3/12/10 2:02 PM
R03_R26_EM_GL_103030.indd R5
720 and 90 are compatible numbers for division because 72 ÷ 9 = 8.
compatible numbers Numbers in a problem or related numbers that are easy to work with mentally.
7×2=2×7
3/12/10 2:03 PM
Glossary/Glosario R5
720 y 90 son números compatibles en la división porque 72 ÷ 9 = 8.
números compatibles Números en un problema o números relacionados con los cuales es fácil trabajar mentalmente.
7×2=2×7
propiedad conmutativa de la multiplicación Propiedad que establece que el orden en el que se multiplican dos o más números no altera el producto.
12 + 15 = 15 + 12 12 + 15 = 15 + 12 Commutative Property of Multiplication The property that states that the order in which two numbers are multiplied does not change the product.
propiedad conmutativa de la suma Propiedad que establece que el orden en el que se suman dos o más números no altera la suma.
círculo Figura cerrada en la cual todos los puntos equidistan de un punto fijo llamado centro.
capacidad Cantidad que puede contener un envase, medida en unidades de volumen.
simetría bilateral Propiedad de una figura que le permite ser doblada de manera que las mitades se correspondan exactamente.
simetría bilateral/números compatibles
Commutative Property of Addition The property that states that the order in which two numbers are added does not change the sum.
circle A closed figure in which all points are the same distance from a fixed point, called the center.
capacity The amount of liquid a container can hold.
Cc
bilateral symmetry The property of a figure that allows it to be folded so the two halves match exactly.
bilateral symmetry/compatible numbers
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R6–R7
figuras congruentes Dos figuras con la misma forma y el mismo tamaño. coordenada Uno de los dos números de un par ordenado.
congruent figures Two figures having the same size and the same shape.
coordinate One of two numbers in an ordered pair.
Glossary/Glosario
R03_R26_EM_GL_101807.indd R6
R6 Glossary/Glosario R
cube A three-dimensional figure with six congruent square faces.
1 2 3 4 5 6 7
cubo Figura tridimensional con seis caras cuadradas congruentes.
0
0
1 2 3 4 5 6 7
8 7 6 5 4 3 2 1
plano de coordenadas Gráfica que representa un conjunto de puntos y da la posición de un punto sobre una recta.
8 7 6 5 4 3 2 1
coordinate plane A graph that displays a set of points and gives the position of a point on a line.
(1, 5) El 1 es el número en el eje x y el 5 está en el eje y.
cono Figura tridimensional con una superficie curva, una base circular y un vértice.
cone A three-dimensional figure with a curved surface, a circular base, and one vertex.
In (1, 5), the 1 is the number on the x-axis. The 5 is on the y-axis.
forma compuesto Una figura que se forma con dos o más figuras.
12 tiene los factores 1, 2, 3, 4, 6 y 12.
12 has the factors 1, 2, 3, 4, 6, and 12.
composite shape A figure made up of two or more shapes.
número compuesto Número entero con más de dos factores.
composite number A whole number that has more than two factors.
número compuesto/cubo
12/14/09 9:41 AM
decimales equivalentes Decimales que representan el mismo número.
decimal equivalents Decimals that represent the same number.
denominador El número de abajo en una fracción. 5 _ 6 es el denominador.
denominator The bottom number in a fraction. In _, 6 is the denominator.
R03_R26_EM_GL_101807.indd R7
diameter
diameter A line segment that connects two points on a circle and passes through the center of a circle.
diámetro
12/14/09 9:41 AM
Glossary/Glosario R7
diámetro Segmento de recta que pasa por el centro de conecta dos puntos en un círculo y del un círculo.
6
grado (°) a. Unidad para medir ángulos. b. Unidad de medida que se usa para describir la temperatura. degree (°) a. A unit for measuring angles. b. A unit of measure used to describe temperature.
5 6
punto decimal Punto que separa las unidades de las décimas en un número decimal. 0.8 ó $3.77 decimal point A period separating the ones and the tenths in a decimal number. 0.8 or $3.77
0.3 y 0.30
decimal Número con uno o más dígitos a la derecha del punto decimal, tales como 8.37 ó 0.05.
decimal A number that uses place value, numbers, and a decimal point to show part of a whole.
0.3 and 0.30
datos Números o símbolos que muestran información, algunas veces reunidos de una encuesta o un experimento.
cilindro Figura tridimensional que tiene dos bases circulares paralelas y congruentes y una superficie curva que las une.
cilindro/diámetro
data Numbers or symbols, sometimes collected from a survey or experiment, to show information. Datum is singular; data is plural.
Dd
cylinder A three-dimensional figure having two parallel congruent circular bases and a curved surface connecting the two bases.
cylinder/diameter
Glossary/Glosario
composite number/cube
Glossary/Glosario
R8–R9 Glossary/Glosario
R8 Glossary/Glosario R
elapsed time The amount of time that has passed from beginning to end.
edge
edge The line segment where two faces of a solid figure meet.
Ee
tiempo transcurrido Cantidad de tiempo que ha pasado entre el principio y el fin.
arista
arista El segmento de recta donde concurren dos caras de una figura sólida.
gráfica de barras dobles Gráfica de barras donde se comparan dos grupos de datos relacionados.
3 es el divisor
double bar graph A bar graph that compares two related groups of data.
3 19 división (dividir) Operación de dos números en que el primer número se separa en tantos grupos iguales como indica el segundo número.
3 is the divisor
19 es el dividendo
divisor El número entre el cual se divide el dividendo.
3 19
dividendo El número que se divide.
division (divide) An operation on two numbers in which the first number is split into the same number of equal groups as the second number.
3 19
divisor The number by which the dividend is being divided.
19 is the dividend
A number that is being
3 19
dividend divided.
4 × (1 + 3) = (4 × 1) + (4 × 3)
propiedad distributiva de la multiplicación Para multiplicar una suma por un número, multiplica cada sumando por el número y suma los productos.
Distributive Property of Multiplication To multiply a sum by a number, multiply each addend by the number and add the products.
4 × (1 + 3) = (4 × 1) + (4 × 3)
dígito Símbolo que se usa para escribir números. Los diez dígitos son 0, 1, 2, 3, 4, 5, 6, 7, 8 y 9.
dígito/tiempo transcurrido
digit A symbol used to write numbers. The ten digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
digit/elapsed time
R03_R26_EM_GL_103030.indd R8
Glossary/Glosario
3/12/10 2:03 PM
8
R03_R26_EM_GL_103030.indd R9
47 + 22 is about 50 + 20 or 70.
estimate A number close to an exact value. An estimate indicates about how much.
4
3 6 _ =_
8
3/12/10 2:03 PM
Glossary/Glosario R9
47 + 22 es aproximadamente 50 + 20; ó 70.
estimación Número cercano a un valor exacto. Una estimación indica aproximadamente cuánto.
4
3 6 _ =_
fracciones equivalentes Fracciones que representan el mismo número.
triángulo equilátero Triángulo con tres lados congruentes.
equilateral triangle A triangle with three congruent sides.
equivalent fractions Fractions that represent the same number.
ecuación Oración matemática que contiene el signo de igualdad, (=), el que indica que las dos expresiones son iguales.
Al lanzar una moneda, es equiprobable que caiga cara o escudo.
equiprobable Que tiene la misma posibilidad de ocurrir.
extremos
extremo El punto en cualquiera de los dos lados en que termina un segmento de recta o el punto al principio de un rayo.
extremo/estimación
equation A sentence that contains an equals sign (=), showing that two expressions are equal.
In a coin toss, you are equally likely to flip a head or a tail.
equally likely Having the same chance of occurring.
endpoints
endpoint The point at either end of a line segment or the point at the beginning of a ray.
endpoint/estimate
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R10–R11
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R10
R10 R
2 3 4 4
1 _ 1 1 3 _ , , _, _
fraction A number that represents part of a whole or part of a set.
2 3 4 4
1 _ 1 1 3 _ , , _, _
fracción Número que representa parte de un todo o parte de un conjunto.
fórmula Ecuación que muestra la relación entre dos o más cantidades.
5 × 3 = 15 3 × 5 = 15 15 ÷ 3 = 5 15 ÷ 5 = 3
formula An equation that shows the relationship between two or more quantities.
5+3=8 3+5=8 8-3=5 8-5=3 factor Número con el que se divide exactamente a otro número entero. También es un número multiplicado por otro número.
5 × 3 = 15 3 × 5 = 15 15 ÷ 3 = 5 15 ÷ 5 = 3
familia de operaciones Grupo de operaciones relacionadas que tienen los mismos números.
cara
factor A number that divides a whole number evenly. Also a number that is multiplied by another number.
5+3=8 3+5=8 8-3=5 8-5=3
fact family A group of related facts using the same numbers.
face
face The flat part of a threedimensional figure.
cara Parte llana de una figura tridimensional.
expresión Combinación de números, variables y por lo menos una operación.
expression A combination of numbers, variables, and at least one operation.
Ff
536 se escribe como 500 + 30 + 6.
forma desarrollada/notación desarrollada Representación de un número como una suma que muestra el valor de cada dígito.
536 is written as 500 + 30 + 6.
expanded form/expanded notation The representation of a number as a sum that shows the value of each digit.
forma desarrollada/fracción
3/12/10 2:03 PM
R03_R26_EM_GL_103030.indd R11
3+0=3ó0+3=3
3 + 0 = 3 or 0 + 3 = 3
3/12/10 2:04 PM
Glossary/Glosario R11
propiedad de identidad de la suma Para todo número, cero más el número es el número.
En el número 4.57, 7 está en el lugar de las centésimas.
centésima Un valor de posición. Una parte de cien partes iguales.
hexágono Polígono con seis lados y seis ángulos.
El máximo común divisor de 12, 18 y 30 es 6.
máximo común divisor (MCD) El mayor de los factores comunes de dos o más números.
tabla de funciones Tabla de pares ordenados que se basa en una regla.
función Relación en que una cantidad depende de otra cantidad.
tabla de frecuencias Tabla para organizar un conjunto de datos que muestra el número de veces que ha ocurrido cada resultado.
tabla de frecuencias/propiedad de identidad de la suma
Identity Property of Addition For any number, zero plus that number is the number.
Ii
In the number 0.05, 5 is in the hundredths place.
hundredth A place value position. One of one hundred equal parts.
hexagon A polygon with six sides and six angles.
Hh
The greatest common factor of 12, 18, and 30 is 6.
Greatest Common Factor (GCF) The greatest of the common factors of two or more numbers.
Gg
function table A table of ordered pairs that is based on a rule.
function A relationship in which one number depends on another number.
frequency table A table for organizing a set of data that shows the number of times each result has occurred.
frequency table/Identity Property of Addition
Glossary/Glosario
expanded form/fraction
Glossary/Glosario
R12–R13
Glossary/Glosario
Glossary/Glosario
4 is less than 7
Glossary/Glosario
R03_R26_EM_GL_103030.indd R12
R12 R
4<7
is less than < An inequality relationship showing that the number on the left side of the symbol is smaller than the number on the right side.
5 es mayor que 3
4<7
4 es menor que 7
es menor que < Relación de desigualidad que muestra que el número a la izquierda del signo es más pequeño que el número a la derecha.
5>3
es mayor que > Relación de desigualdad que muestra que el número a la izquierda del signo es mayor que el número a la derecha.
is greater than > An inequality relationship showing that the number on the left of the symbol is greater than the number on the right.
5 > 3 5 is greater than 3
es igual a = Que tiene el mismo valor. Con el signo (=) se muestra que dos números o expresiones son iguales.
5
is equal to = Having the same value. The (=) sign is used to show two numbers or expressions are equal.
3
rectas secantes Rectas que se intersecan o cruzan en un punto.
5
5 17 _ _ ó
fracción impropia Fracción con un numerador mayor que o igual al denominador.
Es imposible elegir amarillo.
imposible Un evento que no puede suceder, cuya probabilidad es cero.
8×1=8=1×8
propiedad de identidad de la multiplicación Si multiplicas un número por 1, el producto es igual al número dado.
propiedad de identidad de la multiplicación/es menor que
intersecting lines Lines that meet or cross at a point.
3
5 17 _ or _
improper fraction A fraction with a numerator that is greater than or equal to the denominator.
It is impossible to choose yellow.
impossible An event that cannot happen. It has a probability of zero.
8×1=8=1×8
Identity Property of Multiplication If you multiply a number by 1, the product is the same as the given number.
Identity Property of Multiplication/is less than
3/12/10 2:04 PM
2 cm
3 cm
2 cm
3 cm
R03_R26_EM_GL_103030.indd R13
line of symmetry A line on which a figure can be folded so that its two halves match exactly.
1 2 3 4 5 6 7
3/12/10 2:04 PM
Glossary/Glosario R13
eje de simetría Recta sobre la cual se puede doblar una figura de manera que sus mitades se correspondan exactamente.
0
0
1 2 3 4 5 6 7
8 7 6 5 4 3 2 1
gráfica lineal Gráfica que tiene puntos unidos por segmentos de recta para representar datos.
line graph A graph that uses points connected by line segments to represent data. 8 7 6 5 4 3 2 1
recta Conjunto de puntos alineados que se extienden en direcciones opuestas y sin fin.
Es posible que elijas una baldosa roja.
posible Un evento que probablemente sucederá
longitud Medida de la distancia entre dos puntos.
3 cm
triángulo isósceles Un triángulo que tiene por lo menos 2 lados del mismo largo.
triángulo isósceles/eje de simetría
line A straight set of points that extend in opposite directions without ending.
It is likely you will choose a red tile.
likely An event that will probably happen.
length The measurement of a line between two points.
Ll
3 cm
isosceles triangle A triangle with at least 2 sides of the same length.
isosceles triangle/line of symmetry
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R14–R15
B
-
subtrahend
3
= difference
5
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R14
R14 R
3 4
6_
mixed number A number that has a whole number part and a fraction part.
minuend
8
minuend The first number in a subtraction sentence from which a second number is to be subtracted. -
3 4
6_
sustraendo
3
= diferencia
5
número mixto Número formado por un número entero y una parte fraccionaria.
minuendo
8
minuendo El primer número en un enunciado de sustracción del cual se restará un segundo número
La mediana de 3, 5, 6, 7 y 8 es 6.
mediana El número central de un grupo de números ordenados numéricamente.
median The middle number in a group of numbers arranged in numerical order.
The median of 3, 5, 6, 7, and 8 is 6.
masa Cantidad de materia de un cuerpo. El gramo y el kilogramo son dos ejemplos de unidades de masa.
simetría lineal Una figura tiene simetria lineal si puede doblarse de modo que las dos partes de la figura correspondan o sean congruentes.
A
mass The amount of matter in an object. Two examples of units of mass would be gram and kilogram.
Mm
line symmetry A figure has line symmetry if it can be folded so that the two parts of the figure match, or are congruent.
B
segmento de recta Parte de una recta entre dos extremos. La longitud de un segmento de recta se puede medir.
line segment A part of a line between two endpoints. The length of the line segment can be measured.
A
0 1 2 3 4 5 6 7 8 9 10
diagrama lineal Gráfica que tiene columnas de X sobre una recta numérica para representar frecuencias de datos.
0 1 2 3 4 5 6 7 8 9 10
line plot A graph that uses columns of Xs above a number line to show frequency of data.
diagrama lineal/número mixto
3/12/10 2:04 PM
1
2
3
4
5
6
7
8
9 10
R03_R26_EM_GL_103030.indd R15
numerator The number above the bar in a fraction; the part of the fraction that tells how many of the equal parts are being used.
0
number line A line with numbers on it in order at regular intervals.
nonnumeric pattern The regular, repeating design or sequence of shapes or objects.
net A flat pattern that can be folded to make a three-dimensional figure.
Nn
multiply (multiplication) An operation on two numbers to find their product. It can be thought of as repeated addition.
15 is a multiple of 5 because 3 × 5 = 15.
multiple A multiple of a number is the product of that number and any whole number.
7, 4, 7, 10, 7, and 2 The mode is 7.
mode The number(s) that occur(s) most often in a set of numbers.
mode/numerator
1
2
3
4
5
6
7
8
9 10
3/12/10 2:04 PM
Glossary/Glosario R15
numerador El número que está encima de la barra de fracción; la parte de la fracción que te indica cuántas partes iguales se están usando.
0
recta numérica Recta con números ordenados a intervalos regulares.
patrón no numérico El diseño o la secuencia regular y repetitiva de figuras u objetos.
red Patrón llano que se puede doblar para formar una figura tridimensional.
multiplicar (multiplicación) Operación de dos números para calcular su producto. También se puede interpretar como una adición repetida.
15 es múltiplo de 5 porque 3 × 5 = 15.
múltiplo Un múltiplo de un número es el producto de ese número y cualquier otro número entero.
7, 4, 7, 10, 7, y 2 La moda es 7.
moda Número o números que ocurre(n) con mayor frecuencia en un conjunto de números.
moda/numerador
Glossary/Glosario
line plot/mixed number
Glossary/Glosario
R16–R17
Glossary/Glosario (1) Evalúa primero las operaciones dentro de los paréntesis ( ). (2) Multiplica o divide en orden de izquierda a derecha. (3) Suma o resta en orden de izquierda a derecha. par ordenado Par de números que son las coordenadas de un punto en un plano de coordenadas.
(1) Do the operations in parentheses first. (2) Multiply and divide in order from left to right. (3) Add and subtract in order from left to right.
ordered pair A pair of numbers that are the coordinates of a point in a coordinate plane.
Glossary/Glosario
0
1 2 3 4 5 6 7
Glossary/Glosario
R03_R26_EM_GL_103030.indd R16
R16 R
orden de las operaciones Reglas que te indican qué orden seguir cuando evalúas una expresión:
order of operations Rules that tell what order to follow when evaluating an expression:
0
1 2 3 4 5 6 7
(4, 2)
operación Proceso matemático como la suma (+), la resta (-), la multiplicación (×) o la división (÷).
operation A mathematical process such as addition (+), subtraction (-), multiplication (×), or division (÷).
(4, 2)
octágono Polígono de 8 lados y 8 ángulos.
octagon A polygon with 8 sides and 8 angles.
8 7 6 5 4 3 2 1
triángulo obtusángulo Triángulo con un ángulo obtuso.
obtuse triangle A triangle with one obtuse angle.
8 7 6 5 4 3 2 1
ángulo obtuso Ángulo que mide más de 90° pero menos de 180°.
ángulo obtuso/par ordenado
obtuse angle An angle that measures greater than 90° but less than 180°.
Oo
obtuse angle/ordered pair
3/12/10 2:04 PM
valor atípico Número en un conjunto de datos que es mucho mayor o mucho menor que la mayoría de los otros números del conjunto.
outlier A number in a set of data that is much larger or much smaller than most of the other numbers in the set.
D
B
6 ft
2 ft
R03_R26_EM_GL_103030.indd R17
2, 4, 6, 8, 10
pattern A sequence of numbers, figures, or symbols that follows a rule or design.
parentheses The enclosing symbols (), which indicate that the terms within are a unit.
2 ft
parallelogram A quadrilateral with four sides in which each pair of opposite sides are parallel and equal in length. 6 ft
C
A
parallel lines Lines that are the same distance apart. Parallel lines do not meet.
D
B
6 pies
2 pies
3/12/10 2:05 PM
Glossary/Glosario R17
2, 4, 6, 8, 10
patrón Sucesión de números, figuras o símbolos que sigue una regla o un diseño.
paréntesis Los signos con que se encierran los términos (), para indicar que cuando están adentro, forman una unidad.
2 pies
6 pies
paralelogramo Cuadrilátero en el que cada par de lados opuestos son paralelos y de la misma longitud.
C
A
rectas paralelas Rectas separadas por la misma distancia. Las rectas paralelas no se intersecan.
resultado Resultado posible de un experimento.
outcome A possible result of an experiment.
Pp
origen El punto (0, 0) en un plano de coordenadas donde el eje vertical interseca el eje horizontal.
origen/patrón
origin The point (0, 0) on a coordinate plane where the vertical axis meets the horizontal axis.
origin/pattern
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R18–R19
rectas perpendiculares Rectas que se intersecan o cruzan formando ángulos rectos.
valor de posición El valor dado a un dígito según su posición en un número. polígono Figura plana cerrada formada por segmentos de recta que sólo se unen en sus extremos.
número primo Número entero que tiene exactamente dos factores, 1 y sí mismo.
perpendicular lines Lines that meet or cross each other to form right angles.
place value The value given to a digit by its position in a number.
polygon A closed plane figure formed using line segments that meet only at their endpoints.
prime number A whole number with exactly two factors, 1 and itself.
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R18
R18 R
probabilidad Número entre 0 y 1 que mide la posibilidad de que ocurra un evento.
período Nombre dado a cada grupo de tres dígitos en una tabla de valores de posición.
period The name given to each group of three digits on a place-value chart.
probability A number between 0 and 1 that measures the likelihood of an event happening.
perímetro Distancia alrededor de una figura o región.
perimeter The distance around a shape or region.
7, 13, y 19
porcentaje Razón que compara un número con 100.
percent A ratio that compares a number to 100.
