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In Flight with Sixth Grade Math A Publication of Complete Curriculum Rockwood, MI – Key West, FL
©2010 Complete Curriculum All rights reserved; No part of this publication may be reproduced or transmitted in any form or by any means without prior permission from the Publisher or Authorized Agent. Digitally accessible at completecurriculum.com Publishers: Alison Cancilliari; Dino Cancilliari Editorial Director: Rebecca J. Ensign Design Services provided by: Greg Moss; Bill Tite
Published in electronic format in the U.S.A. ISBN: 978-1-60565-007-4 10987654321
Acknowledgements Complete Curriculum’s K-12 textbooks have been team-developed by a consortium of teachers, administrators, educational and subject matter specialists, andFditors. In a collaborative environment, each person contributed to ensuring the quality, integrity and effectiveness of each Compete Curriculum text was commensurate with the required educational benchmarks and contemporary standards Complete Curriculum had set forth at the onset of this publishing program. April Lange; Jennifer Zaborowski; Frank Sinistaj; Alicia Jenkins; Michael Relph; Grace Carpenter; Matt Miller; Matt McCormick; Sarah McLain; Andrea Kehoe; Susan Lattea; Leann Hedke; Marie Maci; Lori Garner; Heather Jones; Carol Paul; Stacy Arnold; Rebecca Brooks; Linda Miller; Jocelyn Farkas; Marge Higdon Amber Plante; Amy Mazolla; Kelly Wells
About Complete Curriculum —1
Complete Curriculum Complete Curriculum’s digital textbooks were developed to provide teachers, homeschoolers, administrators, parents, guardians, tutors and most importantly – students, with affordable, accessible, effective educational content that utilizes the most current digital delivery format while satisfying the demands, requirements and expectations of today’s varied educational arenas. Affordable – each CC textbook offers an entire academic year’s content and activities for less than $30.00 if purchased as Full Digital Text, and far less when texts or Lessons are downloaded as part of a Complete Curriculum Membership. Each Full Digital Text includes the Teacher’s Manual with Answer Key, free Student Text downloads that can also be made available to students’ parents, Activities, Resources and Tests/Assessments. Accessible – Each text is clearly divided into 180 daily Lessons that translate to 1 to 1 ½ hours of daily classroom instruction. Written to the individual student and teacher, this text naturally facilitates differentiated instruction, and is equally user friendly to parents trying to help students study and complete their homework assignments as well as the teacher with a class of 25 students. Effective – Each CC Lesson in each text is template formatted for immediate understanding of each Lesson’s Objective and the method and means by which it will be achieved each day. Designed in a “preparationataglance” format, the core instructional content is clearly and simply stated which allows each teacher ample time to supplement, streamline or customize each Lesson as desired, needed or determined by the level of the student/students. As the 21st century concludes its first decade, educational content has been left on the shores as other industries have been swept up by the digital content delivery wave. But, in addition to cost-effective, attractive imagery, textbook content must be dedicated to providing relevant, real time, real world, user-centric, engaging material that supports the instructor’s ability to teach and the student’s ability to learn and retain. Simply stated, CC’s publishing platform provides streamlined instruction, practice, reinforcement and testing of the educational material required in order for the student to meet today’s rigorous academic standards, and acquire familiarity with the core 21st Century skills such as cooperation, collaboration and communication. By blending academic, social and interpersonal skills development, CC texts afford teachers and parents the opportunity to effectively impact a student’s ability to accelerate – in and out of the classroom.