7, 13, and 19
pentágono Polígono de cinco lados y cinco ángulos.
pentagon A polygon with five sides and five angles.
pentágono/probabilidad
3/12/10 2:05 PM
transportador Instrumento con el que se miden los ángulos. pirámide Figura sólida con un polígono como base y caras triangulares que comparten un vértice común.
protractor An instrument used to measure angles. pyramid A three-dimensional figure with a polygon as a base and triangular shaped faces that share a common vertex.
R03_R26_EM_GL_103030.indd R19
range The difference between the greatest and the least numbers in a set of data.
radius A line segment that connects the center of a circle to a point on the circle. The plural is radii.
Rr
3/12/10 2:05 PM
Glossary/Glosario R19
rango La diferencia entre el mayor y el menor de los números en un conjunto de datos.
radio Segmento de recta que une el centro de un círculo con un punto del círculo.
cociente Respuesta o resultado de un problema de división.
cuadrado, rectángulo y paralelogramo
square, rectangle, and parallelogram
quotient The result of a division problem.
cuadrilátero Figura que tiene 4 lados y 4 ángulos.
quadrilateral A shape that has 4 sides and 4 angles.
Qq
producto Repuesta o resultado de un problema de multiplicación. También se refiere a la expresión de un número como el producto de sus factores.
producto/rango
product The answer or result of a multiplication problem. It also refers to expressing a number as the product of its factors.
product/range
Glossary/Glosario
pentagon/probability
Glossary/Glosario
R20–R21
Glossary/Glosario rombo Paralelogramo con cuatro lados congruentes.
rhombus A parallelogram with four congruent sides.
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R20
R20 R
right triangle A triangle with one right angle.
triángulo rectángulo Triángulo con un ángulo recto.
ángulo recto Ángulo que mide 90°.
residuo Número que queda después de dividir un número entero entre otro número entero.
remainder The number that is left after one whole number is divided by another.
An angle with a measure
reflexión Tipo de transformación en que se le da vuelta a una figura.
reflection A type of transformation that flips a figure.
right angle of 90°.
prisma rectangular Figura tridimensional de seis caras rectangulares.
B
rectangular prism A threedimensional figure with six faces that are rectangles.
A
rectángulo Cuadrilátero con cuatro ángulo rectos; los lados opuestos son de igual longitud y paralelos.
B
rayo Parte de una recta que tiene un extremo y que se extiende en una dirección sin fin.
rayo/triángulo rectángulo
rectangle A quadrilateral with four right angles; opposite sides are equal in length and parallel.
A
ray A part of a line that has one endpoint and extends in one direction without ending.
ray/right triangle
3/12/10 2:05 PM
regla Enunciado que describe la relación entre números u objetos.
rule A statement that describes a relationship between numbers or objects.
3 in.
4 in.
R03_R26_EM_GL_103030.indd R21
simplest form A fraction in which the numerator and the denominator have no common factor greater than 1. 6 3 _ is the simplest form of _. 5 10
similar figures Figures that have the same shape but different sizes.
2 in.
scalene triangle A triangle with no congruent sides.
3 pulg
4 pulg
3/12/10 2:05 PM
Glossary/Glosario R21
forma reducida Fracción en la que el numerador y el denominador no tienen un factor común mayor que 1. 6 3 _ es la forma reducida de _. 5 10
figuras semejantes Figuras que tienen la misma forma, pero diferente tamaño.
2 pulg
triángulo escaleno Triángulo sin lados congruentes.
redondear Cambiar el valor de un número a uno con el cual es más fácil trabajar. Calcular el valor más cercano a un número basado en un valor de posición dado.
round To change the value of a number to one that is easier to work with. To find the nearest value of a number based on a given place value.
Ss
simetría de rotación Una figura posee simetría de rotación si después de rotarla sobre un punto la figura yace en su posición original.
rotación Tipo de transformación en que se hace girar una figura alrededor de un punto central.
rotación/forma reducida
rotational symmetry A figure has rotational symmetry if, after a rotation of the figure about a point, the figure lies in its original position.
rotation A type of transformation in which a figure is turned about a central point.
rotation/simplest form
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R22–R23
cuadrado Rectángulo de cuatro lados congruentes.
unidad cuadrada Unidad para medir el área.
square A rectangle with four congruent sides.
square unit area.
89
1,642
1,642
5 8 9 3 6 5 7 8 = 76°F
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R22
R22 R
14 - 8 = 6
4 1 1 6
Hojas
14 - 8 = 6
6 7 8 7
Tallo
Temperatura (° F)
restar (sustracción o resta) Operación con dos números que indica la diferencia, cuando algunos o todos son eliminados. La sustracción también se usa para comparar dos números.
5 8 9 3 6 5 7 8 = 76°F
Leaf
4 1 1 6
89
diagrama de tallo y hojas Gráfica en la cual los datos están ordenados de menor a mayor y organizados según el valor de posición.
537
subtract (subtraction) An operation on two numbers that tells the difference, when some or all are taken away. Subtraction is also used to compare two numbers.
6 7 8 7
Stem
Temperature (° F)
stem-and-leaf plot A graph in which data are ordered from least to greatest and organized by place value.
537
standard form/standard notation The usual way of writing a number that shows only its digits, no words.
forma estándar/notación estandar Manera habitual de escribir un número que sólo muestra sus dígitos, sin palabras.
esfera Figura tridimensional formada por el conjunto de todos los puntos equidistantes de un punto dado llamado centro.
sphere A solid or three-dimensional figure that is set of all points that are the same distance from a given point, called the center.
A unit for measuring
resolver Despejar una variable y reemplazar este valor en la variable para hacer verdadera la ecuación.
solve To replace a variable with a value that results in a true sentence.
resolver/restar
3/12/10 2:05 PM
10
Una de diez partes iguales
R03_R26_EM_GL_103030.indd R23
transformación Movimiento de una figura.
transformation A movement of a figure.
3/12/10 2:05 PM
Glossary/Glosario R23
figura sólida Una figura sólida tiene tres dimensiones: largo, ancho y alto.
milésima(s) Una de mil partes iguales 1 ó_ . También se refiere a un valor de 1000 posición en un número decimal. En el decimal 0.789, el 9 está en el lugar de las milésimas.
décima 1 ó _.
marca(s) de conteo Marca que se hace para llevar un registro y representar datos reunidos de una encuesta.
Conteo
three-dimensional figure A solid figure has three dimensions: length, width, and height.
thousandth(s) One of a thousand 1 equal parts, or _ . Also refers to a 1000 place value in a decimal number. In the decimal 0.789, the 9 is in the thousandths place.
1 10
tenth One of ten equal parts, or _ .
tally mark(s) A mark made to keep track of and display data recorded from a survey.
verde
Green
Color
¿Cuál es tu color favorito?
azul
Tally Blue
Color
What is Your Favorite Color?
tally chart A way to keep track of data using tally marks to record the number of responses or occurrences.
tabla de conteo Manera de llevar la cuenta de los datos usando marcas de conteo para anotar el número de respuestas o sucesos.
encuesta Método para recolectar datos.
survey A method of collecting data.
Tt
suma Respuesta o resultado de un problema de suma.
sustraendo
14 - 5 = 9
sustraendo Un número que se sustrae de otro número.
sustraendo/transformación
sum The answer to an addition problem.
subtrahend
14 - 5 = 9
subtrahend A number that is subtracted from another number.
subtrahend/transformation
Glossary/Glosario
solve/subtract
Glossary/Glosario
R24–R25
Glossary/Glosario diagrama de árbol Diagrama de todos los resultados posibles de un evento o series de eventos o experimentos. triángulo Polígono con tres lados y tres ángulos.
prisma triangular Prisma cuyas bases son triangulares con paralelogramos como lados.
pirámide triangular Pirámide cuya base es un triángulo.
figura plana Figura que yace completamente en un plano.
tree diagram A diagram of all the possible outcomes of an event or series of events or experiments.
triangle A polygon with three sides and three angles.
triangular prism A prism whose bases are triangular with parallelograms for sides.
triangular pyramid A pyramid whose base is a triangle.
two-dimensional figure A figure that lies entirely within one plane.
Glossary/Glosario
R03_R26_EM_GL_103030.indd R24
Glossary/Glosario
trapecio Cuadrilátero con exactamente un par de lados paralelos.
trapezoid A quadrilateral with exactly one pair of parallel sides.
R24 R
traslación Tipo de transformación en que una figura se desliza en sentido vertical, en sentido horizontal o en ambos sentidos.
traslación/figura plana
translation A type of transformation in which a figure is slid horizontally, vertically, or both.
translation/two-dimensional figure
'BDUPST PG
3/12/10 2:06 PM R03_R26_EM_GL_103030.indd R25
x-axis The horizontal axis (↔) in a coordinate graph.
Xx
weight A measurement that tells how heavy an object is.
Ww
vertex The point where two rays meet in an angle.
'BDUPST PG
Venn diagram A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.
variable A letter or symbol used to represent an unknown quantity.
Vv
It is unlikely you will choose a yellow tile.
unlikely An event that is improbable or will probably not happen.
Uu
unlikely/x-axis
'BDUPSFT EF
3/12/10 2:06 PM
Glossary/Glosario R25
eje x El eje horizontal (↔) en una gráfica de coordenadas.
peso Medida que indica lo pesado que es un cuerpo.
vértice Punto donde concurren dos o más rayos.
'BDUPSFT EF
diagrama de Venn Diagrama con círculos para mostrar elementos de diferentes conjuntos. Los círculos sobrepuestos indican elementos comunes.
variable Letra o símbolo que se usa para representar una cantidad desconocida.
Es improbable que elijas una baldosa amarilla.
improbable Evento que es improbable o que es probable que no suceda.
improbable/eje x
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
Glossary/Glosario
R03_R26_EM_GL_103030.indd R26
R26 R
0×5=0
5×0=0
Zero Property of Multiplication The property that states any number multiplied by zero is zero. 0×5=0
5×0=0
propiedad del cero de la multiplicación Propiedad que establece que cualquier número multiplicado por cero es igual a cero.
coordenada y El segundo número en un par ordenado que indica la distancia hacia arriba o hacia abajo del eje x a la cual se encuentra un punto. En (2, 3), 3 es la coordenada y.
y-coordinate The second number in an ordered pair that indicates how far above or below the x-axis a point is. In (2, 3), 3 is the y-coordinate.
Zz
eje y El eje vertical () en una gráfica de coordenadas.
coordenada x El primer número en un par ordenado que indica la distancia a la izquierda o a la derecha del eje y a la cual se encuentra un punto. En (2, 3), 3 es la coordenada x.
coordenada x/propiedad del cero de la multiplicación
y-axis The vertical axis () in a coordinate graph.
Yy
x-coordinate The first number in an ordered pair that indicates how far to the left or the right of the y-axis a point is. In (2, 3), 2 is the x-coordinate.
x-coordinate/Zero Property of Multiplication
3/12/10 2:06 PM
Glossary/Glosario
Glossary/Glosario
R26
Index
Aa Act It Out Problem-Solving Strategy, 519, 557 Activate Prior Knowledge, 4, 6, 8, 12, 60, 94, 146, 224, 262, 314, 360, 424, 482, 520, 564, 600, 652 Active Math Activities, 24, 75, 110, 224, 284, 336, 396, 602, 658 Activities Active Math, 24, 75, 110, 224, 284, 336, 396, 602, 658 Analyze Graphs, 13 Art, 90, 164, 201, 300, 401, 510 Critical Thinking, 36, 44, 56, 327, 363, 368, 560, 610, 654 Find and Extend the Rule for Each Table, 10 Find Equivalent Fractions, 6 Find Missing Values in Equivalent Fractions Number Sentences, 7 Function Rule Creation Race, 11 Function Tables, 9 Games, 28, 87, 161, 187, 292, 392, 411, 430, 457, 478, 495, 506, 548, 632, 648 Graph Game, 15 Hands-On, 20, 24, 28, 32, 36, 44, 50, 56, 75, 78, 80, 86, 90, 96, 100, 106, 110, 114, 127, 130, 136, 142, 148, 154, 160, 164, 170, 187, 190, 200, 210, 216, 220, 228, 241, 244, 252, 258, 264, 283, 288, 292, 296, 300, 304, 308, 327, 330, 336, 342, 348, 354, 364, 368, 385, 388, 392, 396, 401, 406, 410, 414, 421, 430, 445, 448, 452, 456, 460, 470, 478, 495, 499, 506, 510, 514, 536, 540, 548, 552, 560, 568, 572, 587, 590, 596, 602, 610, 628, 632, 638, 644, 648, 654, 658 Index Question, 20, 32, 80, 96, 142, 171, 190, 220, 264, 296, 308, 330, 354, 406, 421, 445, 470, 499, 536, 568, 590, 628, 644 Math Game, 241 Math in Action, 155 Mental Math, 131 Music, 100, 106, 216, 252 Real-World Math, 137, 388 Virtual Manipulatives, 50, 127, 414, 452, 552, 587 Virtual Math, 114, 514 Visual Math, 210, 385, 448, 540, 638 Word Problem Exchange, 5 Acute angles, 492C, 507–508, 510–513, 525, EP31 Acute triangles, 510–513, 525, EP31 Add/addition Associative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Commutative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Decimals, 442, 468–469, 470–473, 484, 487 Equations, 140–141, 142–144, 176 Estimating decimal sums, 460–463, 484, 486, EP28, EP29 Estimating sums, 36–39, 44–47, 64, 65, EP3
INDEX 1
Expressions, 136–139, 176 Fractions, 442, 445–447, 448–451, 484, 485 Functions, 160–163, 178 Identity Property of Addition, 16C, 32–35 Like fractions, 445–447, 484, 485, EP27 Money, 45–46, 65 Multi-digit numbers, 44–47, 65, EP4, EP5 Properties, 32–35, 62, 64 Repeated addition, 73–74, 185–186 Unlike fractions, 448–451, 484, 485, EP27 Whole numbers, 16, 36–39, 40–41, 44–47, 62, 65 Addition Properties, 32–35, 62, 64 Associative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Commutative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Identity Property of Addition, 16C, 32–35 Algebra, Concepts of algebra develop informally with the awareness of patterns, sorting/ classifying, use of symbols and variables in expressions and equations, and initial exposure to functions. Algebra, 7, 8–11, 39, 43, 67, 72, 76–77, 82–83, 85, 88–89, 93, 107–108, 117, 118, 121, 124, 127–129, 130–133, 136–139, 140–141, 142–144, 145, 146–147, 148–150, 151, 152–153, 154–157, 158–159, 160–163, 164–167, 168–169, 170–173, 174–178, 179, 180–181, 189, 192, 222, 230, 235, 272, 273, 287, 313, 335, 403, 412, 425, 454, 455, 462, 475, 489, 503, 519, 557, 607, 620, 621, 650, 663, EP5, EP9, EP10 Addition equations, 140–141, 142–144, 176 Addition expressions, 136–139, 176 Addition functions, 160–163, 178 Division equations, 152–153, 154–157, 177 Division expressions, 148–150, 177 Division functions, 164–167, 178 Equations, 124C, 124, 140–141, 142–144, 145, 146–147, 152–153, 154–157, 174, 176, 177, EP9, EP10, EP11 Expression Race Game, 151 Expressions, 124C, 124, 136–139, 148–150, 151, 152–153, 174, 176, 177, EP9, EP10 Function rules, 8–11, 160–163, 164–167, 170–173, 174, 178 Functions, 8–11, 124C, 124, 160–163, 164–167, 168–169, 170–173, 174, 178, EP11 Functions with two operations, 168–169, 170–173, 178 Function tables, 8–11, 124C, 160–163, 164–167, 170–173, 178, EP11 Input, 9–11, 160–163, 164–167, 178 Make a Game Chapter Project, 124, 174 Multiplication equations, 152–153, 154–155, 177 Multiplication expressions, 148–150, 177 Multiplication functions, 164–167, 178 Output, 9–11, 160–163, 164–167, 178 Parentheses ( ), 100–102, 106–109, 120, 124C, 137–139, 148–150, 176, 178 Solving equations, 140–141, 142–144, 146–147, 152–153, 154–157, 176, 177, EP9, EP10, EP11
Solving expressions, EP9, EP10 Subtraction equations, 140–141, 142–144, 176 Subtraction expressions, 136–139, 176 Subtraction functions, 160–163, 178 Values of expressions, 136–139, 148–150, 151, 176, 177 Variables, 124C, 124, 136–139, 140–141, 148–150, 151, 152–153, 154–157, 160–163, 164–167, 168–169, 174, 176, 177, 178 Writing equations, 681, EP9, EP10, EP11 Writing expressions, 137–139, 148–150, 176, EP9, EP10 Alternative Manipulative Fraction Kit, 398A Analyze Graphs, 13 Analyze the Strategy, 41, 195, 287, 405, 465, 503, 545, 593, 637 Analyzing data, 12–15 Angles, 492C, 492, 495–498, 504–505, 506–508, 509, 510–513, 514–517, 523, 525, EP31 Acute, 492C, 507–508, 510–513, 525, EP31 Classifying, 504–505, 506–508, 525 Degrees (º), 504–505, 506–508, 525 Endpoints, 530C, 506–508, 523, 536–539 Obtuse, 492C, 507–508, 510–513, 525, 510–513, 525, EP31 On a circle graph, 508 On a clock, 506–508 On a pie chart, 508 Right, 492C, 507–508, 510–513, 525, EP31 Turns, 506–508, 525 Animated Graphic Novel, 17, 71, 78, 125, 144, 149, 183, 222, 239, 258, 279, 285, 304, 325, 329, 381, 417, 443, 460, 480, 493, 508, 531, 583, 591, 625, 634 Approaching Grade Level, T13, 19C, 32C, 44C, 73C, 84C, 96C, 110B, 127C, 136C, 148C, 160C, 185C, 196C, 206C, 226B, 241C, 250B, 256B, 264B, 241C, 250B, 256B, 264B, 241C, 250B, 256B, 264B, 281C, 288B, 296D, 327B, 334C, 348C, 362C, 383C, 399D, 420C, 445C, 456C, 468C, 495C, 504B, 510C, 533C, 546C, 560B, 566C, 585C, 594B, 602B, 608C, 627C, 642C, 658B Area, 582C, 608–609, 610–613, 614–615, 616, 620, 678–679, EP38 Area-perimeter relationship, 611–615 Formula for area of rectangle, 609, 610–613, 616, 620 Formula for area of square, 611–613, 620 Map Your Home Chapter Project, 582, 616 Models for multiplication, 86–89, 90–92, 100–102, 118, 119, 198–199, 256–257, 258–261, EP6, EP7 Rectangle, 608–609, 610–613, 616, 620 Squares, 611–613, 616, 620 Square units, 582C, 608–609, 610–613, 614–615, 616, 620, EP38 Are You Ready?, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Arrays, 73–74, 75–77, 86–89, 117, 118, 119, EP6, EP7
Art Cross Curricular Connection, 520–521 Making Mosaics, 520–521 Art Learning Stations, 16E, 70E, 182E, 238E, 278E, 380E, 442E, 492E, 530E, 582E, 624E Assess, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Assessment, T16–T17 Assess, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Assessment Tips, 19E, 127E, 19E, 241E, 281E, 296F, 445E, 533E, 585E, 627E Comprehensive Assessment, T16 Data-Driven Decision Making, T7, 43, 67, 83, 123, 145, 179, 205, 235, 255, 275, 295, 321, 347, 377, 419, 439, 467, 489, 509, 527, 558, 579, 599, 621, 641, 669 Diagnose and Prescribe, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Diagnostic Assessment, T16, 18–18A, 72–72A, 126–126A, 184–184A, 240–240A, 280–280A, 326–326A, 382–382A, 444–444A, 494–494A, 532–532A, 584–584A, 626–626A End-of-Year Assessment, 2 ExamView, 43, 67, 69, 93, 121, 123, 145, 179, 181, 205, 235, 237, 255, 275, 277, 295, 321, 323, 347, 377, 379, 419, 439, 441, 467, 489, 491, 509, 527, 529, 558, 579, 581, 599, 621, 623, 641, 669, 671 Formative Assessment, T17, 22, 27, 31, 35, 39, 41, 43, 47, 53, 55, 59, 68, 77, 79, 83, 85, 89, 92, 93, 99, 102, 105, 109, 113, 115, 122, 129, 133, 135, 139, 144, 145, 150, 157, 159, 163, 167, 173, 180, 189, 193, 195, 203, 205, 213, 215, 219, 223, 230, 236, 243, 247, 249, 254, 255, 261, 266, 269, 276, 285, 287, 291, 294, 295, 299, 302, 307, 310, 313, 322, 329, 333, 335, 339, 344, 347, 351, 356, 359, 367, 370, 378, 387, 391, 395, 398, 403, 405, 409, 413, 418, 419, 423, 427, 432, 440, 447, 451, 455, 459, 463, 465, 467, 473, 475, 481, 490, 497, 501, 503, 508, 509, 513, 517, 519, 528, 539, 543, 545, 551, 555, 557, 558, 562, 571, 574, 580, 589, 591, 593, 598, 599, 604, 607, 613, 622, 631, 634, 637, 640, 641, 647, 651, 657, 661, 663, 670 Initial Assessment, T16 Mid-Chapter Check, 43, 93, 145, 205, 255, 295, 347, 419, 467, 509, 558, 599, 641 Online Readiness Quiz, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Options for Review, 4, 6, 8, 13 Practice Chapter Test, 67, 121, 179, 235, 275, 321, 377, 439, 489, 527, 579, 621, 669 Quick Assessment through Observation, 127E Quick Check, 18, 22, 27, 31, 35, 39, 41, 47, 53, 55, 59, 72, 77, 79, 83, 85, 89, 92, 99, 102, 105, 109, 113, 115, 126, 129, 133, 135, 139, 144, 150, 157, 159, 163, 167, 173, 184, 189, 193, 195, 203, 213, 215, 219, 223, 230, 240, 243, 247, 249, 254, 261, 266, 269, 280, 285, 287, 291, 294, 299,
302, 307, 310, 313, 326, 329, 333, 335, 339, 344, 351, 356, 359, 367, 370, 382, 387, 391, 395, 398, 403, 405, 409, 413, 418, 423, 427, 432, 444, 447, 451, 455, 459, 463, 465, 473, 475, 481, 494, 497, 501, 503, 508, 513, 517, 519, 532, 539, 543, 545, 551, 555, 557, 562, 571, 574, 584, 589, 591, 593, 598, 604, 607, 613, 626, 631, 634, 637, 640, 647, 651, 657, 661, 663, Reassess, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Response to Intervention (RtI), T12–T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Spiral Review, 35, 39, 47, 53, 59, 83, 89, 99, 109, 133, 139, 157, 163, 167, 173, 193, 203, 213, 219, 223, 247, 261, 291, 299, 307, 333, 339, 367, 395, 409, 413, 418, 463, 473, 481, 513, 517, 539, 551, 555, 571, 613, 647, 651, 661 Stop and Reflect, 31, 41, 59, 83, 92, 109, 115, 135, 144, 159, 173, 195, 203, 223, 230, 249, 254, 261, 269, 287, 294, 313, 333, 346, 359, 371, 398, 418, 432, 455, 465, 481, 503, 508, 519, 545, 557, 563, 574, 593, 598, 607, 615, 640, 657, 663 Summative Assessment, T17, 67, 121, 179, 235, 275, 321, 377, 439, 489, 527, 579, 621, 669 Test Practice, 35, 39, 47, 53, 59, 68–69, 83, 89, 99, 109, 122–123, 133, 139, 157, 163, 167, 173, 180–181, 193, 203, 213, 219, 223, 236–237, 247, 261, 276–277 , 291, 299, 307, 322–323, 333, 339, 367, 378–379, 395, 409, 413, 418, 440–441, 463, 473, 481, 490–491, 513, 517, 528–529, 539, 551, 555, 571, 580–581, 613, 622–623, 631, 634, 647, 651, 661, 670–671 Assessment Tips, 19E, 127E, 19E, 241E, 281E, 296F, 445E, 533E, 585E, 627E Associative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Associative Property of Multiplication, 80–83, 106–109, 116, 117, 241–243, EP5 Authors, T22–T23 Axis, 530C, 540–543 X-axis, 530C, 540–543 Y-axis, 530C, 540–543
Bb Bake Sale Equivalents Chapter Project, 380, 434
Bar graphs, 13–15, 324C, 324, 348–351, 357, 372, 375, 679, EP21, EP22 Creating double bar graphs, 352–353 Double bar graphs, 324C, 352–353, 354–356, 375 Beyond Grade Level, 18A, 19D, 32D, 44D, 72A, 73D, 84D, 96D, 110B, 126A, 127D, 136D, 148D, 160D, 184A, 185D, 196D, 206D, 226B, 240A, 241D, 250B, 256B, 264B, 280A, 281D, 288B, 296E, 326A, 327B, 334D, 348D, 362D, 382A, 383D, 399E, 420D, 444A, 445D, 456D, 468D, 494A, 495D, 504B, 510D, 532A, 533D, 546D, 560B, 566D, 584A, 585D, 594B, 602B, 608D, 626A, 627D, 642D, 658B The Big Idea, 16A, 16, 62, 70A, 70, 116, 124A, 124, 174, 182A, 182, 231, 238A, 238, 270, 278A, 278, 316, 324, 372, 380A, 380, 434, 442A, 442, 484, 492A, 492, 523, 530A, 530, 575, 582A, 582, 616, 624A, 624, 664 Building Math Vocabulary, 20, 24, 28, 32, 36, 44, 50, 56, 75, 80, 86, 90, 96, 100, 106, 111, 127, 130, 136, 143, 148, 154, 160, 164, 170, 187, 190, 200, 210, 216, 220, 228, 241, 244, 252, 259, 264, 283, 288, 292, 296, 300, 304, 308, 327, 330, 336, 342, 348, 354, 364, 368, 385, 388, 392, 396, 401, 406, 410, 414, 421, 430, 445, 448, 452, 456, 460, 470, 478, 495, 499, 506, 510, 514, 536, 540, 548, 552, 560, 568, 572, 587, 590, 596, 602, 610, 628, 632, 638, 644, 648, 654, 658
Cc Calculating total cost, 677, 680–681 Calendars, 676–677, 681 Capacity, 624C, 624, 627, 628–631, 632–634, 635, 638–640, 641, 664, 665, EP38 Capacity Estimates Game, 635 Converting customary units, 632–634, 665, EP38 Converting metric units, 639–640, 657, 665 Cups, 627, 628–631, 632–634, 635, 664, 665, EP38 Estimating, 627, 628–631, 635, 638–640, 665, 666, EP38, EP39 Fluid ounces, 628–631, 632–634, 635, 664, 665, EP38 Gallons, 624, 627, 628–631, 632–634, 635, 664, 665, EP38 Liters, 638–640, 657, 664, 666, EP39 Milliliters, 638–640, 657, 664, 666, EP39 Pints, 627, 628–631, 632–634, 635, 664, 665, EP38 Quarts, 627, 628–631, 632–634, 635, 664, 665, EP38
A Banner of Shapes Chapter Project, 492, 523
Capacity Estimates Game, 635
Bar Diagrams, 241E
Centimeters, 594–595, 596–598, 600–601, 616, 618, 657, EP37
Bar diagrams, T11, 4–5, 84, 105, 109, 158, 163, 167, 179, 192, 194, 203, 205, 214–215, 269, 286–287, 474–475, 479, 489, 557, 607
Index
Art Activities, 90, 164, 201, 300, 401, 510
Center of circles, 492C, 498
Certain, 368–371, 376, EP23
INDEX 2
Index
Challenge H.O.T. Problems, 92, 108, 112, 166, 203, 223, 291, 310, 391, 403, 409, 423, 432, 459, 463, 481, 591, 604, 640, 650, 656, 661 Chance, 362–363, 364–367, 376 Chapter at a Glance, 16B, 70B, 124B, 182B, 238B, 278B, 324B, 380B, 442B, 492B, 530B, 582B, 624B Chapter Projects, 16, 62, 70, 116, 124, 174, 182, 231, 238, 270, 278, 316, 324, 372, 380, 434, 442, 484, 492, 523, 531, 575, 582, 616, 624, 664 Bake Sale Equivalents, 380, 434 A Banner of Shapes, 492, 523 Choosing to Help, 324, 372 Classroom Quilt, 530, 575 Daily Multiples Book, 70, 116 Division Game Day, 278, 316 Healthy Foods Party, 182, 231 Healthy Snacks, 624, 664 Make a Game, 124, 174 Map Your Home, 582, 616 Name that Digit, 238, 270 Recycle It!, 16, 62 Shopping List, 442, 484 Chapter Study Guide and Review, 62–66, 116–120, 174–178, 231–234, 270–274, 316–320, 372–376, 434–438, 484–488, 523–526, 575–578, 616–620, 664–668 Check for reasonableness, 44–47, 201–202, 220–223, 228–230, 233, 234 Check What You Know, 21, 26, 30, 33, 37, 46, 51, 57, 76, 82, 87, 91, 97, 101, 107, 112, 114, 128, 131, 137, 143, 149, 155, 161, 165, 171, 188, 191, 201, 212, 217, 221, 229, 242, 245, 253, 259, 265, 284, 289, 293, 298, 301, 303, 305, 310, 328, 331, 337, 343, 349, 355, 365, 369, 386, 389, 394, 397, 402, 407, 411, 416, 422, 431, 446, 450, 454, 457, 461, 471, 479, 496, 500, 507, 511, 515, 538, 541, 549, 553, 561, 569, 573, 588, 591, 597, 603, 611, 629, 633, 639, 645, 649, 655, 659 Choose an Operation Problem-Solving Strategy, 84–85, 105, 118, 159, 214–215, 269, 359, 425, 475, 557, EP6 Choose the Best Answer Problem-Solving Strategy, 662–663, 668 Choose the Best Strategy Problem-Solving Strategy, 54–55, 66, 104–105, 119, 158–159, 177, 214–215, 233, 268–269, 274, 312–313, 320, 358–359, 376, 424–425, 438, 474–475, 488, 518–519, 526, 556–557, 577, 606–607, 619, 662–663, 668, EP4, EP7, EP10, EP13, EP16, EP19, EP22, EP26, EP29, EP32, EP34, EP37, EP40 Choosing to Help Chapter Project, 324, 372 Circle graphs, 351, 508 Angles on, 508 Circles, 492C, 496, 498 Center, 492C, 498 Compass, 504–505 Diameter, 492C, 498 Radius, 492C, 498
INDEX 3
Classifying angles, 504–505, 506–508, 525 Classroom Quilt Chapter Project, 530, 575 Clips Video Library, T15 Clocks, 681 Angles on, 506–508 Collecting data, 327–329, 345–346, 372, 373, 678–679 Experiments, 362–363, 364–367 Surveys, 324C, 327–329, 351, 372, 373, 679 Tally marks, 327–329, 336–339, 372, 373 Combining three-dimensional figures, 501 Common decimal-fraction equivalents, 430–432 Common Error!, 21, 26, 30, 33, 38, 41, 46, 51, 55, 57, 77, 79, 82, 85, 88, 92, 98, 105, 107, 112, 129, 132, 135, 138, 142, 150, 156, 159, 162, 166, 172, 188, 192, 195, 202, 212, 215, 217, 221, 229, 242, 245, 249, 253, 260, 265, 268, 285, 287, 290, 294, 298, 302, 305, 310, 313, 328, 331, 335, 339, 343, 350, 366, 387, 390, 395, 398, 402, 405, 408, 412, 417, 423, 427, 431, 446, 450, 454, 457, 461, 465, 471, 475, 479, 497, 500, 503, 507, 511, 516, 519, 538, 541, 545, 549, 553, 557, 562, 569, 574, 588, 593, 597, 604, 607, 612, 630, 633, 637, 639, 645, 650, 655, 660, 663 Common factor, 70C, 113, 410–413 Greatest common factor, 380C, 380, 410–413, 434, 437 Common fraction-decimal equivalents, 430–432 Common multiples, 70C, 113 Communication, Opportunities to develop mathematical fluency and vocabulary are provided in Talk Math and Write Math features. Students talk, listen, and write mathematically. Communication Read Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51 Talk Math, A4, A7, A8, A9, A11, A12, A13, A15, A16, A17, A18, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A36, A37, A38, A39, A40, A41, A42, A43, A46, A47, A48, A49, A50, A51, 21, 26, 30, 33, 37, 45, 46, 51, 57, 76, 79, 82, 87, 91, 97, 101, 107, 108, 111, 112, 114, 115, 128, 131, 137, 143, 144, 149, 155, 161, 165, 171, 186, 188, 191, 201, 212, 217, 221, 222, 229, 242, 245, 253, 254, 259, 265, 284, 285, 289, 293, 298, 301, 305, 309, 310, 328, 331, 337, 343, 349, 355, 365, 369, 386, 389, 391, 394, 397, 402, 407, 411, 416, 417, 422, 431, 446, 450, 454, 457, 461, 471, 479, 496, 500, 507, 511, 515, 537, 538, 541, 549, 553, 561, 569, 573, 588, 591, 597, 603, 611, 629, 633, 639, 645, 649, 655, 659 Think Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A19, A20, A21, A22, A23, A24, A26, A27, A28,
A31, A32, A34, A35, A36, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A49, A50, A51 Write Math, A4, A6, A7, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A43, A44, A45, A47, A48, A49, A51, 5, 7, 11, 15, 16, 22, 23, 27, 31, 34, 38, 41, 43, 47, 49, 52, 53, 55, 58, 61, 67, 70, 74, 77, 79, 83, 88, 89, 92, 93, 95, 98, 99, 102, 105, 108, 112, 113, 115, 121, 124, 129, 132, 133, 135, 138, 141, 144, 145, 147, 150, 153, 156, 157, 159, 162, 166, 169, 172, 173, 179, 182, 189, 192, 193, 195, 197, 202, 203, 205, 207, 209, 212, 213, 215, 218, 219, 222, 223, 225, 227, 230, 235, 238, 243, 246, 247, 249, 251, 254, 255, 260, 263, 266, 269, 275, 278, 282, 285, 287, 290, 291, 294, 295, 298, 299, 302, 306, 310, 313, 315, 321, 324, 329, 332, 333, 335, 338, 339, 341, 344, 346, 347, 350, 353, 356, 359, 361, 363, 366, 370, 377, 380, 384, 387, 390, 391, 395, 398, 400, 403, 405, 408, 409, 412, 417, 419, 420, 423, 425, 427, 429, 432, 439, 442, 447, 451, 455, 458, 459, 462, 463, 465, 467, 469, 472, 475, 477, 480, 481, 483, 489, 492, 497, 501, 503, 505, 508, 509, 513, 516, 519, 521, 527, 530, 535, 539, 542, 543, 545, 550, 554, 555, 557, 558, 562, 565, 570, 574, 579, 582, 586, 589, 591, 593, 595, 598, 599, 601, 604, 607, 612, 615, 621, 624, 627, 630, 631, 634, 637, 640, 641, 643, 650, 653, 656, 663, 669 Commutative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Commutative Property of Multiplication, 80–83, 116, 117, 241–243, EP5 Compare/comparing Data on graphs, 348–351, 352–353, 354–356, 372, 375 Decimals, 396–398, 433, 436, EP24 Decimals and fractions, 433 Fractions, 406–409, 433, 437, EP25 Fractions and decimals, 433 Fractions on a number line, 406–409 Is equal to (=), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is greater than (>), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is less than (<), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 More About Comparing and Ordering Numbers, 27 Whole numbers, 24–27, EP2 Whole numbers on a number line, 24–27 Compass, 504–505 Compatible numbers, 278C, 292–294, 316 Component and Manipulatives, T34–T35 Composite numbers, 70C, 114–115, 120, EP8 Prime numbers, 70C, 114–115, 120, EP8 Compound figures, 497 Comprehensive Assessment, T16 Cones, 499–501 Congruent, 530C
Cups, 627, 628–631, 632–634, 635, 664, 665, EP38
Congruent figures, 530, 560–562, 563, 575, 578, EP34
Customary measurement system, 582C, 585–586, 587–589, 590–591, 599, 616, 617, 627, 628–631, 632–634, 635, 642–643, 644–647, 648–651, 664, 665, 666, EP36, EP38, EP39, EP40 Converting units of capacity, 632–634, 665, EP38 Converting units of length, 590–591, 616, 617, EP36 Converting units of weight, 648–651, 666, EP40 Cups, 627, 628–631, 632–634, 635, 664, 665, EP38 Fluid ounces, 628–631, 632–634, 635, 664, 665, EP38 Foot (feet), 587–589, 590–591, 616, 617, EP36 Gallons, 624, 627, 628–631, 632–634, 635, 664, 665, EP38 Half inch, 585–586, 587–589, 617, EP36 Inches, 587–589, 590–591, 616, 617, EP36 Miles, 590–591, 680–681 Ounces, 642–643, 644–647, 648–651, 664, 666, EP39 Pints, 627, 628–631, 632–634, 635, 664, 665, EP38 Pounds, 642–643, 644–647, 648–651, 664, 666, EP39 Quarter inch, 585–586, 587–589, 617, EP36 Quarts, 627, 628–631, 632–634, 635, 664, 665, EP38 Tons, 644–647, 648–651, 664, 666, EP39 Yards, 587–589, 590–591, 616, 617, EP36
ConnectED, T2, T14, 324 Constructing geometric figures, 543 Consultants, T24 Consultant Website, T15 Contributing author, T23 Convert/converting, 582C, 582 Customary units of capacity, 632–634, 665, EP38 Customary units of length, 590–591, 616, 617, EP36 Customary units of weight, 648–651, 666, EP40 Metric units of capacity, 639–640, 657, 665 Metric units of length, 657 Coordinate planes, 530C, 540–543, 575, 576, EP33 Coordinates, 530C, 530, 540–543, 576 Grids, 540–543, 576 More About Points on a Grid, 543 Ordered pair, 530C, 540–543, 576, EP33 Origin, 530C, 540–543 Plotting points on a grid, 540–543, 576 Points, 533, 540–543 X-axis, 530C, 540–543 X-coordinate, 540–543 Y-axis, 530C, 540–543 Y-coordinate, 540–543 Coordinates, 530C, 530, 540–543, 576 Coordinate planes, 530C, 540–543, 575, 576, EP33 X-coordinate, 540–543 Y-coordinate, 540–543 Copying patterns, EP8 Coral Reefs Science Cross Curriculum Connection, 600–601 Cost, 677, 679 Creating Double bar graphs, 352–353 Line graphs, 345–346 Table, 680–681 Tessellation patterns, 552–555 Critical Thinking Activities, 36, 44, 56, 327, 363, 368, 560, 610, 654 Cross Curricular Connections, 60–61, 94–95, 146–147, 224–225, 262–263, 314–315, 360–361, 424–425, 482–483, 520–521, 564–565, 600–601, 652–653 Art, 520–521 Extend the Activity, 61, 95, 147, 225, 263, 315, 361, 425, 483, 521, 565, 601, 653 Geography, 262–263 History, 94–95, 482–483 Music, 424–425 Science, 60–61, 146–147, 224–225, 314–315, 360–361, 600–601, 652–653 Social Studies, 564–565 Cubes, 499–501