About Complete Curriculum —2
Complete Curriculum texts organize and present content that enables: Parents to actually participate in helping their child to study or complete their homework Beginning teachers to produce on the first day of class Home-schoolers to affordably ensure the curriculum they are teaching their children meets the required Grade Level Content Expectations Experienced educators to creatively adapt each Lesson and text to their preferred teaching style and methods Complete Curriculum publishes distinctive K-12 digital texts in each of the core Subjects: Math, Language Arts, Science and Social Studies. Each Lesson is introduced through an Engaging Question to capture the student’s interest and provide much needed relevance. Lessons are also supported with supplemental Engaging Activities, Real-World application exercises, 21st Century Skills Development and activities based upon technology resources and integration. The result: Complete Curriculum’s texts and Lessons offer a full year’s and full day’s worth of contemporary content that can also be utilized to supplement or customize existing material. This distinctive feature assists educators to adjust to the accelerating demands that today’s ever-evolving learning environments place upon them and their students; demands such as differentiated instructional challenges, disparity between available and desired technological resources, and functional, effective online instruction. Scheduled for Publication 2010 . . . Higher Altitudes in 9th Grade Language Arts 10th Grade Language Arts 11th Grade Language Arts 12th Grade Language Arts Escape Velocity: Algebra I Algebra II Geometry Economics Coming 2011 . . . . “Culture Clips” – World-wide cultural nuances and insight provide the backdrop for these supplemental readers/Activity guides for K-12 LA and Social Studies
In Flight! with Sixth Grade Math — 1
In Flight with Sixth Grade Math In Flight is Complete Curriculum’s series for 6th through 8th grade Math, Language Arts, Science, and Social Studies. Consistent with Complete Curriculum’s dedication to flexible, efficient delivery and sustained acquisition of the core curriculum requirements, the In Flight series shows the student preparing for high school and college that learning can be fun, rewarding and meaningful. How to Use this Text: Written to the individual Ueacher and student in alternating gender, as a comprehensive or “flex-text”, each Lesson naturally facilitates individualized instruction, while accommodating all types of learning environments – the traditional classroom setting, the home-school classroom, the kitchen table as parents assist with homework, and private or institutional professional tutoring.
The Teacher’s Manual [TM] includes the Student Manual in its entirety with answers placed either at the end of the TM portion or within all Xorksheets, Fxercises, Bssessments, etc.
To the Teacher Each Lesson in the Teacher’s Manual begins in a “Preparation at a Glance” format written and to and for the teacher. An annotated Teacher’s Manual front matter template has been provided on the next page. Note that only those fields that have lesson-relevant content are provided in each Lesson’s front matter. The following elements are included in every lesson: Lesson# and Title Objective Engaging Question Additional Notes to the Teacher The following elements are Optional, provided on a per Lesson basis, but of course, you may wish to include these Optional elements in a Lesson if or as you have the supplementary content. Key Vocabulary Materials Needed Literary Selections Supplemental Engaging Activities Extensions Technology Integration – There are a minimum of 10 Lessons per each Math 6-8 text that are focused on integrating technology and 21st century skills.
In Flight! with Sixth Grade Math — 2
Here is how each Lesson of the Teacher’s Manual begins. Lesson# Title Objective: [Pertains to specific lesson, compliant with standard grade level and content expectations.] Key Vocabulary: [List of new terms and concepts utilized in the lesson, but not necessarily assessed; these word lists include words that are recommended to use/explain while teaching the Lesson; spelling and Wocabulary words, words and meanings needed in advance for reading comprehension.] Materials Needed: [All materials needed for instruction, project based activities, or in order for the student to complete the Lesson exercises or activities.] Literary Selections: [Most pertinent to Language Arts; lists the title and author of literary works or articles read in the Lesson; the title of each Progressive Reader [K-3 Language Arts]; supplemental or Lesson based readings – all subject/grade levels; most Literary Selections, or chapters, are placed at the end of each Student Lesson.] Engage: Engaging Question: [Each Lesson begins with at least one Engaging Question; it is recommended to begin each day by first asking this question and encouraging dialogue with the student(s) until they begin to see how the Lesson ties into their world and lives.] Supplemental Engagement Activities: [Optional; Provided for various Lessons throughout text; Ideal for inserting Lesson-specific Activities from other sources; this is also a placeholder for additional practice exercises and activities that may be needed to supplement a particular Lesson.] Extensions: [Optional; Provided for various Lessons throughout text; Can be used as a supplement for accelerated students, or additional practice for students needing reinforcement.] Technology Integration: [Optional; Provided for various Lessons throughout text; Ties the Lesson content into accessing, utilizing or integrating technology resources, tools and skills. When internet searches are suggested, specific urls or search engines have not been provided due to the dynamic evolution of the ever-changing internet terrain; sophisticated search techniques and “hints” are provided when available to facilitate productive and efficient searches.] Additional Notes to the Teacher: [This is essentially the daily Lesson plan; this field summarizes the Lesson and provides insight, guidance, reminders and suggestions for preparing and teaching the lesson.] Advance Preparation or Homework Required: [While some Lessons have prescribed homework – either before or after the Lesson has been taught – this area also enables the teacher to assure compatibility between the student level and the length and scope of each lesson. For example, if a Lesson seems to have too much material for one class period, one solution is to select a portion of the Lesson to assign as homework. ] Lesson Wrap-Up: [Grades 6-8 LA texts have a Lesson Wrap-up at the end of the TM front matter and again at the end of the SM Lesson before any Worksheets, Assessments, Study Questions, or Literary Selections.] The Student Manual then follows.