Cylinders, 499–501
Double bar graphs, 324C, 352–353, 354–356, 375 Experiments, 362–363, 364–367 Frequency tables, 13–15, 324C, 327–329, 336–339, 352–353, 372, 373, EP19 Interpreting graphs, 342–344, 348–351, 352–353, 354–356, 375 Line graphs, 324C, 342–344, 345–346, 372, 375 Line plots, 13–15, 324C, 324, 336–339, 374, EP20 More About Graphs, 351 Organizing, 324, 327–329, 340–341, 345–346, 351, 372, 373, 374, 676–677, 680–681, EP19, EP20, EP21 Pictographs, 12–15 Pie charts, 351, 508 Recording, 674–675 Statistics, 330–333, 373, EP20 Stem-and-leaf plots, 324C, 340–341, EP21 Surveys, 324C, 327–329, 351, 372, 373, 679 Tally charts, 324C, 327–329, 336–339, 372, 373, EP19 Tally marks, 327–329, 336–339, 372, 373 Time lines, 94–95, 676–677
Index
Congruent Cases Social Studies Cross Curricular Connection, 564–565
Data-Driven Decision Making, T7, 43, 67, 83, 123, 145, 179, 205, 235, 255, 275, 295, 321, 347, 377, 419, 439, 467, 489, 509, 527, 558, 579, 599, 621, 641, 669 Data File, 52, 77, 150, 218, 246, 294, 366, 403, 472, 512, 542, 604, 646, 77 Days, 676–677 Decagons, 495–498 Decimal Note-ation Music Cross Curricular Connection, 424–425 Decimal points, 383–384, 385–387, 388–391, 392–395, 442C, 470–473, 484
Dd Daily Multiples Book Chapter Project, 70, 116 Data Collection, Real-world situations encourage students to gather, organize, and analyze data. Data, 12–15, 324C, 324, 327–329, 330–333, 334–335, 336–339, 340–341, 342–344, 345–346, 347, 348–351, 352–353, 354–356, 357, 372–376, 377, 378–379, EP19, EP20, EP21 Analyzing, 12–15 Bar graphs, 13–15, 324C, 324, 348–351, 357, 372, 375, 679, EP21, EP22 Choosing to Help Chapter Project, 324, 372 Circle graphs, 351, 508 Collecting, 327–329, 345–346, 372, 373, 678–679 Comparing data on graphs, 348–351, 352–353, 354–356, 372, 375 Creating a table, 680–681 Creating double bar graphs, 352–353 Creating line graphs, 345–346 Displaying, 12–15, 324, 336–339, 345–346, 348–351, 354–356, 372, 373, 679, 680–681, EP21, EP22
Decimals, 380C, 380, 383–384, 385–387, 388–391, 392–395, 396–398, 419, 420, 421–423, 424–425, 426–427, 428–429, 430–432, 433, 434–438, 439, 440–441, 442C, 442, 456–459, 460–463, 466, 468–469, 470–473, 476–477, 478–481, 486, 487, 488, 489, 490–491, EP23, EP27, EP29 Addition, 442, 468–469, 470–473, 484, 487 Bake Sale Equivalents Chapter Project, 380, 434 Common decimal-fraction equivalents, 430–432 Comparing, 396–398, 433, 436, EP24 Comparing decimals and fractions, 433 Decimal-fraction relationship, 420, 421–423, 428–429, 430–432, 433, 438, EP26, EP27 Decimal Note-ation Music Cross Curricular Connection, 424–425 Equivalent decimals-fractions, 420, 421–423, 428–429, 430–432, 433, 438 Equivalent decimals-fractions on a number line, 428–429, 430–432 Estimating differences, 460–463, 484, 486, EP28 Estimating sums, 460–463, 484, 486, EP28, EP29 Fraction and Decimal Game, 433 Greater than one, 392–395, 435
INDEX 4
Index
Hundredths, 380C, 383–384, 388–391, 421–423, 434, 435 Match Up Game, 466 Money, EP23 More About Decimals, 391 More About Rounding Decimals, 459 On a number line, 396–398, 428–429, 430–432, 456–459, 486 Ordering, 396–398, 433, 436, EP24 Place value, 383–384, 385–387, 388–391, 392–395, 396–398, 421–423 Points, 383–384, 385–387, 388–391, 392–395, 442C, 470–473, 484 Reading, 385–387, 388–391, 392–395, 435 Rounding, 456–459, 460–463, 466, 484, 486, EP28 Shopping List Chapter Project, 442, 484 Subtraction, 442, 476–477, 478–481, 484, 488, EP30 Tenths, 380C, 383–384, 385–387, 421–423, 434, 435, EP23 Thousandths, 380C, 391, 434 Writing, 385–387, 388–391, 392–395, 435, EP23, EP24 Degrees of angles (º), 504–505, 506–508, 525 Fractions, EP31 Depth, T11 A Desert Safari Science Cross Curricular Connection, 314–315 Determine Whether an Answer Is Reasonable Problem-Solving Strategy, 194–195, 214–215, 232, 359, EP12 Determining possible outcomes, 364–367 Developmental Research, T18, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Diagnostic Check, A quick assessment of prerequisite skills required for each chapter is provided. Diagnose and Prescribe, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Diagnostic Assessment, T16, 18–18A, 72–72A, 126–126A, 184–184A, 240–240A, 280–280A, 326–326A, 382–382A, 444–444A, 494–494A, 532–532A, 584–584A, 626–626A Assess, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Diagnose and Prescribe, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Intensive Intervention, T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Reassess, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Response to Intervention (RtI), T12–T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Strategic Intervention, T13, 18A, 72A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A
INDEX 5
Diameter, 492C, 498 Did You Know?, 60, 95, 147, 224, 263, 315, 361, 424, 483, 520, 564, 600, 653 Differences Estimating, 36–39, 50–53, 64, 66 Estimating decimal, 460–463, 484, 486, EP28 Differentiated Instruction, T12–T13, 19C–19D, 32C–32D, 44C–44D, 73C–73D, 84C–84D, 96C–86D, 110B, 127C–127D, 136C–136D, 148C–148D, 160C–160D, 185C–185D, 196C–196D, 206C–206D, 226B, 241C–241D, 250B, 256B, 264B, 281C–281D, 288B, 296D–296E, 327B, 334C–334D, 348C–348D, 362C–362D, 383C–383D, 399D–399E, 420C–420D, 445C–445D, 456C–456D, 468ZC–468D, 495C–495D, 504B, 510C–510D, 533C–533D, 546C–546D, 560B, 566C–566D, 585C–585D, 594B, 602B, 608C–608D, 627C–627D, 642C–642D, 658B Approaching Grade Level, T13, 19C, 32C, 44C, 73C, 84C, 96C, 110B, 127C, 136C, 148C, 160C, 185C, 196C, 206C, 226B, 241C, 250B, 256B, 264B, 241C, 250B, 256B, 264B, 241C, 250B, 256B, 264B, 281C, 288B, 296D, 327B, 334C, 348C, 362C, 383C, 399D, 420C, 445C, 456C, 468C, 495C, 504B, 510C, 533C, 546C, 560B, 566C, 585C, 594B, 602B, 608C, 627C, 642C, 658B Beyond Grade Level, 18A, 19D, 32D, 44D, 72A, 73D, 84D, 96D, 110B, 126A, 127D, 136D, 148D, 160D, 184A, 185D, 196D, 206D, 226B, 240A, 241D, 250B, 256B, 264B, 280A, 281D, 288B, 296E, 326A, 327B, 334D, 348D, 362D, 382A, 383D, 399E, 420D, 444A, 445D, 456D, 468D, 494A, 495D, 504B, 510D, 532A, 533D, 546D, 560B, 566D, 584A, 585D, 594B, 602B, 608D, 626A, 627D, 642D, 658B English Language Learners, T13, 19D, 32D, 44D, 73D, 84D, 96D, 110B, 127D, 136D, 148D, 160D, 185D, 196D, 206D, 226B, 241D, 250B, 256B, 264B, 281D, 288B, 296E, 327B, 334D, 348D, 362D, 383D, 399E, 420D, 445D, 456D, 468D, 495D, 504B, 510D, 533D, 546D, 560B, 566D, 585D, 594B, 602B, 608D, 627D, 642D, 658B Far Below Grade Level, T13 On Grade Level, 18A, 19C, 32C, 44C, 72A, 73C, 84C, 96C, 110B, 126A, 127C, 136C, 148C, 160C, 184A, 185C, 196C, 206C, 226B, 240A, 241C, 250B, 256B, 264B, 280A, 281C, 288B, 296D, 326A, 327B, 334C, 348C, 362C, 382A, 383C, 399D, 420C, 444A, 445C, 456C, 468C, 494A, 495C, 504B, 510C, 532A, 533C, 546C, 560B, 566C, 584A, 585C, 594B, 602B, 608C, 626A, 627C, 642C, 658B Differentiated Practice, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 Digits, 16C, 20–23, 62, EP2 Hundreds, 19, 20–23 Hundred thousands, 20–23
Hundredths, 380C, 383–384, 388–391, 421–423, 434, 435 Ones, 19, 20–23 Tens, 19, 20–23 Ten thousands, 20–23 Tenths, 380C, 383–384, 385–387, 421–423, 434, 435, EP23 Thousands, 19, 20–23 Thousandths, 380C, 391, 434 Displaying data, 12–15, 324, 336–339, 345–346, 348–351, 354–356, 372, 373, 679, 680–681, EP21, EP22 Bar graphs, 13–15, 324C, 324, 348–351, 357, 372, 375, 679, EP21, EP22 Circle graphs, 351, 508 Creating a table, 680–681 Creating double bar graphs, 352–353 Creating line graphs, 345–346 Double bar graphs, 324C, 352–353, 354–356, 375 Frequency tables, 13–15, 324C, 327–329, 336–339, 352–353, 372, 373, EP19 Line graphs, 324C, 342–344, 345–346, 372, 375 Line plots, 13–15, 324C, 324, 336–339, 374, EP20 Pictographs, 12–15 Pie charts, 351, 508 Stem-and-leaf plots, 324C, 340–341, EP21 Tally charts, 324C, 327–329, 336–339, 372, 373, EP19 Tally marks, 327–329, 336–339, 372, 373 Time lines, 94–95, 676–677 Distributive Property of Multiplication, 206F Distributive Property of Multiplication, 70C, 100–102, 210–213, 216–219, 228–230, 231, 233, 250–251, 273, EP13 Divide/division, 70, 73–74, 75–77, 78–79, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 116–119, 278, 281–282, 283–285, 288–291, 292–294, 295, 296–299, 300–302, 303, 304–307, 308–310, 311, 316–320, EP17, EP18, EP19 By 0, 81–83 By 1, 81–83, 86–89, 118 By 2, 86–89, 118 By 3, 86–89, 118 By 4, 86–89, 118 By 5, 86–89, 118 By 6, 90–92, 118 By 7, 90–92, 118 By 8, 90–92, 118 By 9, 90–92, 118 By 10, 96–99, 119 By 11, 100–102, 119 By 12, 100–102, 119 By multiples of 10, 288–291, 318 By multiples of 100, 288–291, 318 By multiples of 1,000, 288–291, 318 Compatible numbers, 278C, 292–294, 316 Daily Multiples Book Chapter Project, 70, 116 Dividends, 74, 278C, 278, 281–282, 283–285, 288–291, 316 Division Game Day Chapter Project, 278, 316
Dividends, 74, 278C, 278, 281–282, 283–285, 288–291, 316 Division Game Day Chapter Project, 278, 316 Division Shuffle Game, 311 Division strategies, 73–74, 78–79, 86–89, 90–92, 96–99, 100–102 Compatible numbers, 278C, 292–294, 316 Modeling, 73–74, 86–89, 90–92, 96–99, 100–102, 281–282, 283–285, 288–291, 292–294, 296–299, 300–302, 304–307, 308–310 Related facts, 75–77, 86–89, 90–92, 117, EP5 Repeated subtraction, 78–79, 117, EP5 Divisors, 74, 278C, 278, 281–282, 283–285, 316 Do Flying Squirrels Really Fly? Science Cross Curricular Connection, 146–147 Double bar graphs, 324C, 352–353, 354–356, 375 Creating, 352–353 Doubling recipes, 677 Draw a Picture Problem-Solving Strategy, 134–135, 159, 175, 313, 557, 607, 663, EP9 Drawing figures, 522
Ee Edges, 492C, 499–501, 524, EP30 Elapsed time, 624C, 624, 658–661, 664, 668, 676–677, 681, EP40 ELL: In Your Own Words, 112, 156, 243, 260, 302, 310, 387, 412, 432, 458, 472 ELL: Rephrase the Question, 22, 102, 138, 162, 172, 246, 290, 403, 462 ELL Resources, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D ELL: Retell, 88, 192, 222 ELL Support, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D ELL: Word List, 108, 129, 166, 218, 298, 306, 423, 550 ELL: Writing Prompt, 98, 132, 202, 570 ELL: Writing Sequence, 390 Emperors on the Ice Science Cross Curricular Connection, 224–225 End-of-Year Assessment, 2 Endpoints, 530C, 506–508, 523, 536–539 English Language Learners, Concepts are presented visually to aid in reading comprehension. Opportunities are provided throughout the program to build math concepts as well as language skills. The ELL teaching suggestions assist in teaching not only the vocabulary but the concepts needed to understand the mathematics. English Language Learners, T13, 19D, 32D, 44D, 73D, 84D, 96D, 110B, 127D, 136D, 148D, 160D, 185D, 196D, 206D, 226B, 241D, 250B, 256B, 264B, 281D, 288B, 296E, 327B, 334D, 348D, 362D, 383D, 399E, 420D, 445D, 456D, 468D, 495D, 504B, 510D, 533D, 546D, 560B, 566D, 585D, 594B, 602B, 608D, 627D, 642D, 658B In Your Own Words, 112, 156, 243, 260, 302, 310, 387, 412, 432, 458, 472 Language Alert!, 21, 33, 51, 73, 85, 97, 110, 127, 142, 153, 160, 191, 199, 215, 229, 243, 258, 265, 284, 289, 297, 335, 340, 349, 369, 383, 402, 427, 428, 445, 457, 468, 476, 507, 510, 537, 549, 587, 609, 611, 629, 645, 659 Rephrase the Question, 22, 102, 138, 162, 172, 246, 290, 403, 462 Resources, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D Retell, 88, 192, 222 Support, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D Word List, 108, 129, 166, 218, 298, 306, 423, 550 Writing Prompt, 98, 132, 202, 570 Writing Sequence, 390
Enrichment Chapter Projects, 16, 62, 70, 116, 124, 174, 182, 231, 238, 270, 278, 316, 324, 372, 380, 434, 442, 484, 492, 523, 531, 575, 582, 616, 624, 664 Cross Curricular Connections, 60–61, 94–95, 146–147, 224–225, 262–263, 314–315, 360–361, 424–425, 482–483, 520–521, 564–565, 600–601, 652–653 Differentiated Instruction, T12–T13, 19C–19D, 32C–32D, 44C–44D, 73C–73D, 84C–84D, 96C–86D, 110B, 127C–127D, 136C–136D, 148C–148D, 160C–160D, 185C–185D, 196C–196D, 206C–206D, 226B, 241C–241D, 250B, 256B, 264B, 281C–281D, 288B, 296D–296E, 327B, 334C–334D, 348C–348D, 362C–362D, 383C–383D, 399D–399E, 420C–420D, 445C–445D, 456C–456D, 468C–468D, 495C–495D, 504B, 510C–510D, 533C–533D, 546C–546D, 560B, 566C–566D, 585C–585D, 594B, 602B, 608C–608D, 627C–627D, 642C–642D, 658B Game Time, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 H.O.T. Problems, 11, 15, 22, 27, 31, 34, 39, 47, 53, 58, 77, 79, 83, 89, 92, 99, 102, 108, 113, 115, 129, 133, 138, 144, 150, 157, 162, 166, 173, 189, 193, 203, 212, 219, 223, 230, 243, 247, 254, 260, 266, 285, 291, 294, 299, 302, 306, 310, 329, 333, 339, 344, 350, 356, 366, 370, 387, 391, 395, 398, 403, 409, 412, 417, 423, 432, 447, 451, 455, 459, 463, 472, 481, 497, 501, 508, 513, 516, 539, 542, 550, 555, 562, 570, 574, 589, 591, 598, 604, 612, 631, 634, 640, 647, 656, 661 Learning Stations, 16E–16F, 70E–70F, 124E–124F, 182E–182F, 238E–238F, 278E–278F, 324E–324F, 380E–380F, 442E–442F, 492E–492F, 530E–530F, 582E–582F, 624E–624F Problem-Solving Projects, 672–681 Real-World Problem Solving, 22, 30, 38, 58, 82, 88, 92, 98, 102, 115, 156, 162, 166, 189, 192, 202, 243, 260, 266, 290, 298, 302, 306, 332, 338, 387, 417, 447, 451, 458, 462, 498, 538, 570, 630, 650, 660
Index
Division-multiplication relationship, 75–77 Division Shuffle Game, 311 Divisors, 74, 278C, 278, 281–282, 283–285, 316 Equations, 152–153, 154–157, 177 Estimating quotients, 292–294, 296–299, 316, 318, EP18 Expressions, 148–150, 177 Facts, 70, 73–74, 75–77, 78–79, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 116–119, EP5, EP6, EP7 Functions, 164–167, 178 Greater numbers, 308–310, 318 Modeling, 73–74, 86–89, 90–92, 96–99, 100–102, 281–282, 283–285, 288–291, 292–294, 296–299, 300–302, 304–307, 308–310 Multi-digit, 281–282, 283–285, 288–291, 292–294, 295, 296–299, 300–302, 304–307, 308–310, 311, 316–320, EP18, EP19 Number by itself, 81–83 On a number line, 78–79 Patterns, 288–291, 318, EP17 Quotients, 74, 278C, 278, 281–282, 283–285, 292–294, 300–302, 304–307, 316–320 Quotients with zeros, 304–307, 318 Related facts, 75–77, 86–89, 90–92, 117, EP5 Remainders, 278C, 278, 283–285, 297–299, 300–302, 304–307, 316, 317, EP18, EP19 Repeated subtraction, 78–79, 117, EP5 Rules, 80–83, 117 Strategies, 73–74, 78–79, 86–89, 90–92, 96–99, 100–102 Three-digit quotients, 300–302, 318 Two-digit, 296–299, 318 Zeros in, EP5
Equal to (=), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Equally likely, 368–371, 376, EP23 Equations, 124C, 124, 140–141, 142–144, 145, 146–147, 152–153, 154–157, 174, 176, 177, EP9, EP10, EP11 Addition, 140–141, 142–144, 176 Division, 152–153, 154–157, 177 Multiplication, 152–153, 154–155, 177 Solving equations, 140–141, 142–144, 146–147, 152–153, 154–157, 176, 177, EP9, EP10, EP11 Subtraction, 140–141, 142–144, 176 Writing equations, 681, EP9, EP10, EP11 Equilateral triangles, 511–513, 525, EP31
INDEX 6
Index
Equivalent Decimals and fractions, 420, 421–423, 428–429, 430–432, 433, 438 Decimals-fractions on a number line, 428–429, 430–432 Fractions, 6–7, 380C, 380, 399–400, 401–403, 410–413, 428–429, 434, 435, 448–451, 452–455, 484, EP24 Fractions-decimals, 420, 421–423, 428–429, 430–432, 433, 438 Fractions-decimals on a number line, 428–429, 430–432 Fractions on a number line, 400, 428–429 Essential Questions, 16, 19A, 32A, 44A, 70, 73A, 84A, 96A, 110A, 124, 127A, 136A, 148A, 160A, 182, 185A, 196A, 206A, 226A, 238, 241A, 250A, 256A, 264A, 278, 281A, 288A, 296A, 324, 327A, 334A, 348A, 362A, 380, 383A, 399A, 420A, 442, 445A, 456A, 468A, 492, 495A, 504A, 510A, 530, 533A, 546A, 560A, 566A, 582, 585A, 594A, 602A, 608A, 624, 627A, 642A, 658A Estimate/estimation, 16C, 16, 28–31, 36–39, 40–41, 44–47, 50–53, 62, 64, 65, 66, 182C, 182, 190–193, 204, 228–230, 231, 232, 238C, 238, 244–247, 270, 442C, 442, 460–463, 484, 486 Capacity, 627, 628–631, 635, 638–640, 665, 666, EP38, EP39 Costs, 680–681 Decimal differences, 460–463, 484, 486, EP28 Decimal sums, 460–463, 484, 486, EP28, EP29 Differences, 36–39, 50–53, 64, 66 Estimate or Exact Answer ProblemSolving Strategy, 40–41, 65, EP3 Estimation Station Game, 204 Length, 585–586, 587–589, 594–595, 596–598, 617, EP36, EP37 Mass, 654–657, 666 Money, 191–193 Products, 190–193, 204, 228–230, 232, 244–247, 270, EP12, EP15 Quotients, 292–294, 296–299, 316, 318, EP18 Sums, 36–39, 44–47, 64, 65, EP3 Time, 681 Weight, 642–643, 644–647, 648–651, 666, EP39 Estimate or Exact Answer Problem-Solving Strategy, 40–41, 65, EP3 Estimation Station Game, 204 ExamView, 43, 67, 69, 93, 121, 123, 145, 179, 181, 205, 235, 237, 255, 275, 277, 295, 321, 323, 347, 377, 379, 419, 439, 441, 467, 489, 491, 509, 527, 529, 558, 579, 581, 599, 621, 623, 641, 669, 671 Expanded form, 16C, 20–23, 63, 393–395, EP2, EP24 Expanding tessellation patterns, 552–555 Experiments, 362–363, 364–367 Expression Race Game, 151 Expressions, 124C, 124, 136–139, 148–150, 151, 152–153, 174, 176, 177, EP9, EP10
INDEX 7
Addition, 136–139, 176 Division, 148–150, 177 Expression Race Game, 151 Expressions, 148–150, 177 Solving expressions, EP9, EP10 Subtraction, 136–139, 176 Values, 136–139, 148–150, 151, 176, 177 Writing expressions, 137–139, 148–150, 176, EP9, EP10 Extending patterns, 127–129, 130–133, 175, EP8 Extending the Concept, 49, 74, 153, 169, 186, 197, 207, 209, 226, 251, 257, 282, 341, 346, 353, 363, 384, 400, 429, 469, 505, 535, 547, 567, 586, 595, 609, 615, 643 Extend the Activity, 61, 95, 147, 225, 263, 315, 361, 425, 483, 521, 565, 601, 653 Extend the Game, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 Extend the Strategy, 249 Extra Practice, EP2–EP40
Ff Faces, 492C, 499–501, 524, EP30 Fact families, 70C, 70, 75–77, 116, 278, 283–285, EP5 Factors, 70C, 70, 73–74, 110–113, 116, 120, 182C, 238C, 238, 244–247, 270, EP8 Common factor, 70C, 113, 410–413 Greatest common factor, 380C, 380, 410–413, 434, 437 More About Factors and Multiples, 113 Facts Division, 70, 73–74, 75–77, 78–79, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 116–119, EP5, EP6, EP7 Fact families, 70C, 70, 75–77, 116, 278, 283–285, EP5 Multiplication, 70, 73–74, 75–77, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 103, 116–119, EP5, EP6, EP7 Far Below Grade Level, T13 Find and Extend the Rule for Each Table, 10 Find Equivalent Fractions, 6 Find Missing Values in Equivalent Fractions Number Sentences, 7 Find the Error H.O.T. Problems, 11, 31, 58, 79, 99, 173, 212, 260, 299, 398, 403, 455, 459, 562, 631, 661 Flips, 546–547, 548–551, 552–555, 560–562, EP33 Fluid ounces, 628–631, 632–634, 635, 664, 665, EP38 Focus on Math Background, 19A, 32A, 44A, 73A, 84A, 96A, 110A, 127A, 136A, 148A, 160A, 185A, 196A, 206A, 226A, 241A, 250A, 256A, 264A, 281A, 288A, 296A, 327A, 334A, 348A, 362A, 383A, 399A, 420A, 445A, 456A,
468A, 495A, 504A, 510A, 533A, 546A, 560A, 566A, 585A, 594A, 602A, 608A, 627A, 642A, 658A Foldables, 16, 43, 62, 70, 93, 116, 124, 145, 174, 182, 205, 231, 238, 255, 270, 278, 295, 316, 324, 347, 372, 380, 419, 434, 442, 467, 484, 492, 509, 523, 530, 554, 558, 575, 582, 599, 616, 624, 641, 664 Foot (feet), 587–589, 590–591, 616, 617, EP36 Formative Assessment, T17, 22, 27, 31, 35, 39, 41, 43, 47, 53, 55, 59, 68, 77, 79, 83, 85, 89, 92, 93, 99, 102, 105, 109, 113, 115, 122, 129, 133, 135, 139, 144, 145, 150, 157, 159, 163, 167, 173, 180, 189, 193, 195, 203, 205, 213, 215, 219, 223, 230, 236, 243, 247, 249, 254, 255, 261, 266, 269, 276, 285, 287, 291, 294, 295, 299, 302, 307, 310, 313, 322, 329, 333, 335, 339, 344, 347, 351, 356, 359, 367, 370, 378, 387, 391, 395, 398, 403, 405, 409, 413, 418, 419, 423, 427, 432, 440, 447, 451, 455, 459, 463, 465, 467, 473, 475, 481, 490, 497, 501, 503, 508, 509, 513, 517, 519, 528, 539, 543, 545, 551, 555, 557, 558, 562, 571, 574, 580, 589, 591, 593, 598, 599, 604, 607, 613, 622, 631, 634, 637, 640, 641, 647, 651, 657, 661, 663, 670 Formative Research, T18 Formulas, 602–604, 605, 609, 610–613, 616, 619, 620 Area of rectangle, 609, 610–613, 616, 620 Area of square, 611–613, 620 Perimeter of a rectangle, 602–604, 605, 616, 619 Four Step Plan Problem-Solving Strategy, 4–5, 40–41, 54–55, 65, 66, 84–85, 104–105, 118, 119, 134–135, 158–159, 175, 177, 194–195, 214–215, 232, 233, 248–249, 268–269, 272, 274, 286–287, 312–313, 317, 320, 334–335, 358–359, 374, 376, 404–405, 426–427, 436, 438, 464–465, 474–475, 487, 488, 502–503, 518–519, 524, 526, 544–545, 556–557, 592–593, 606–607, 618, 619, 636–637, 662–663, 666, 668 Fraction and Decimal Game, 433 Fractions, 6–7, 380, 399–400, 401–403, 406–409, 410–413, 414–418, 419, 420, 421–423, 424–425, 426–427, 428–429, 430–432, 433, 434–438, 439, 440–441, 442, 445–447, 448–451, 452–455, 484, 485, 489, 490–491, EP24, EP25, EP26, EP27, EP28 Addition, 442, 445–447, 448–451, 484, 485 Addition of like, 445–447, 484, 485, EP27 Addition of unlike, 448–451, 484, 485, EP27 Alternative Manipulative Fraction Kit, 398A Bake Sale Equivalents Chapter Project, 380, 434 Common decimal-fraction equivalents, 430–432 Comparing, 406–409, 433, 437, EP25 Comparing fractions and decimals, 433 Comparing on a number line, 406–409 Degrees, EP31
Frequency tables, 13–15, 324C, 327–329, 336–339, 352–353, 372, 373, EP19 From Concrete to Abstract, 19, 49, 74, 141, 153, 169, 186, 197, 199, 207, 209, 226, 251, 282, 353, 363, 384, 400, 420, 429, 469, 477, 505, 535, 547, 567, 586, 595, 609, 615, 627, 643 Function Rule Creation Race, 11 Functions, 8–11, 124C, 124, 160–163, 164–167, 168–169, 170–173, 174, 178, EP11 Addition, 160–163, 178 Division, 164–167, 178 Find and Extend the Rule for Each Table, 10 Function Rule Creation Race, 11 Function Tables, 9 Input, 9–11, 160–163, 164–167, 178 Multiplication, 164–167, 178 Output, 9–11, 160–163, 164–167, 178 Rules, 8–11, 160–163, 164–167, 170–173, 174, 178 Subtraction, 160–163, 178 Tables, 8–11, 124C, 160–163, 164–167, 170–173, 178, EP11 With two operations, 168–169, 170–173, 178
Function Tables, 9 Fun Facts, 60, 94, 146, 206F, 224, 262, 314, 327, 360, 398A, 424, 445E, 492, 495E, 520, 564, 585E, 600, 608E, 627E, 652
Gg Gallons, 624, 627, 628–631, 632–634, 635, 664, 665, EP38 Game Activities, 28, 87, 161, 187, 292, 392, 411, 430, 457, 478, 495, 506, 548, 632, 648 Game Time, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 Capacity Estimates, 635 Differentiated Practice, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 Division Shuffle, 311 Estimation Station, 204 Expression Race, 151 Extend the Game, 42, 103, 151, 204, 267, 311, 357, 433, 466, 522, 559, 605, 635 Fraction and Decimal, 433 Geometric Sketch, 522 Geometry Match, 559 Graph Race, 357 Greatest Product, 267 Make a Big Difference, 42 Match Up, 466 Multiplication Bingo, 103 Perimeter Guess, 605 Geography Cross Curricular Connection, 262–263 A Walk in the Park, 262–263 Geometric patterns, 127–129, 175, EP8 Geometric Sketch Game, 522 Geometry, 492, 495–498, 499–501, 502–503, 504–505, 506–508, 509, 510–513, 514–517, 518–519, 520–521, 522, 523–526, 527, 528–529, 530, 533, 534–535, 536–539, 546–547, 548–551, 552–555, 556–557, 558, 559, 560–562, 563, 566–567, 568–571, 572–574, 575–578, 579, 580–581, EP30, EP31, EP32, EP33, EP34, EP35 Acute angles, 492C, 507–508, 510–513, 525, EP31 Acute triangles, 510–513, 525, EP31 Angles, 492C, 492, 495–498, 504–505, 506–508, 509, 510–513, 514–517, 523, 525, EP31 A Banner of Shapes Chapter Project, 492, 523 Center of circles, 492C, 498 Circles, 492C, 496, 498 Classifying angles, 504–505, 506–508, 525 Classroom Quilt Chapter Project, 530, 575 Combining three-dimensional figures, 501 Compass, 504–505 Compound figures, 497 Cones, 499–501 Congruent, 530C Congruent Cases Social Studies Cross Curricular Connection, 564–565
Congruent figures, 530C, 530, 560–562, 563, 575, 578, EP34 Constructing geometric figures, 543 Cubes, 499–501 Cylinders, 499–501 Decagons, 495–498 Diameter, 492C, 498 Drawing figures, 522 Edges, 492C, 499–501, 524, EP30 Endpoints, 530C, 506–508, 523, 536–539 Equilateral triangles, 511–513, 525, EP31 Faces, 492C, 499–501, 524, EP30 Flips, 546–547, 548–551, 552–555, 560–562, EP33 Geometric Sketch Game, 522 Geometry Match Game, 559 Hexagons, 492C, 495–498 Intersecting lines, 530C, 534–535, 537–539, 575, 576, EP32 Isosceles triangles, 511–513, 525, EP31 Lines, 530C, 530, 533, 534–535, 536–539, 575, 576, EP32 Line segments, 495–498, 530C, 530, 533, 536–539, 575, 576, EP32 Lines of symmetry, 530C, 568–571, 572–574, 578, EP35 Line symmetry, 530C, 566–567, 568–571, 578 More About Two-Dimensional Figures, 498 Nets, 492C, 500–501 Obtuse angles, 492C, 507–508, 510–513, 525, 510–513, 525, EP31 Octagons, 492C, 495–498 Parallel lines, 530C, 534–535, 537–539, 575, 576, EP32 Parallelograms, 492C, 514–517, 526, EP32 Patterns, 127–129, 175, EP8 Pentagons, 492C, 495–498, 543 Perpendicular lines, 530C, 534–535, 537–539, 575, 576, EP32 Plane figures, 492, 495–498, 523, 524, 525 Polygons, 492C, 492, 495–498, 523, 524, 525, 543, EP30 Quadrilaterals, 492C, 495–498, 514–517, 523, 526, EP32 Radius, 492C, 498 Rays, 506–508, 523, 530C, 536–539, 575, 576, EP32 Rectangles, 492C, 514–517, 526, EP32 Rectangular prisms, 499–501 Reflections, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Rhombus, 492C, 514–517, 526 Right angles, 492C, 507–508, 510–513, 525, EP31 Right triangles, 510–513, 525, EP31 Rotational symmetry, 530C, 566–567, 572–574, 578, EP35 Rotations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Scalene triangles, 511–513, 525, EP31 Sides, 492C, 495–498, 510–513, 514–517 Slides, 546–547, 548–551, 552–555, 560–562, EP33 Solid figures, 492, 499–501, 523, 524
Index
Equivalent, 6–7, 380C, 380, 399–400, 401–403, 410–413, 428–429, 434, 435, 448–451, 452–455, 484, EP24 Equivalent fractions-decimals, 420, 421–423, 428–429, 430–432, 433, 438 Equivalent fractions-decimals on a number line, 428–429, 430–432 Equivalent fractions on a number line, 400, 428–429 Find Equivalent Fractions, 6 Find Missing Values in Equivalent Fractions Number Sentences, 7 Fraction and Decimal Game, 433 Fraction-decimal relationship, 420, 421–423, 428–429, 430–432, 433, 438, EP26, EP27 Greatest common factor, 380C, 380, 410–413, 434, 437 Improper fractions, 380C, 414–418, 437, EP26 Like fractions, 442C, 442, 445–447, 484 Mixed numbers, 380C, 380, 414–418, 434, 437, 448–451, EP26 Mixed numbers on a number line, 414–418, 434 More About Factors and Multiples, 113 On a number line, 400, 406–409, 428–429 Ordering, 406–409, 437 Ordering on a number line, 406–409 Probability, 371 Shopping List Chapter Project, 442, 484 Simplest form, 380C, 380, 410–413, 434, 437, 445–447, 448–451, 452–455, 485, EP25, EP27, EP28 Subtraction, 442, 445–447, 452–455, 484, 485 Subtraction of like fraction, 445–447, 484, 485, EP27 Subtraction of unlike fractions, 452–455, 484, 485, EP28 Unlike, 448–451, 484, 485, EP27
INDEX 8
Index
Spatial reasoning, 530, 533, 536–539, 540–543, 544–545, 546–547, 548–551, 552–555, 556–557, 558, 559, 560–562, 563, 566–567, 568–571, 572–574, 575–578, 579, 580–581 Spheres, 499–501 Square pyramids, 499–501 Squares, 492C, 514–517, 526, EP32 Symmetry, 566–567, 568–571, 572–574, 578, EP35 Tessellations, 530C, 552–555, EP34 Three-dimensional figures, 492C, 492, 497, 499–501, 523, 524, EP30 Transformations, 530C, 530, 546–547, 548–551, 552–555, 559, 575, 577, EP33, EP34 Translations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Trapezoids, 492C, 514–517, 526, EP32 Triangles, 492C, 495–498, 510–513, 525, 543, EP31 Triangular prisms, 499–501 Triangular pyramids, 499–501 Turns, 546–547, 548–551, 552–555, 560–562, EP33 Two-dimensional figures, 492C, 492, 495–498, 523, 524, 525, EP30, EP31, EP32 Vertex (vertices), 499–501, 524, EP30 Geometry Match Game, 559 Gifted and Talented, See Enrichment. Grams, 654–657, 657, 664, 666, EP40 Graph Game, 15 Graphic Novel, T10, 3, 17, 46, 71, 108, 125, 144, 183, 222, 239, 254, 279, 285, 325, 329, 381, 417, 443, 480, 493, 508, 531, 554, 583, 591, 625, 634 Animated Graphic Novel, 17, 71, 78, 125, 144, 149, 183, 222, 239, 258, 279, 285, 304, 325, 329, 381, 417, 443, 460, 480, 493, 508, 531, 583, 591, 625, 634 Reading Graphic Novels, A5, A8, A11, A13, A20, A23, A26, A28, A32, A37, A39, A42, A47, A49, A50 Text Features Specific to Graphic Novels, A5 Using Comprehension Strategies with Graphic Novels, A5 Graph Race Game, 357 Graphs, 12–15, 342–344, 345–346, 348–351, 352–353, 354–356, 357, 372, 374, 375, 679, EP21, EP22 Analyze Graphs, 13 Bar graphs, 13–15, 324C, 324, 348–351, 357, 372, 375, 679, EP21, EP22 Circle graphs, 351, 508 Comparing data on graphs, 348–351, 352–353, 354–356, 372, 375 Coordinate planes, 530C, 540–543, 575, 576, EP33 Coordinates, 530C, 530, 540–543, 576 Creating double bar graphs, 352–353 Creating line graphs, 345–346 Double bar graphs, 324C, 352–353, 354–356, 375 Graph Game, 15 Graph Race Game, 357
INDEX 9
Interpreting, 342–344, 348–351, 352–353, 354–356, 375 Line, 324C, 342–344, 345–346, 372, 375 More About Graphs, 351 Ordered pair, 530C, 540–543, 576, EP33 Origin, 530C, 540–543 Pictographs, 12–15 Pie charts, 351, 508 Plotting points on a grid, 540–543, 576 Points, 533, 540–543 Scales, 345–346, 352–353 Titles, 345–346, 352–353 X-axis, 530C, 540–543 X-coordinate, 540–543 Y-axis, 530C, 540–543 Y-coordinate, 540–543 Greater than (>), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Greatest common factor, 380C, 380, 410–413, 434, 437 Greatest Product Game, 267 Gridded Response Questions, 69, 123, 181, 237, 277, 323, 379, 441, 491, 523, 581, 623, 670, 671 Grids, 540–543, 576 More About Points on a Grid, 543 Plotting points on a grid, 540–543, 576 Points, 533, 540–543 Growing patterns, 128–129 Guess, Check, and Revise Problem-Solving Strategy, 286–287, 313, 317, 519, 607, 663, EP17
Hh Half inch, 585–586, 587–589, 617, EP36 Hands-On Activities, 20, 24, 28, 32, 36, 44, 50, 56, 75, 78, 80, 86, 90, 96, 100, 106, 110, 114, 127, 130, 136, 142, 148, 154, 160, 164, 170, 187, 190, 200, 210, 216, 220, 228, 241, 244, 252, 258, 264, 283, 288, 292, 296, 300, 304, 308, 327, 330, 336, 342, 348, 354, 364, 368, 385, 388, 392, 396, 401, 406, 410, 414, 421, 430, 445, 448, 452, 456, 460, 470, 478, 495, 499, 506, 510, 514, 536, 540, 548, 552, 560, 568, 572, 587, 590, 596, 602, 610, 628, 632, 638, 644, 648, 654, 658 A Head Above the Rest Science Cross Curricular Connection, 360–361 Health Learning Stations, 16F, 70E, 124E, 182E, 238F, 278F, 324F, 380F, 442E, 492F, 530F, 582F, 624E Healthy Foods Party Chapter Project, 182, 231
Olympic Games, 482–483 Pop Culture, 94–95 H.O.T. Problems, Higher Order Thinking skills are developed and utilized in these problems found throughout the Student Edition. H.O.T. Problems, 11, 15, 22, 27, 31, 34, 39, 47, 53, 58, 77, 79, 83, 89, 92, 99, 102, 108, 113, 115, 129, 133, 138, 144, 150, 157, 162, 166, 173, 189, 193, 203, 212, 219, 223, 230, 243, 247, 254, 260, 266, 285, 291, 294, 299, 302, 306, 310, 329, 333, 339, 344, 350, 356, 366, 370, 387, 391, 395, 398, 403, 409, 412, 417, 423, 432, 447, 451, 455, 459, 463, 472, 481, 497, 501, 508, 513, 516, 539, 542, 550, 555, 562, 570, 574, 589, 591, 598, 604, 612, 631, 634, 640, 647, 656, 661 Challenge, 92, 108, 112, 166, 203, 223, 291, 310, 391, 403, 409, 423, 432, 459, 463, 481, 591, 604, 640, 650, 656, 661 Find the Error, 11, 31, 58, 79, 99, 173, 212, 260, 299, 398, 403, 455, 459, 562, 631, 661 Number Sense, 27, 39, 83, 92, 144, 193, 203, 247, 266, 291, 350, 398, 451, 612, 647 Open Ended, 15, 22, 34, 39, 47, 58, 77, 83, 89, 92, 99, 102, 108, 112, 115, 133, 138, 144, 150, 157, 162, 166, 189, 219, 223, 230, 243, 247, 266, 285, 294, 299, 302, 306, 310, 329, 339, 344, 356, 366, 370, 387, 391, 395, 403, 409, 412, 417, 423, 432, 447, 463, 481, 497, 501, 508, 513, 516, 539, 542, 550, 555, 562, 570, 574, 589, 598, 612, 631, 634, 640, 650, 656 Reasoning, 516, 539 Which One Doesn’t Belong?, 34, 53, 89, 108, 129, 138, 157, 219, 230, 243, 254, 310, 409, 412, 451, 455, 463, 472, 497, 501, 513, 550, 555, 574, 634 Hours, 676–677 How Language Arts and Reading Connect to Math, A2 How to Use the Student Handbook, EP1 Hundreds, 19, 20–23 Hundred thousands, 20–23 Hundredths, 380C, 383–384, 388–391, 421–423, 434, 435
Ii Identifying patterns, 127–129, 130–133, 175 Identity Property of Addition, 16C, 32–35 Identity Property of Multiplication, 80–83, 116, 117 IMPACT Mathematics, T8–T9
Healthy Snacks Chapter Project, 624, 664
Impossible, 368–371, 376, EP23
Helping Student Read Mathematics Texts, A4
Improper fractions, 380C, 414–418, 437, EP26
Hexagons, 492C, 495–498
Inches, 587–589, 590–591, 616, 617, EP36 Half inch, 585–586, 587–589, 617, EP36 Quarter inch, 585–586, 587–589, 617, EP36
History Cross Curricular Connections, 94–95, 482–483
Initial Assessment, T16 Input, 9–11, 160–163, 164–167, 178 Inservice, T15 Intensive Intervention, T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Interpreting graphs, 342–344, 348–351, 352–353, 354–356, 375 Intersecting lines, 530C, 534–535, 537–539, 575, 576, EP32 Intervention, 63, 117, 175, 232, 271, 317, 373, 435, 485, 524, 576, 617, 665 Into the Future, 39, 89, 92, 163, 193, 243, 285, 294, 307, 344, 367, 387, 451, 473, 508, 551, 613, 631 Introduce the Chapter, 16, 70, 124, 182, 238, 278, 324, 380, 442, 492, 530, 582, 624 Is equal to (=), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is greater than (>), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is less than (<), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Isosceles triangles, 511–513, 525, EP31