In Flight! with Sixth Grade Math — 3
In Flight with Sixth Grade Math In Flight with Sixth Grade Math launches this Math series by showing Complete Curriculum’s commitment to offering comprehensive educational Math content that is structured, yet adaptable to the needs and preferences of the student and teacher. Consistent in its sequencing and presentation, the new or review material in each Lesson is introduced, explained, clarified, then illustrated through examples provided. Practice problems are then assigned for the student to complete independently. After reviewing the problems and answers with the student, a Worksheet or Lesson Wrap-Up activity is assigned. This format ensures comprehensive coverage of daily material, but also accommodates the need and or desire to condense, supplement, or combine Lessons and Lesson content. In Flight with Sixth Grade Math is dedicated to supporting each Lesson’s Objective by capturing the student’s immediate interest in the topic or concept. This can be accomplished by asking and allowing time for discussion of the student’s answer to the thematically tied Engaging Questions. Designed to be each Lesson’s opener, the Engaging Question can increase the student’s understanding and acquisition of the skill or principle being introduced or expanded.
The following features of this text will assist students in acquiring, developing and building upon their 6th Grade Math skills and aptitude: Geometry Lessons are presented in a manner that encourages the student to first visualize, imagine, and think about the relationship between Geometry and other subjects and applications, such as Art and Industry, thereby helping the student bridge the gap between Math and other skill sets and fields of study. Writing and sketching assignments, to be completed in the student’s Math Journal, offer an alternative, appealing way for the student to develop and demonstrate his or her understanding of the mathematical principles and concepts. Many Lessons encourage the student to learn or create word associations and pneumonic devices for retaining the meanings of new terms presented through the course. Material and concepts are introduced and reinforced by showing their purpose and relevance to the sixth grader’s perspective and familiar aspects of his or her daily life.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 1 Understanding Place Value Objective: The student will learn how to express, compare, and order Whole Numbers through the use of Place Value. Lesson 2 Estimating with Whole Numbers Objective: The student will be able to find Sums, Differences, Products, and Quotients using different estimation techniques. Lesson 3 Addition and Subtraction Objective: The student will apply Addition and Subtraction to real-life problems. Lesson 4 Multiplication and Division Objective: The student will be able to solve real-life applicable word problems using Multiplication and Division. Lesson 5 Algebraic Expressions Objective: The student will be able to identify, write, and evaluate Algebraic Expressions with whole numbers. Lesson 6 Algebraic Equations Objective: The student will be able to use mental math and substitution to solve Algebraic Equations. Lesson 7 Algebraic Properties Objective: The student will be able to identify and apply the Commutative, Associative, Distributive, and Identity properties of addition and multiplication. Lesson 8 Exponents Objective: The student will be able to represent numbers using Exponents. Lesson 9 Order of Operations Objective: The student will be able to understand and use the Order of Operations. Lesson 10 Representing, Comparing, and Ordering Decimals Objective: The student will be able to represent, order, and compare decimals using Place Value Lesson 11 Estimation with Decimals Objective: The student will be able to estimate sums, differences, products, and quotients with decimals.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 12 Decimals and Percents Objective: The student will be able to express a decimal as a percent and a percent as a decimal. Lesson 13 Adding and Subtracting Decimals Objective: The student will be able to add and subtract decimals Lesson 14 Multiplying Decimals Objective: The student will be able to multiply decimals. Lesson 15 Dividing Decimals by a Whole Number Objective: The student will be able to divide a decimal by a whole number. Lesson 16 Dividing Decimals by Decimals Objective: The student will be able to divide decimals by decimals. Lesson 17 Evaluating Decimal Expressions and Equations Objective: The student will be able to use various strategies such as mental math and substitution to solve expressions