Jj Journals, 383E
Kk Key Concepts, 29, 32–33, 80–81, 114, 210, 250, 393, 411, 431, 445, 446, 460, 461, 499, 506, 507, 510, 511, 514, 536, 537, 549, 587, 590, 596, 610–611, 632, 655 Key Vocabulary, 16, 62, 70, 116, 124, 174, 182, 231, 238, 270, 278, 316, 324, 372, 380, 434, 442, 484, 492, 523, 530, 575, 582, 616, 624, 664 Kilograms, 654–657, 657, 664, 666, EP40 Kilometers, 596–598, 616, EP37
Ll Language Alert!, 21, 33, 51, 73, 85, 97, 110, 127, 142, 153, 160, 191, 199, 215, 229, 243, 258, 265, 284, 289, 297, 335, 340, 349, 369, 383, 402, 427, 428, 445, 457, 468, 476, 507, 510, 537, 549, 587, 609, 611, 629, 645, 659 Lead authors, T22 Leaf/leaves 340–341
Learning Stations, 16E–16F, 70E–70F, 124E–124F, 182E–182F, 238E–238F, 278E–278F, 324E–324F, 380E–380F, 442E–442F, 492E–492F, 530E–530F, 582E–582F, 624E–624F Art, 16E, 70E, 182E, 238E, 278E, 380E, 442E, 492E, 530E, 582E, 624E Health, 16F, 70E, 124E, 182E, 238F, 278F, 324F, 380F, 442E, 492F, 530F, 582F, 624E Music, 70F, 124F, 182F, 278F, 324F, 442F, 492F, 582F, 624F Reading, 16E, 124E, 238E, 324F, 380E, 492E, 530E Science, 16F, 70F, 124F, 182F, 238F, 278F, 324E, 380F, 442F, 492F, 530F, 582F, 624F Social Studies, 16F, 70F, 124F, 182F, 238F, 278E, 324E, 380F, 442F, 530F, 582E, 624F Writing, 16E, 70E, 124E, 182E, 238E, 278E, 324E, 380E, 442E, 492E, 530E, 582E, 624E Length, 582C, 582, 585–586, 587–589, 590–591, 594–595, 596–598, 599, 600–601, 602–604, 605, 616, 617, 618, EP36, EP37 Centimeters, 594–595, 596–598, 600–601, 616, 618, 657, EP37 Converting customary units, 590–591, 616, 617, EP36 Converting metric units, 657 Estimating, 585–586, 587–589, 594–595, 596–598, 617, EP36, EP37 Foot (feet), 587–589, 590–591, 616, 617, EP36 Half inch, 585–586, 587–589, 617, EP36 Inches, 587–589, 590–591, 616, 617, EP36 Kilometers, 596–598, 616, EP37 Meters, 596–598, 600–601, 616, 657, EP37 Miles, 590–591, 680–681 Millimeters, 596–598, 600–601, 616, 657, EP37 Quarter-inch, 585–586, 587–589, 617, EP36 Yards, 587–589, 590–591, 616, 617, EP36 Less than (<), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Lesson Planners, 19A–19B, 32A–32B, 44A–44B, 73A–73B, 84A–84B, 96A–96B, 110A, 127A–127B, 136A–136B, 148A–148B, 160A–160B, 185A–185B, 196A–196B, 206A–206C, 226A, 241A–241B, 250A, 256A, 264A, 281A–281B, 288A, 296A–296C, 327A, 334A–334B, 348A–348B, 362A–362B, 383A–383B, 399A–399C, 420A–420B, 445A–445B, 456A–456B, 468A–468B, 495A–495B, 504A, 510A–510B, 533A–533B, 546A–546B, 560A, 566A–566B, 585A–585B, 594A, 602A, 08A–608B, 627A–627B, 642A–642B, 658A Library Books, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D Like fractions, 442C, 442, 445–447, 484 Addition, 445–447, 484, 485, EP27 Subtraction, 445–447, 484, 485, EP27 Likely, 368–371, 376, EP23
Line graphs, 324C, 342–344, 345–346, 372, 375 Line plots, 13–15, 324C, 324, 336–339, 374, EP20
Index
Index Question Activities, 20, 32, 80, 96, 142, 171, 190, 220, 264, 296, 308, 330, 354, 406, 421, 445, 470, 499, 536, 568, 590, 628, 644
Lines, 530C, 530, 533, 534–535, 536–539, 575, 576, EP32 Intersecting, 530C, 534–535, 537–539, 575, 576, EP32 Parallel, 530C, 534–535, 537–539, 575, 576, EP32 Perpendicular, 530C, 534–535, 537–539, 575, 576, EP32 Line segments, 495–498, 530C, 530, 533, 536–539, 575, 576, EP32 Lines of symmetry, 530C, 568–571, 572–574, 578, EP35 Line symmetry, 530C, 566–567, 568–571, 578 Literature Library Books, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D Real-World Problem-Solving Library, 16D, 40, 70D, 84, 124D, 134, 182D, 194, 228, 238D, 248, 278D, 286, 324D, 334, 342, 380D, 404, 442D, 464, 492D, 502, 530D, 544, 572, 582D, 592, 624D, 636 Liters, 638–640, 657, 664, 666, EP39 Look for a Pattern Problem-Solving Strategy, 502–503, 524, EP31
Mm Maintenance, See Spiral Review. Make a Big Difference Game, 42 Make a Game Chapter Project, 124, 174 Make a Game Problem-Solving Project, 674–675 Make a Model Problem-Solving Strategy, 404–405, 425, 436, EP25 Make an Organized List Problem-Solving Strategy, 544–545, 576, EP33 Make a Table Problem-Solving Strategy, 248–249, 269, 272, 313, 334–335, 359, 374, 425, 475, 519, 557, 607, EP15, EP20 Make Your Home Your Own ProblemSolving Project, 678–679 Making Mosaics Art Cross Curricular Connection, 520–521 Maps, 680–681 Changing scale, 679 Scale, 679 Map Your Home Chapter Project, 582, 616 Mass, 624C, 624, 654–657, 657, 664, EP40 Estimating, 654–657, 666 Grams, 654–657, 657, 664, 666, EP40 Kilograms, 654–657, 657, 664, 666, EP40 Match Up Game, 466
INDEX 10
Index
Math at Home Letter, 17, 71, 125, 183, 239, 279, 381, 443, 493, 531, 583, 625, 533E Math Connects, T8–T9 Math Game Activity, 241 Math in Action Activity, 155 Math Tool Chest, 303, 563 Math Vocabulary, 16C, 70C, 124C, 182C, 238C, 278C, 324C, 380C, 442C, 492C, 530C, 582C, 624C Measure/measurement, 582, 585–586, 587–589, 590–591, 592–593, 594–595, 596–598, 599, 600–601, 602–604, 605, 608–609, 610–613, 614–615, 616–620, 621, 622–623, 624, 627, 628–631, 632–634, 635, 636–637, 638–640, 641, 642–643, 644–647, 648–651, 652–653, 654–657, 658–661, 662–663, 664–668, 669, 670–671, EP36, EP37, EP38, EP39 Angles, 492C, 492, 495–498, 504–505, 506–508, 509, 510–513, 514–517, 523, 525, EP31 Area, 582C, 608–609, 610–613, 614–615, 616, 620, 678–679, EP38 Capacity, 624C, 624, 627, 628–631, 632–634, 635, 638–640, 641, 664, 665, EP38 Capacity Estimates Game, 635 Centimeters, 594–595, 596–598, 600–601, 616, 618, 657, EP37 Converting customary units of capacity, 632–634, 665, EP38 Converting customary units of length, 590–591, 616, 617, EP36 Converting customary units of weight, 648–651, 666, EP40 Converting metric units of capacity, 639–640, 657, 665 Converting metric units of length, 657 Cups, 627, 628–631, 632–634, 635, 664, 665, EP38 Customary system, 582C, 585–586, 587–589, 590–591, 599, 616, 617, 627, 628–631, 632–634, 635, 642–643, 644–647, 648–651, 664, 665, 666, EP36, EP38, EP39, EP40 Degrees of angles (º), 504–505, 506–508, 525 Estimating capacity, 627, 628–631, 635, 638–640, 665, 666, EP38, EP39 Estimating length, 585–586, 587–589, 594–595, 596–598, 617, EP36, EP37 Estimating mass, 654–657, 666 Estimating weight, 642–643, 644–647, 648–651, 666, EP39 Fluid ounces, 628–631, 632–634, 635, 664, 665, EP38 Foot (feet), 587–589, 590–591, 616, 617, EP36 Formula for area of rectangle, 609, 610–613, 616, 620 Formula for area of square, 611–613, 620 Formula for perimeter of a rectangle, 602–604, 605, 616, 619 Gallons, 624, 627, 628–631, 632–634, 635, 664, 665, EP38 Grams, 654–657, 657, 664, 666, EP40
INDEX 11
Half inch, 585–586, 587–589, 617, EP36 Healthy Snacks Chapter Project, 624, 664 Inches, 587–589, 590–591, 616, 617, EP36 Kilograms, 654–657, 657, 664, 666, EP40 Kilometers, 596–598, 616, EP37 Length, 582C, 582, 585–586, 587–589, 590–591, 594–595, 596–598, 599, 600–601, 602–604, 605, 616, 617, 618, EP36, EP37 Liters, 638–640, 657, 664, 666, EP39 Map Your Home Chapter Project, 582, 616 Mass, 624C, 624, 654–657, 657, 664, EP40 Meters, 596–598, 600–601, 616, 657, EP37 Metric system, 582C, 582, 594–595, 596–598, 599, 600–601, 616, 618, 638–640, 654–657, 664, 666, EP37, EP39, EP40 Miles, 590–591, 680–681 Milliliters, 638–640, 657, 664, 666, EP39 Millimeters, 596–598, 600–601, 616, 657, EP37 More About Metric Units, 657 Ounces, 642–643, 644–647, 648–651, 664, 666, EP39 Perimeter, 582C, 582, 602–604, 605, 614–615, 616, 619, EP37 Perimeter Guess Game, 605 Pints, 627, 628–631, 632–634, 635, 664, 665, EP38 Pounds, 642–643, 644–647, 648–651, 664, 666, EP39 Quarter inch, 585–586, 587–589, 617, EP36 Quarts, 627, 628–631, 632–634, 635, 664, 665, EP38 Square units, 582C, 608–609, 610–613, 614–615, 616, 620, EP38 Time, 658–661, 668 Tons, 644–647, 648–651, 664, 666, EP39 Weight, 624C, 624, 642–643, 644–647, 648–651, 664, 666, EP39 Yards, 587–589, 590–591, 616, 617, EP36 Median, 324C, 330–333, 373, EP20 Mental math, 142–144, 187–189, 208–209, 211 Mental Math Activity, 131 Meters, 596–598, 600–601, 616, 657, EP37 Metric measurement system, 582C, 582, 594–595, 596–598, 599, 600–601, 616, 618, 638–640, 654–657, 664, 666, EP37, EP39, EP40 Centimeters, 594–595, 596–598, 600–601, 616, 618, 657, EP37 Converting metric units of capacity, 639–640, 657, 665 Converting metric units of length, 657 Estimating mass, 654–657, 666 Grams, 654–657, 657, 664, 666, EP40 Kilograms, 654–657, 657, 664, 666, EP40 Kilometers, 596–598, 616, EP37 Liters, 638–640, 657, 664, 666, EP39 Mass, 624C, 624, 654–657, 657, 664, EP40 Meters, 596–598, 600–601, 616, 657, EP37 Milliliters, 638–640, 657, 664, 666, EP39 Millimeters, 596–598, 600–601, 616, 657, EP37 More About Metric Units, 657 Mid-Chapter Check, 43, 93, 145, 205, 255, 295, 347, 419, 467, 509, 558, 599, 641 Miles, 590–591, 680–681
Milliliters, 638–640, 657, 664, 666, EP39 Millimeters, 596–598, 600–601, 616, 657, EP37 Minuend, 16C Mixed numbers, 380C, 380, 414–418, 434, 437, 448–451, EP26 On a number line, 414–418, 434 Mixed Problem Solving, 55, 105, 159, 215, 269, 313, 359, 425, 475, 519, 557, 607, 663 Mode, 324C, 330–333, 373 Modeling Division, 73–74, 86–89, 90–92, 96–99, 100–102, 281–282, 283–285, 288–291, 292–294, 296–299, 300–302, 304–307, 308–310 Multiplication, 73–74, 86–89, 90–92, 96–99, 100–102, 196–197, 198–199, 200–203, 206–207, 208–209, 216–219, 220–223, 226–227, 228–230 Subtraction, 48–49, 50–53, 56–59 Money, 676–677 Addition, 45–46, 65 Calculating total cost, 677, 680–681 Cost, 677, 679 Decimals, EP23 Estimating, 191–193 Estimating costs, 680–681 Multiplication, 221, 253–254, 259–260 Subtraction, 51–52, 66 Transactions, 38, 40, 41, 46, 47, 51, 52, 53, 54, 59, 61, 65, 66, 67, 84, 85, 89, 91, 95, 101, 105, 108, 118, 119, 130, 139, 145, 156, 157, 161, 162, 164, 165, 166, 170, 171, 172, 175, 177, 179, 180, 181, 189, 191, 192, 195, 212, 215, 218, 221, 223, 228, 230, 233, 234, 235, 237, 242, 249, 253, 259, 263, 269, 271, 272, 273, 275, 276, 277, 285, 286, 287, 289, 290, 291, 294, 295, 298, 299, 303, 306, 307, 309, 313, 317, 320, 332, 335, 337, 347, 356, 438, 462, 471, 472, 473, 475, 480, 481, 486, 491, 519, 529, 559, 593, 607, 663, 677, 681, EP3, EP4, EP6, EP8, EP11, EP14, EP16, EP17, EP18, EP20, EP21, EP22, EP27, EP30, EP35, EP36, EP37, EP40 More About Comparing and Ordering Numbers, 27 Decimals, 391 Factors and Multiples, 113 Graphs, 351 Metric Units, 657 Place Value, 23 Points on a Grid, 543 Probability, 371 Rounding Decimals, 459 Rounding Numbers, 31 Two-Dimensional Figures, 498 Multiple Choice Questions, 35, 39, 43, 47, 53, 59, 67, 68–69, 83, 89, 93, 99, 109, 121, 122–123, 133, 139, 145, 157, 163, 167, 173, 179, 180–181, 193, 203, 205, 213, 219, 223, 235, 236–237, 247, 255, 261, 275, 276–277, 291, 295, 299, 307, 321, 322–323, 333, 339, 347, 367, 377, 378–379, 395, 409, 413, 418, 419, 439, 440–441, 463, 467, 473, 481, 489, 490–491, 509, 513, 517, 527, 528–529, 539, 551, 555,
Multiples, 70C, 70, 111–113, 116, 120, 182C, 182, 185–186, 187–189, 231, 232, 238C, 238, 241–243, 270 , EP8 Common multiple, 70C, 113 More About Factors and Multiples, 113 Multiplication Bingo Game, 103 Multiplication properties, 80–83, 100–102, 106–109, 116, 117, 210–213 Associative Property of Multiplication, 80–83, 106–109, 116, 117, 241–243, EP5 Commutative Property of Multiplication, 80–83, 116, 117, 241–243, EP5 Distributive Property of Multiplication, 70C, 100–102, 210–213, 216–219, 228–230, 231, 233, 250–251, 273, EP13 Identity Property of Multiplication, 80–83, 116, 117 Zero Property of Multiplication, 80–83, 116, 117, EP5 Multiplication strategies, 73–74, 86–89, 90–92, 96–99, 100–102 Area models for, 86–89, 90–92, 100–102, 118, 119, 198–199, 256–257, 258–261, EP6, EP7 Arrays, 73–74, 75–77, 86–89, 117, 118, 119, EP6, EP7 Estimating products, 190–193, 204, 228–230, 232, 244–247, 270, EP12, EP15 Modeling, 73–74, 86–89, 90–92, 96–99, 100–102, 196–197, 198–199, 200–203, 206–207, 208–209, 216–219, 220–223 Partial products, 198–199, 208–209, 216–219, 220–223, 228–230, 250–251, 252–254, 264–266 Regrouping for, 206–207, 216–219 Related facts, 75–77, 86–89, 90–92, 117, EP5 Repeated addition, 73–74, 185–186 Skip counting, 86–89, 96–99, 185–186 Multiply/multiplication, 70, 73–74, 75–77, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 103, 106–109, 110–113, 116–119, 182C, 182, 185–186, 187–189, 190–193, 196–197, 198–199, 200–203, 204, 205, 206–207, 208–209, 210–213, 216–219, 220–223, 226–227, 228–230, 231, 232, 233, 234, 235, 236–237, 238, 241–243, 244–247, 250–251, 252–254, 255, 256–257, 258–261, 262–263, 264–266, 267, 270–274, EP12, EP13, EP14, EP15, EP16 Across zeros, 226–227, 228–230, 234 Area models for, 86–89, 90–92, 100–102, 118, 119, 198–199, 256–257, 258–261, EP6, EP7 Arrays, 73–74, 75–77, 86–89, 117, 118, 119, EP6, EP7 Associative Property of Multiplication, 80–83, 106–109, 116, 117, 241–243, EP5 By 1, 86–89, 118 By 2, 86–89, 118 By 3, 86–89, 118 By 4, 86–89, 118 By 5, 86–89, 118
By 6, 90–92, 118 By 7, 90–92, 118 By 8, 90–92, 118 By 9, 90–92, 118 By 10, 96–99, 119 By 11, 100–102, 119 By 12, 100–102, 119 By multiples of 10, 185–186, 187–189, 231, 232, EP12, EP13 By multiples of 100, 187–189, 231, 232, EP12 By multiples of 1,000, 187–189, 231, 232, EP12 By one-digit numbers, 182, 196–197, 198–199, 200–203, 206–207, 208–209, 231, 232, 233, 234 By tens, 241–243, 271 By three numbers, 106–109, 120, EP7 Commutative Property of Multiplication, 80–83, 116, 117, 241–243, EP5 Daily Multiples Book Chapter Project, 70, 116 Distributive Property of Multiplication, 70C, 100–102, 210–213, 216–219, 228–230, 231, 233, 250–251, 273, EP13 Equations, 152–153, 154–155, 177 Estimating products, 190–193, 204, 228–230, 232, 244–247, 270, EP12, EP15 Expressions, 148–150, 177 Factors, 70C, 70, 73–74, 110–113, 116, 120, 182C, 238C, 238, 244–247, 270, EP8 Facts, 70, 73–74, 75–77, 80–83, 86–89, 90–92, 93, 96–99, 100–102, 103, 116–119, EP5, EP6, EP7 Functions, 164–167, 178 Greater numbers, 264–266, 274 Greatest Product Game, 267 Healthy Foods Party Chapter Project, 182, 231 Identity Property of Multiplication, 80–83, 116, 117 Modeling, 73–74, 86–89, 90–92, 96–99, 100–102, 196–197, 198–199, 200–203, 206–207, 208–209, 216–219, 220–223, 226–227, 228–230 Money, 221, 253–254, 259–260 More About Factors and Multiples, 113 Multi-digit, 182, 185–186, 187–189, 190–193, 196–197, 198–199, 206–207, 208–209, 210–213, 216–219, 220–223, 226–227, 228–230, 231, 232, 233, 234, 235, 236–237, 238, 241–243, 244–247, 250–251, 252–254, 255, 256–257, 258–261, 264–266, 267, 270–274, EP13, EP15, EP16 Multiples, 70C, 70, 111–113, 116, 120, 182C, 182, 185–186, 187–189, 231, 232, 238C, 238, 241–243, 270 , EP8 Multiplication-division relationship, 75–77 Multiplication Bingo Game, 103 Name that Digit Chapter Project, 238, 270 Partial products, 198–199, 208–209, 216–219, 220–223, 228–230, 250–251, 252–254, 264–266 Patterns, 96–99, 187–189, 231, 232, 288–291, 318, EP12 Products, 73–74, 182C, 238C, 238, 244–247, 270, 271
Properties, 80–83, 100–102, 106–109, 116, 117, 210–213 Regrouping for, 206–207, 216–219 Related facts, 75–77, 86–89, 90–92, 117, EP5 Repeated addition, 73–74, 185–186 Skip counting, 86–89, 96–99, 185–186 Strategies, 73–74, 86–89, 90–92, 96–99, 100–102 Three-digit numbers, 256–257, 258–261, 273 Zero Property of Multiplication, 80–83, 116, 117, EP5 Zeros, 226–227, 228–230, 234
Index
558, 571, 579, 580–581, 599, 613, 621, 622–623, 631, 641, 647, 651, 661, 669, 670–671
Multi-Step Problems, 22, 41, 52, 55, 85, 98, 102, 105, 107, 135, 156, 195, 218, 222, 249, 260, 266, 269, 287, 289–290, 335, 405, 407, 425, 446, 447, 462, 465, 475, 480, 557, 593, 612, 663 Music Activities, 100, 106, 216, 252 Music Cross Curricular Connection, 424–425 Decimal Note-ation, 424–425 Music Learning Stations, 70F, 124F, 182F, 278F, 324F, 442F, 492F, 582F, 624F
Nn Name that Digit Chapter Project, 238, 270 Name the Math, 27, 35, 47, 79, 99, 102, 113, 133, 144, 150, 157, 230, 254, 266, 291, 299, 339, 371, 395, 398, 418, 432, 463, 498, 517, 543, 604, 634, 647, 657 NCTM Process Standards, T32–T33 Nearest whole number, 457–459, 484, 486 Nets, 492C, 500–501 The Next Generation Classroom, T4–T5 Nonnumeric patterns, 124C, 127–129, 175 Number lines, 16, 24–27, 336–339 Comparing fractions on, 406–409 Comparing whole numbers, 24–27 Decimals on, 396–398, 428–429, 430–432, 456–459, 486 Division on, 78–79 Equivalent decimals-fractions on, 428–429, 430–432 Equivalent fractions-decimals on, 428–429, 430–432 Equivalent fractions on, 400, 428–429 Fractions on, 400, 406–409, 428–429 Mixed numbers, 414–418, 434 Ordering fractions on, 406–409 Probability, 371 Rounding, 28–31 Rounding decimals, 456–459, 486 Number patterns, 19, 187–189, 231, 232 Number properties, 16, 32–35, 62, 64, 80–83, 100–102, 106–109, 116, 117, 210–213, 241–243, 250–251, EP3, EP5, EP13 Addition Properties, 32–35, 62, 64
INDEX 12
Index
Associative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Associative Property of Multiplication, 80–83, 106–109, 116, 117, 241–243, EP5 Commutative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Commutative Property of Multiplication, 80–83, 116, 117, 241–243, EP5 Distributive Property of Multiplication, 70C, 100–102, 210–213, 216–219, 228–230, 231, 233, 250–251, 273, EP13 Identity Property of Addition, 16C, 32–35 Identity Property of Multiplication, 80–83, 116, 117 Zero Property of Multiplication, 80–83, 116, 117, EP5 Number relationships, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is equal to (=), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is greater than (>), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is less than (<), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25
Order/ordering Decimals, 396–398, 433, 436, EP24 Fractions, 406–409, 437 Fractions on a number line, 406–409 More About Comparing and Ordering Numbers, 27 Whole numbers, 24–27, EP2 Ordered pair, 530C, 540–543, 576, EP33 X-coordinate, 540–543 Y-coordinate, 540–543 Organizing data, 324, 327–329, 340–341, 345–346, 351, 372, 373, 374, 676–677, 680–681, EP19, EP20, EP21
Oo Observation Journal, 281E Obtuse angles, 492C, 507–508, 510–513, 525, 510–513, 525, EP31 Octagons, 492C, 495–498 Olympic Games History Cross Curricular Connection, 482–483 Ones, 19, 20–23 On Grade Level, 18A, 19C, 32C, 44C, 72A, 73C, 84C, 96C, 110B, 126A, 127C, 136C, 148C, 160C, 184A, 185C, 196C, 206C, 226B, 240A, 241C, 250B, 256B, 264B, 280A, 281C, 288B, 296D, 326A, 327B, 334C, 348C, 362C, 382A, 383C, 399D, 420C, 444A, 445C, 456C, 468C, 494A, 495C, 504B, 510C, 532A, 533C, 546C, 560B, 566C, 584A, 585C, 594B, 602B, 608C, 626A, 627C, 642C, 658B Online Guide, T2 Online Readiness Quiz, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Open Ended H.O.T. Problems, 15, 22, 34, 39, 47, 58, 77, 83, 89, 92, 99, 102, 108, 112, 115, 133, 138, 144, 150, 157, 162, 166, 189, 219, 223, 230, 243, 247, 266, 285, 294, 299, 302, 306, 310, 329, 339, 344, 356, 366, 370, 387, 391, 395, 403, 409, 412, 417, 423, 432, 447, 463, 481, 497, 501, 508, 513, 516, 539, 542, 550, 555, 562, 570, 574, 589, 598, 612, 631, 634, 640, 650, 656 Options for Review, 4, 6, 8, 13
INDEX 13
Periods (place value), 16C, 20–23 Perpendicular lines, 530C, 534–535, 537–539, 575, 576, EP32 Pictographs, 12–15 Pie charts, 351, 508 Angles on, 508 Pints, 627, 628–631, 632–634, 635, 664, 665, EP38
Parallelograms, 492C, 514–517, 526, EP32
Place value, 16C, 16, 19, 20–23, 24–27, 62–63, 383–384, 385–387, 388–391, 392–395, 396–398, 421–423, EP2 Charts, 20–23, 25–27, 383–384, 385–387, 388–391, 393 Decimal, 383–384, 385–387, 388–391, 392–395, 396–398, 421–423 Digits, 16C, 20–23, 62, EP2 Hundreds, 19, 20–23 Hundred thousands, 20–23 Hundredths, 380C, 383–384, 388–391, 421–423, 434, 435 More About Place Value, 23 Ones, 19, 20–23 Periods (place value), 16C, 20–23 Recycle It! Chapter Project, 16, 62 Tens, 19, 20–23 Ten thousands, 20–23 Tenths, 380C, 383–384, 385–387, 421–423, 434, 435, EP23 Thousands, 19, 20–23 Thousandths, 380C, 391, 434
Parentheses ( ), 100–102, 106–109, 120, 124C, 137–139, 148–150, 176, 178
Plan a Family Celebration Problem-Solving Project, 676–677
Partial products, 198–199, 208–209, 216–219, 220–223, 228–230, 250–251, 252–254, 264–266
Plan a Trip Problem-Solving Project, 680–681
Patterns, 8–11, 124C, 124, 127–129, 130–133, 174, 175, EP8 Blocks, 534–535, 546–547, 552–555 Copying, EP8 Creating tessellation patterns, 552–555 Division, 288–291, 318, EP17 Expanding tessellation patterns, 552–555 Extending, 127–129, 130–133, 175, EP8 Geometric, 127–129, 175, EP8 Growing, 128–129 Identifying, 127–129, 130–133, 175 Look for a Pattern Problem-Solving Strategy, 502–503, 524, EP31 Multiplication, 96–99, 187–189, 231, 232, 288–291, 318, EP12 Nonnumeric, 124C, 127–129, 175 Number, 19, 187–189, 231, 232 Numeric, 130–133, 175, EP8 Repeating, 127–129 Rules, 130–133 Tessellations, 530C, 552–555, EP34
Plane figures, 492, 495–498, 523, 524, 525 Acute triangles, 510–513, 525, EP31 Circles, 492C, 496, 498 Decagons, 495–498 Equilateral triangles, 511–513, 525, EP31 Hexagons, 492C, 495–498 Isosceles triangles, 511–513, 525, EP31 Octagons, 492C, 495–498 Parallelograms, 492C, 514–517, 526, EP32 Pentagons, 492C, 495–498, 543 Quadrilaterals, 492C, 495–498, 514–517, 523, 526, EP32 Rectangles, 492C, 514–517, 526, EP32 Rhombus, 492C, 514–517, 526 Right triangles, 510–513, 525, EP31 Scalene triangles, 511–513, 525, EP31 Squares, 492C, 514–517, 526, EP32 Trapezoids, 492C, 514–517, 526, EP32 Triangles, 492C, 495–498, 510–513, 525, 543, EP31
Pentagons, 492C, 495–498, 543
Points, 533, 540–543
Perimeter, 582C, 582, 602–604, 605, 614–615, 616, 619, EP37 Area-perimeter relationship, 611–615 Formula for rectangle, 602–604, 605, 616, 619 Perimeter Guess Game, 605
Polygons, 492C, 492, 495–498, 523, 524, 525, 543, EP30 Acute triangles, 510–513, 525, EP31 Decagons, 495–498 Equilateral triangles, 511–513, 525, EP31 Hexagons, 492C, 495–498 Isosceles triangles, 511–513, 525, EP31
Origin, 530C, 540–543 Ounces, 642–643, 644–647, 648–651, 664, 666, EP39 Outcomes, 324C, 324, 362–363, 364–367, 372, 376 Determining possible outcomes, 364–367 Outliers, 324C, 330–333, 373, EP20 Output, 9–11, 160–163, 164–167, 178
Number Sense H.O.T. Problems, 27, 39, 83, 92, 144, 193, 203, 247, 266, 291, 350, 398, 451, 612, 647 Numeric patterns, 130–133, 175, EP8
Perimeter Guess Game, 605
Pp Pacing, T36 Parallel lines, 530C, 534–535, 537–539, 575, 576, EP32
Plotting points on a grid, 540–543, 576
Problem Solving, A three-pronged approach helps students apply skills to problem situations. ProblemSolving Strategy lessons teach strategies; Problem Solving Investigations afford students diverse opportunities to select these strategies; Real-World Problem Solving exercises strengthen students’ abilities to apply and solve problems outside the mathematics classroom. Problem Solving, 185E Problem Solving in Art, 520–521 Making Mosaics, 520–521
Pop Culture History Cross Curricular Connection, 94–95
Problem Solving in Geography, 262–263 A Walk in the Park, 262–263
Possible combinations, 680–681
Problem Solving in History, 94–95, 482–483 Olympic Games, 482–483 Pop Culture, 94–95
Possible outcomes, 362–363, 364–367, 376, EP22 Determining, 364–367 Tree diagrams, 324C, 364–367, 372, 376, EP22 Pounds, 642–643, 644–647, 648–651, 664, 666, EP39 Practice and Apply It, 49, 74, 141, 153, 169, 186, 197, 207, 209, 227, 251, 282, 341, 346, 353, 363, 384, 400, 420, 429, 469, 477, 505, 533, 535, 586, 595, 615, 627, 643 Practice and Problem Solving, 5, 7, 10, 14, 22, 26, 30, 34, 38, 46, 52, 58, 77, 79, 82, 88, 92, 98, 102, 107, 113, 115, 129, 132, 138, 144, 150, 156, 162, 166, 172, 189, 192, 202, 212, 218, 222, 230, 243, 246, 254, 260, 266, 285, 290, 294, 298, 302, 306, 310, 329, 332, 338, 344, 350, 356, 366, 370, 387, 390, 394, 398, 408, 412, 416, 423, 432, 447, 450, 454, 458, 462, 472, 480, 497, 501, 508, 512, 516, 538, 542, 550, 554, 562, 570, 574, 589, 591, 598, 604, 612, 630, 633, 640, 646, 650, 656, 660 Practice Chapter Test, 67, 121, 179, 235, 275, 321, 377, 439, 489, 527, 579, 621, 669 Predictions, 342–344 Prime numbers, 70C, 114–115, 120, EP8 Composite numbers, 70C, 114–115, 120, EP8 Prisms Rectangular, 499–501 Triangular, 499–501 Probability, 324C, 324, 368–371, 372, 376, EP22, EP23 Certain, 368–371, 376, EP23 Chance, 362–363, 364–367, 376 Determining possible outcomes, 364–367 Equally likely, 368–371, 376, EP23 Fractions as, 371 Impossible, 368–371, 376, EP23 Likely, 368–371, 376, EP23 More About Probability, 371 On a number line, 371 Outcomes, 324C, 324, 362–363, 364–367, 372, 376 Possible outcomes, 362–363, 364–367, 376, EP22 Unlikely, 368–371, 376, EP23
Problem Solving in Music, 424–425 Decimal Note-ation, 424–425 Problem Solving in Science, 60–61, 146–147, 224–225, 314–315, 360–361, 600–601, 652–653 Coral Reefs, 600–601 A Desert Safari, 314–315 Do Flying Squirrels Really Fly?, 146–147 Emperors on the Ice, 224–225 A Head Above the Rest, 360–361 Ready, Set, Click!, 60–61 Tide Pool Ecosystems, 652–653 Problem Solving in Social Studies, 564–565 Congruent Cases, 564–565 Problem-Solving Investigations, 54–55, 66, 104–105, 119, 158–159, 177, 214–215, 233, 268–269, 274, 312–313, 320, 358–359, 376, 424–425, 438, 474–475, 488, 518–519, 526, 556–557, 577, 606–607, 619, 662–663, 668 Problem-Solving Projects, 672–681 Make a Game, 674–675 Make Your Home Your Own, 678–679 Plan a Family Celebration, 676–677 Plan a Trip, 680–681 Problem-Solving Strategies, 4–5, 40–41, 54–55, 65, 66, 84–84, 104–105, 118, 119, 134–135, 158–159, 175, 177, 194–195, 214–215, 232, 233, 248–249, 268–269, 272, 274, 286–287, 312–313, 317, 320, 334–335, 358–359, 374, 376, 404–405, 424–425, 436, 438, 464–465, 474–475, 487, 488, 502–503, 518–519, 524, 526, 544–545, 556–557, 576, 577, 592–593, 606–607, 618, 619, 636–637, 662–663, 666, 668, EP3, EP4, EP6, EP7, EP9, EP10, EP12, EP13, EP15, EP16, EP17, EP19, EP20, EP22, EP25, EP26, EP29, EP31, EP32, EP33, EP34, EP36, EP37, EP40 Act It Out, 519, 557 Choose an Operation, 84–85, 105, 118, 159, 214–215, 269, 359, 425, 475, 557, EP6 Choose the Best Answer, 662–663, 668 Choose the Best Strategy, 54–55, 66, 104–105, 119, 158–159, 177, 214–215, 233, 268–269, 274, 312–313, 320, 358–359, 376, 424–425, 438, 474–475, 488, 518–519, 526, 556–557, 577, 606–607, 619, 662–663, 668,
EP4, EP7, EP10, EP13, EP16, EP19, EP22, EP26, EP29, EP32, EP34, EP37, EP40 Determine Whether an Answer Is Reasonable, 194–195, 214–215, 232, 359, EP12 Draw a Picture, 134–135, 159, 175, 313, 557, 607, 663, EP9 Estimate or Exact Answer, 40–41, 65, EP3 Guess, Check, and Revise, 286–287, 313, 317, 519, 607, 663, EP17 Look for a Pattern, 502–503, 524, EP31 Make a Model, 404–405, 425, 436, EP25 Make an Organized List, 544–545, 576, EP33 Make a Table, 248–249, 269, 272, 313, 334–335, 359, 374, 425, 475, 519, 557, 607, EP15, EP20 Solve a Simpler Problem, 592–593, 607, 618, EP36 Use a Bar Diagram, 475 Use Logical Reasoning, 464–465, 475, 487, 663, EP29 Work Backwards, 636–637, 663, 666
Index
Octagons, 492C, 495–498 Parallelograms, 492C, 514–517, 526, EP32 Pentagons, 492C, 495–498, 543 Polygons that compose figures, 497 Quadrilaterals, 492C, 495–498, 514–517, 523, 526, EP32 Rectangles, 492C, 514–517, 526, EP32 Rhombus, 492C, 514–517, 526 Right triangles, 510–513, 525, EP31 Scalene triangles, 511–513, 525, EP31 Squares, 492C, 514–517, 526, EP32 Trapezoids, 492C, 514–517, 526, EP32 Triangles, 492C, 495–498, 510–513, 525, 543, EP31
Products, 73–74, 182C, 238C, 238, 244–247, 270, 271 Estimating, 190–193, 204, 228–230, 232, 244–247, 270, EP12, EP15 Partial, 198–199, 208–209, 216–219, 220–223, 228–230, 250–251, 252–254, 264–266 Professional Development, T15, 16A, 19E, 70A, 124A, 127E, 182A, 206F, 238A, 278A, 281E, 296F, 324A, 380A, 383E, 442A, 492A, 530A, 533E, 582A, 624A, 627E Program authors, T23 Projects, 672–681 Make a Game, 674–675 Make Your Home Your Own, 678–679 Plan a Family Celebration, 676–677 Plan a Trip, 680–681 Project Wrap-Ups, 675, 677, 679, 681 Properties of numbers, 16, 32–35, 62, 64, 80–83, 100–102, 106–109, 116, 117, 210–213, 241–243, 250–251, EP3, EP5, EP13 Addition Properties, 32–35, 62, 64 Associative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Associative Property of Multiplication, 80–83, 106–109, 116, 117, 241–243, EP5 Commutative Property of Addition, 16C, 16, 32–35, 62, 64, EP3 Commutative Property of Multiplication, 80–83, 116, 117, 241–243, EP5 Distributive Property of Multiplication, 70C, 100–102, 210–213, 216–219, 228–230, 231, 233, 250–251, 273, EP13 Identity Property of Addition, 16C, 32–35 Identity Property of Multiplication, 80–83, 116, 117 Zero Property of Multiplication, 80–83, 116, 117, EP5 Pyramids Square, 499–501 Triangular, 499–501
INDEX 14
Index
Qq Quadrilaterals, 492C, 495–498, 514–517, 523, 526, EP32 Parallelograms, 492C, 514–517, 526, EP32 Rectangles, 492C, 514–517, 526, EP32 Rhombus, 492C, 514–517, 526 Squares, 492C, 514–517, 526, EP32 Trapezoids, 492C, 514–517, 526, EP32 Quarter inch, 585–586, 587–589, 617, EP36 Quarts, 627, 628–631, 632–634, 635, 664, 665, EP38 Quick Assessment through Observation, 127E Quick Check, 18, 22, 27, 31, 35, 39, 41, 47, 53, 55, 59, 72, 77, 79, 83, 85, 89, 92, 99, 102, 105, 109, 113, 115, 126, 129, 133, 135, 139, 144, 150, 157, 159, 163, 167, 173, 184, 189, 193, 195, 203, 213, 215, 219, 223, 230, 240, 243, 247, 249, 254, 261, 266, 269, 280, 285, 287, 291, 294, 299, 302, 307, 310, 313, 326, 329, 333, 335, 339, 344, 351, 356, 359, 367, 370, 382, 387, 391, 395, 398, 403, 405, 409, 413, 418, 423, 427, 432, 444, 447, 451, 455, 459, 463, 465, 473, 475, 481, 494, 497, 501, 503, 508, 513, 517, 519, 532, 539, 543, 545, 551, 555, 557, 562, 571, 574, 584, 589, 591, 593, 598, 604, 607, 613, 626, 631, 634, 637, 640, 647, 651, 657, 661, 663, Quotients, 74, 278C, 278, 281–282, 283–285, 292–294, 300–302, 304–307, 316–320 Estimating, 292–294, 296–299, 316, 318, EP18 Three-digit, 300–302, 318 With zeros, 304–307, 318
Rr Radius, 492C, 498 Range, 324C, 330–333, 373 Rays, 506–508, 523, 530C, 536–539, 575, 576, EP32 Reading and Language Arts Support, 16D, 70D, 124D, 182D, 238D, 278D, 324D, 380D, 442D, 492D, 530D, 582D, 624D, A2–A56 Helping Student Read Mathematics Texts, A4 How Language Arts and Reading Connect to Math, A2 Read Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51 Reading Graphic Novels, A5, A8, A11, A13, A20, A23, A26, A28, A32, A37, A39, A42, A47, A49, A50 Talk Math, A4, A7, A8, A9, A11, A12, A13, A15, A16, A17, A18, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A36, A37, A38, A39, A40,
INDEX 15
A41, A42, A43, A46, A47, A48, A49, A50, A51 Tennessee’s Reading Standards, A52–A56 Text Features Specific to Graphic Novels, A5 Think Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A19, A20, A21, A22, A23, A24, A26, A27, A28, A31, A32, A34, A35, A36, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A49, A50, A51 Using Comprehension Strategies with Graphic Novels, A5 Using Language Arts to Teach Math Vocabulary, A2 Why Integrate Reading and Language Arts in the Math Classroom?, A2 Write Math, A4, A6, A7, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A43, A44, A45, A47, A48, A49, A51 Reading decimals, 385–387, 388–391, 392–395, 435 Reading Graphic Novels, A5, A8, A11, A13, A20, A23, A26, A28, A32, A37, A39, A42, A47, A49, A50 Reading in the content areas, See Reading and Language Arts Support. Reading Learning Stations, 16E, 124E, 238E, 324F, 380E, 492E, 530E Reading numbers, 20–23, 63 Read Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51 Ready Access Math-Personalized Professional Development, T15 Ready, Set, Click! Science Cross Curricular Connection, 60–61 Real-World Math, 61, 95, 147, 225, 263, 315, 361, 425, 483, 521, 601, 653, 95 Real-World Math Activities, 137, 388 Real-World Problem Solving, 22, 30, 38, 58, 82, 88, 92, 98, 102, 115, 156, 162, 166, 189, 192, 202, 243, 260, 266, 290, 298, 302, 306, 332, 338, 387, 417, 447, 451, 458, 462, 498, 538, 570, 630, 650, 660 Real-World Problem-Solving Library, 16D, 40, 70D, 84, 124D, 134, 182D, 194, 228, 238D, 248, 278D, 286, 324D, 334, 342, 380D, 404, 442D, 464, 492D, 502, 530D, 544, 572, 582D, 592, 624D, 636 Reasoning H.O.T. Problems, 516, 539 Reassess, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Recipes, 677 Doubling, 677 Recording data, 674–675
Frequency tables, 13–15, 324C, 327–329, 336–339, 352–353, 372, 373, EP19 Tally charts, 324C, 327–329, 336–339, 372, 373, EP19 Tally marks, 327–329, 336–339, 372, 373 Rectangles, 492C, 514–517, 526, EP32 Area, 608–609, 610–613, 616, 620 Formula for area, 609, 610–613, 616, 620 Formula for perimeter, 602–604, 605, 616, 619 Rectangular prisms, 499–501 Recycle It! Chapter Project, 16, 62 Reflect and Clarify, 19, 49, 74, 141, 153, 169, 186, 197, 199, 207, 209, 226, 251, 257, 282, 341, 346, 353, 363, 384, 400, 420, 429, 469, 477, 505, 533, 535, 547, 567, 586, 595, 609, 615, 627, 643 Reflections, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Regroup, 182C Multiplication, 206–207, 216–219 Subtraction, 48–49, 50–53, 56–59, 66 Related facts, 75–77, 86–89, 90–92, 117, EP5 Relating area and perimeter, 614–615 Relating perimeter and area, 614–615 Relationship symbols, 24–27, 62, 63, 396–398, 436, 437 Is equal to (=), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is greater than (>), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Is less than (<), 16C, 24–27, 62, 63, 396–398, 433, 436, 437, EP2, EP24, EP25 Remainders, 278C, 278, 283–285, 297–299, 300–302, 304–307, 316, 317, EP18, EP19 Repeated addition, 73–74, 185–186 Repeated subtraction, 78–79, 117, EP5 Repeating patterns, 127–129 Research Base, T18–T19 Response to Intervention (RtI), T12–T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Reviewers, T25 Rhombus, 492C, 514–517, 526 Right angles, 492C, 507–508, 510–513, 525, EP31 Right triangles, 510–513, 525, EP31 Rigor, T11 Rotational symmetry, 530C, 566–567, 572–574, 578, EP35 Rotations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Round/rounding, 190–193, 232, 244–247 Decimals, 456–459, 460–463, 466, 484, 486, EP28 Decimals on a number line, 456–459, 486 More About Rounding Decimals, 459 More About Rounding Numbers, 31 Nearest whole number, 457–459, 484, 486
RtI: Response to Intervention, T12–T13, 18A, 72A, 126A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Rules, 124C
Solve a Simpler Problem Problem-Solving Strategy, 592–593, 607, 618, EP36 Spatial reasoning, 530, 533, 536–539, 540–543, 544–545, 546–547, 548–551, 552–555, 556–557, 558, 559, 560–562, 563, 566–567, 568–571, 572–574, 575–578, 579, 580–581 Spheres, 499–501
Ss Scale Changing, 679 Map, 679 Scalene triangles, 511–513, 525, EP31 Science Cross Curricular Connections, 60–61, 146–147, 224–225, 314–315, 360–361, 600–601, 652–653 Coral Reefs, 600–601 A Desert Safari, 314–315 Do Flying Squirrels Really Fly?, 146–147 Emperors on the Ice, 224–225 A Head Above the Rest, 360–361 Ready, Set, Click!, 60–61 Tide Pool Ecosystems, 652–653 Science Learning Stations, 16F, 70F, 124F, 182F, 238F, 278F, 324E, 380F, 442F, 492F, 530F, 582F, 624F Shopping List Chapter Project, 442, 484 Sides, 492C, 495–498, 510–513, 514–517 Simplest form, 380C, 380, 410–413, 434, 437, 445–447, 448–451, 452–455, 485, EP25, EP27, EP28 Skills Trace, 16A, 70A, 124A, 182A, 238A, 278A, 324A, 380A, 442A, 492A, 530A, 582A, 624A Skip counting, 86–89, 96–99, 185–186 Slides, 546–547, 548–551, 552–555, 560–562, EP33 Social Studies Cross Curricular Connection, 564–565 Congruent Cases, 564–565 Social Studies Learning Stations, 16F, 70F, 124F, 182F, 238F, 278E, 324E, 380F, 442F, 530F, 582E, 624F Solid figures, 492, 499–501, 523, 524 Cones, 499–501 Cubes, 499–501 Cylinders, 499–501 Rectangular prisms, 499–501 Spheres, 499–501 Square pyramids, 499–501 Triangular prisms, 499–501 Triangular pyramids, 499–501 Solve/solving, 124C Equations, 140–141, 142–144, 146–147, 152–153, 154–157, 176, 177, EP9, EP10, EP11 Expressions, EP9, EP10
Spiral Review, These systematic and continuous reviews help maintain previously acquired skills and improve retention. Spiral Review, 35, 39, 47, 53, 59, 83, 89, 99, 109, 133, 139, 157, 163, 167, 173, 193, 203, 213, 219, 223, 247, 261, 291, 299, 307, 333, 339, 367, 395, 409, 413, 418, 463, 473, 481, 513, 517, 539, 551, 555, 571, 613, 647, 651, 661 Square pyramids, 499–501 Squares, 492C, 514–517, 526, EP32 Area, 611–613, 616, 620 Formula for area, 611–613, 620 Square units, 582C, 608–609, 610–613, 614–615, 616, 620, EP38 Standard form, 16C, 20–23, 63, 393–395, EP24 Start Smart, 2–15 Statistics, 330–333, 373, EP20 Median, 324C, 330–333, 373, EP20 Mode, 324C, 330–333, 373 Outliers, 324C, 330–333, 373, EP20 Range, 324C, 330–333, 373 Stem-and-leaf plots, 324C, 340–341, EP21 Leaf, 324C, 340–341 Stems, 324C, 340–341 Stems, 324C, 340–341 Stop and Reflect, 31, 41, 59, 83, 92, 109, 115, 135, 144, 159, 173, 195, 203, 223, 230, 249, 254, 261, 269, 287, 294, 313, 333, 346, 359, 371, 398, 418, 432, 455, 465, 481,503, 508, 519, 545, 557, 563, 574, 593, 598, 607, 615, 640, 657, 663 Strategic Intervention, T13, 18, 72A, 184A, 240A, 280A, 326A, 382A, 444A, 494A, 532A, 584A, 626A Student errors, See Common Error! Student Handbook, EP0–EP40 Extra Practice, EP2–EP40 How to Use the Student Handbook, EP1 Study Organizers, 16, 62, 70, 124, 182, 231, 238, 270, 278, 324, 372, 380, 442, 484, 492, 523, 530, 566, 572, 599, 606, 646 Subtract/subtraction Across zeros, 56–59, 66 Any number from itself, 33–35 Decimals, 442, 476–477, 478–481, 484, 488, EP30 Equations, 140–141, 142–144, 176 Estimating decimal differences, 460–463, 484, 486, EP28 Estimating differences, 36–39, 50–53, 64, 66
Expressions, 136–139, 176 Fractions, 442, 445–447, 452–455, 484, 485 Functions, 160–163, 178 Like fraction, 445–447, 484, 485, EP27 Make a Big Difference Game, 42 Minuend, 16C Modeling, 48–49, 50–53, 56–59 Money, 51–52, 66 Multi-digit, EP4 Number sentences, EP3 Regrouping for, 48–49, 50–53, 56–59, 66 Repeated, 78–79, 117, EP5 Rules, 33–35, EP3 Subtrahend, 16C Unlike fractions, 452–455, 484, 485, EP28 Whole numbers, 16, 36–39, 40–41, 42, 48–49, 50–53, 56–59, 62, 66 Zero, 33–35 Zeros in, 56–59, 66
Index
On a number line, 28–31 Whole numbers, 28–31, 36–39, 62, 63, EP2, EP3
Subtrahend, 16C Suggested Pacing, T36 Summative Assessment, T17, 67, 121, 179, 235, 275, 321, 377, 439, 489, 527, 579, 621, 669 Summative Research, T19 Sums, EP4 Estimating, 36–39, 44–47, 64, 65 Estimating decimal, 460–463, 484, 486, EP28, EP29 Surveys, 324C, 327–329, 351, 372, 373, 679 Symmetry, 566–567, 568–571, 572–574, 578, EP35 Lines of symmetry, 530C, 568–571, 572–574, 578, EP35 Line symmetry, 530C, 566–567, 568–571, 578 Rotational symmetry, 530C, 566–567, 572–574, 578, EP35
Tt Talk Math, A4, A7, A8, A9, A11, A12, A13, A15, A16, A17, A18, A20, A21, A22, A23 A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A36, A37, A38, A39, A40, A41, A42, A43, A46, A47, A48, A49, A50, A51, 21, 26, 30, 33, 37, 45, 46, 51, 57, 76, 79, 82, 87, 91, 97, 101, 107, 108, 111, 112, 114, 115, 128, 131, 137, 143, 144, 149, 155, 161, 165, 171, 186, 188, 191, 201, 212, 217, 221, 222, 229, 242, 245, 253, 254, 259, 265, 284, 285, 289, 293, 298, 301, 305, 309, 310, 328, 331, 337, 343, 349, 355, 365, 369, 386, 389, 391, 394, 397, 402, 407, 411, 416, 417, 422, 431, 446, 450, 454, 457, 461, 471, 479, 496, 500, 507, 511, 515, 537, 538, 541, 549, 553, 561, 569, 573, 588, 591, 597, 603, 611, 629, 633, 639, 645, 649, 655, 659 Tally charts, 324C, 327–329, 336–339, 372, 373, EP19 Tally marks, 327–329, 336–339, 372, 373
INDEX 16
Index
Targeted Standards, 16A, 70A, 124A, 182A, 238A, 278A, 324A, 380A, 442A, 492A, 530A, 582A, 624A Teacher’s Bulletin Board, 19E, 73E, 127E, 185E, 206F, 241E, 281E, 296F, 327E, 383E, 398A, 445E, 495E, 533E, 585E, 608E, 627E Alternative Manipulative Fraction Kit, 398A Bar Diagrams, 241E Distributive Property of Multiplication, 206F Journals, 383E Observation Journal, 281E Problem Solving, 185E Professional Development, 19E, 127E, 206F, 281E, 296F, 383E, 533E, 627E Quick Assessment through Observation, 127E Teach with Tech, 495E Teacher Tips, 73E, 185E, 241E, 327E, 383E, 445E, 495E, 585E, 608E Why might ELLs find learning mathematics difficult?, 73E Teacher Tips, 73E, 185E, 241E, 327E, 383E, 445E, 495E, 585E, 608E Teach with Tech, 87, 130, 196, 258, 281, 327, 369, 399, 470, 495E, 588, 629 Tech Training, T15 Technology, 303, 563 Math Tool Chest, 303, 563 Online Readiness Quiz, 18, 72, 126, 184, 240, 280, 326, 382, 444, 494, 532, 584, 626 Teach with Tech, 87, 130, 196, 258, 281, 327, 369, 399, 470, 495E, 588, 629 Tech Training, T15
Think Math, A4, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A19, A20, A21, A22, A23, A24, A26, A27, A28, A31, A32, A34, A35, A36, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A49, A50, A51 Thousands, 19, 20–23 Thousandths, 380C, 391, 434 Three-digit quotients, 300–302, 318 Three-dimensional figures, 492C, 492, 497, 499–501, 523, 524, EP30 Combining, 501 Cones, 499–501 Cubes, 499–501 Cylinders, 499–501 Edges, 492C, 499–501, 524, EP30 Faces, 492C, 499–501, 524, EP30 Nets, 492C, 500–501 Rectangular prisms, 499–501 Sides, 492C, 495–498, 510–513, 514–517 Spheres, 499–501 Square pyramids, 499–501 Triangular prisms, 499–501 Triangular pyramids, 499–501 Ticket Out the Door, 23, 53, 77, 83, 109, 129, 139, 173, 189, 203, 223, 261, 302, 329, 351, 391, 403, 423, 447, 481, 501, 539, 571, 589, 640, 661 Tide Pool Ecosystems Science Cross Curricular Connections, 652–653
Tens, 19, 20–23
Time, 658–661, 668 Calendars, 676–677, 681 Clocks, 681 Days, 676–677 Elapsed time, 624C, 624, 658–661, 664, 668, 676–677, 681, EP40 Estimating, 681 Hours, 676–677 Weeks, 676–677
Ten thousands, 20–23
Time lines, 94–95, 676–677
Tenths, 380C, 383–384, 385–387, 421–423, 434, 435, EP23
Tons, 644–647, 648–651, 664, 666, EP39
Tennessee’s Reading Standards, A52–A56 Tennessee’s Mathematics Curriculum Framework, T26–T31
Tessellations, 530C, 552–555, EP34 Creating tessellation patterns, 552–555 Expanding tessellation patterns, 552–555 Test Practice, 35, 39, 47, 53, 59, 68–69, 83, 89, 99, 109, 122–123, 133, 139, 157, 163, 167, 173, 180–181, 193, 203, 213, 219, 223, 236–237, 247, 261, 276–277 , 291, 299, 307, 322–323, 333, 339, 367, 378–379, 395, 409, 413, 418, 440–441, 463, 473, 481, 490–491, 513, 517, 528–529, 539, 551, 555, 571, 580–581, 613, 622–623, 631, 634, 647, 651, 661, 670–671 Test-Taking Tips, 122, 180, 236, 322, 378, 440, 490, 670 Text Features Specific to Graphic Novels, A5 Think About It, 19, 49, 74, 141, 153, 169, 186, 197, 199, 207, 208, 227, 251, 257, 282, 341, 346, 353, 363, 384, 400, 429, 469, 477, 505, 533, 535, 547, 567, 586, 595, 608–609, 615, 627, 643
INDEX 17
Transactions, 38, 40, 41, 46, 47, 51, 52, 53, 54, 59, 61, 65, 66, 67, 84, 85, 89, 91, 95, 101, 105, 108, 118, 119, 130, 139, 145, 156, 157, 161, 162, 164, 165, 166, 170, 171, 172, 175, 177, 179, 180, 181, 189, 191, 192, 195, 212, 215, 218, 221, 223, 228, 230, 233, 234, 235, 237, 242, 249, 253, 259, 263, 269, 271, 272, 273, 275, 276, 277, 285, 286, 287, 289, 290, 291, 294, 295, 298, 299, 303, 306, 307, 309, 313, 317, 320, 332, 335, 337, 347, 356, 438, 462, 471, 472, 473, 475, 480, 481, 486, 491, 519, 529, 559, 593, 607, 663, 677, 681, EP3, EP4, EP6, EP8, EP11, EP14, EP16, EP17, EP18, EP20, EP21, EP22, EP27, EP30, EP35, EP36, EP37, EP40 Transformations, 530C, 530, 546–547, 548–551, 552–555, 559, 575, 577, EP33, EP34 Flips, 546–547, 548–551, 552–555, 560–562, EP33 Reflections, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Rotations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34
Slides, 546–547, 548–551, 552–555, 560–562, EP33 Translations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Turns, 546–547, 548–551, 552–555, 560–562, EP33 Translations, 530C, 546–547, 548–551, 552–555, 560–562, 575, 577, EP33, EP34 Trapezoids, 492C, 514–517, 526, EP32 Tree diagrams, 324C, 364–367, 372, 376, EP22 Triangles, 492C, 495–498, 510–513, 525, 543, EP31 Acute, 510–513, 525, EP31 Equilateral, 511–513, 525, EP31 Isosceles, 511–513, 525, EP31 Right, 510–513, 525, EP31 Scalene, 511–513, 525, EP31 Triangular prisms, 499–501 Triangular pyramids, 499–501 Turns, 546–547, 548–551, 552–555, 560–562, EP33 Angles, 506–508, 525 Two-dimensional figures, 492C, 492, 495–498, 523, 524, 525, EP30, EP31, EP32 Acute triangles, 510–513, 525, EP31 Circles, 492C, 496, 498 Decagons, 495–498 Equilateral triangles, 511–513, 525, EP31 Hexagons, 492C, 495–498 Isosceles triangles, 511–513, 525, EP31 More About Two-Dimensional Figures, 498 Octagons, 492C, 495–498 Parallelograms, 492C, 514–517, 526, EP32 Pentagons, 492C, 495–498, 543 Quadrilaterals, 492C, 495–498, 514–517, 523, 526, EP32 Rectangles, 492C, 514–517, 526, EP32 Rhombus, 492C, 514–517, 526 Right triangles, 510–513, 525, EP31 Scalene triangles, 511–513, 525, EP31 Squares, 492C, 514–517, 526, EP32 Trapezoids, 492C, 514–517, 526, EP32 Triangles, 492C, 495–498, 510–513, 525, 543, EP31
Uu Unlike fractions, 448–451, 484, 485, EP27 Addition, 448–451, 484, 485, EP27 Subtraction, 452–455, 484, 485, EP28 Unlikely, 368–371, 376, EP23 Use a Bar Diagram Problem-Solving Strategy, 475 Use Logical Reasoning Problem-Solving Strategy, 464–465, 475, 487, 663, EP29 Using Comprehension Strategies with Graphic Novels, A5 Using Language Arts to Teach Math Vocabulary, A2
Values of expressions, 136–139, 148–150, 151, 176, 177 Variables, 124C, 124, 136–139, 140–141, 148–150, 151, 152–153, 154–157, 160–163, 164–167, 168–169, 174, 176, 177, 178 Vertex (vertices), 499–501, 524, EP30
Rounding, 28–31, 36–39, 62, 63, EP2, EP3 Subtraction, 16, 36–39, 40–41, 42, 48–49, 50–53, 56–59, 62, 66 Tens, 19, 20–23 Ten thousands, 20–23 Thousands, 19, 20–23 Writing, 20–23, 63, 393–395, EP2, EP24 Why Integrate Reading and Language Arts in the Math Classroom?, A2
Xx
Index
Vv
X-axis, 530C, 540–543 X-coordinate, 540–543
Yy
Vertical Alignment, T20–T21, 16A, 70A, 124A, 182A, 238A, 278A, 324A, 380A, 442A, 492A, 530A, 582A, 624A
Why might ELLs find learning mathematics difficult?, 73E
Yards, 587–589, 590–591, 616, 617, EP36
Word form, 16C, 20–23, 63, 393–395, EP2
Y-axis, 530C, 540–543
Vertical Alignment and Backmapping, 16A, 70A, 124A, 182A, 238A, 278A, 324A, 380A, 442A, 492A, 530A, 582A, 624A
Word Problem Exchange, 5
Y-coordinate, 540–543
Work Backwards Problem-Solving Strategy, 636–637, 663, 666
Virtual Manipulatives Activities, 50, 127, 414, 452, 552, 587
Workshops Onsite, T15
Yesterday’s News, 31, 59, 167, 219, 247, 310, 333, 356, 409, 413, 455, 459, 513, 555, 562, 574, 598, 651
Virtual Math Activities, 114, 514 Visual Math Activities, 210, 385, 448, 540, 638 Vocabulary and Language Connections, 16C–16D, 70C–70D, 124C–124D, 182C–182D, 238C–238D, 278C–278D, 324C–324D, 380C–380D, 442C–442D, 492C–492D, 530C–530D, 582C–582D, 624C–624D
Ww A Walk in the Park Geography Cross Curricular Connection, 262–263 Weeks, 676–677 Weight, 624C, 624, 642–643, 644–647, 648–651, 664, 666, EP39 Converting customary units, 648–651, 666, EP40 Estimating, 642–643, 644–647, 648–651, 666, EP39 Ounces, 642–643, 644–647, 648–651, 664, 666, EP39 Pounds, 642–643, 644–647, 648–651, 664, 666, EP39 Tons, 644–647, 648–651, 664, 666, EP39 When Will I Use This?, 17, 71, 125, 183, 239, 279, 325, 381, 443, 493, 531, 583, 625 Which One Doesn’t Belong? H.O.T. Problems 34, 53, 89, 108, 129, 138, 157, 219, 230, 243, 254, 310, 409, 412, 451, 455, 463, 472, 497, 501, 513, 550, 555, 574, 634 Whole numbers Addition, 16, 36–39, 40–41, 44–47, 62, 65 Comparing, 24–27, EP2 Comparing on a number line, 24–27 Composite numbers, 70C, 114–115, 120, EP8 Hundreds, 19, 20–23 Hundred thousands, 20–23 More About Rounding Numbers, 31 Ones, 19, 20–23 Ordering, 24–27, EP2 Prime numbers, 70C, 114–115, 120, EP8 Reading, 20–23, 63
Write Math, A4, A6, A7, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A43, A44, A45, A47, A48, A49, A51, 5, 7, 11, 15, 16, 22, 23, 27, 31, 34, 38, 41, 43, 47, 49, 52, 53, 55, 58, 61, 67, 70, 74, 77, 79, 83, 88, 89, 92, 93, 95, 98, 99, 102, 105, 108, 112, 113, 115, 121, 124, 129, 132, 133, 135, 138, 141, 144, 145, 147, 150, 153, 156, 157, 159, 162, 166, 169, 172, 173, 179, 182, 189, 192, 193, 195, 197, 202, 203, 205, 207, 209, 212, 213, 215, 218, 219, 222, 223, 225, 227, 230, 235, 238, 243, 246, 247, 249, 251, 254, 255, 260, 263, 266, 269, 275, 278, 282, 285, 287, 290, 291, 294, 295, 298, 299, 302, 306, 310, 313, 315, 321, 324, 329, 332, 333, 335, 338, 339, 341, 344, 346, 347, 350, 353, 356, 359, 361, 363, 366, 370, 377, 380, 384, 387, 390, 391, 395, 398, 400, 403, 405, 408, 409, 412, 417, 419, 420, 423, 425, 427, 429, 432, 439, 442, 447, 451, 455, 458, 459, 462, 463, 465, 467, 469, 472, 475, 477, 480, 481, 483, 489, 492, 497, 501, 503, 505, 508, 509, 513, 516, 519, 521, 527, 530, 535, 539, 542, 543, 545, 550, 554, 555, 557, 558, 562, 565, 570, 574, 579, 582, 586, 589, 591, 593, 595, 598, 599, 601, 604, 607, 612, 615, 621, 624, 627, 630, 631, 634, 637, 640, 641, 643, 650, 653, 656, 663, 669
Your Turn!, 17, 71, 125, 183, 239, 279, 325, 381, 443, 493, 531, 583, 625
Zz Zero Property of Multiplication, 80–83, 116, 117, EP5 Zeros Division, EP5 Multiplication, 226–227, 228–230, 234 Subtraction, 56–59, 66
Writing Decimals, 385–387, 388–391, 392–395, 435, EP23, EP24 Equations, 681, EP9, EP10, EP11 Expressions, 137–139, 148–150, 176, EP9, EP10 Whole numbers, 20–23, 63, 393–395, EP2, EP24 Expanded form, 16C, 20–23, 63, 393–395, EP2, EP24 Standard form, 16C, 20–23, 63, 393–395, EP24 Word form, 16C, 20–23, 63, 393–395, EP2 Writing Learning Stations, 16E, 70E, 124E, 182E, 238E, 278E, 324E, 380E, 442E, 492E, 530E, 582E, 624E
INDEX 18