and equations with decimals. Lesson 18 Divisibility Objective: The student will be able to use divisibility rules correctly. Lesson 19 Prime and Composite Numbers Objective: The student will be able to identify whether a number is Prime or Composite. Lesson 20 Prime Factorization Objective: The student will be able to write a composite number as a product of prime numbers. Lesson 21 Least Common Multiple and Greatest Common Factor Objective: The student will be able to find the Least Common Multiple and Greatest Common Factor of a number and use these to solve problems. Lesson 22 Equivalent Fractions and Simplest Form Objective: The student will be able to write Equivalent Fractions and fractions in the Simplest Form. Lesson 23 Mixed Numbers Objective: The student will be able to write Mixed Numbers as fractions, and write fractions as Mixed Numbers.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 24 Comparing and Ordering Fractions Objective: The student will be able to compare and order fractions. Lesson 25 Fractions and Decimals Objective: The student will be able to convert fractions to decimals. Lesson 26 Fractions, Decimals and Percents Objective: The student will be able to convert fractions to decimals, decimals to fractions, and fractions to percents. Lesson 27 Estimating Sums and Differences Objective: The student will be able to estimate sums and differences of fractions and mixed numbers Lesson 28 Adding and Subtracting Fractions Objective: The student will be able to add and subtract fractions. Lesson 29 Adding and Subtracting Mixed Numbers Objective: The student will be able to add and subtract mixed numbers. Lesson 30 Subtracting Mixed Numbers with Renaming Objective: The student will be able to subtract mixed numbers that require renaming. Lesson 31 Multiplication of Fractions Objective: The student will be able to multiply two fractions. Lesson 32 More Multiplication of Fractions Objective: The student will be able to multiply a fraction by a whole number. Lesson 33 Multiplication with Mixed Fractions Objective: The student will be able to multiply a proper fraction by a mixed fraction or two mixed fractions Lesson 34 Dividing Fractions Objective: The student will be able to divide two fractions. Lesson 35 More Division of Fractions Objective: The student will be able to divide a fraction by a whole number. Lesson 36 Dividing Fractions and Mixed Numbers Objective: The student will be able to divide a fraction by a mixed number.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 37 Dividing Two Mixed Fractions Objective: The student will be able to divide two mixed fractions. Lesson 38 Multiplication and Division of Fractions Review Objective: The student will review the skills learned in the previous Lessons teaching multiplication and division of fractions. Lesson 39 Multiplication and Division of Fractions Assessment Objective: The student will be able to display knowledge and understanding of multiplication and division of fractions. Lesson 40 Working with Algebraic Expressions Objective: The student will be able to write Algebraic Expressions Lesson 41 Evaluating Algebraic Expressions Objective: The student will be able to write Algebraic Expressions Lesson 42 Working with Square Roots Objective: The student will be able to evaluate expressions with square roots. Lesson 43 Writing Equations Objective: The student will be able to write an Algebraic Equation from a verbal or written statement. Lesson 44 Solving One-step Addition Equations Objective: The student will learn how to solve addition equations. Lesson 45 Solving Subtraction Equations Objective: The student will be able to solve subtraction equations. Lesson 46 Expressions and Equations Review Objective: The student will review all the skills learned in Lessons 40 through 45. Lesson 47 Expressions and Equations Assessment Objective: The student will be able to display a knowledge and understanding of expressions and equations on an Assessment. Lesson 48 Solving Multiplication Equations Objective: The student will be able to solve multiplication equations.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 49 Solving Division Equations Objective: The student will be able to solve a division equation. Lesson 50 Inequality Basics Objective: The student will be able to identify what an Inequality is, and what symbols are used in mathematical sentences representing Inequalities. Lesson 51 Solving Inequalities Part 1 Objective: The student will be able to solve addition and subtraction inequalities and graph the solution on a number line. Lesson 52 Solving Inequalities Part 2 Objective: The student will be able to solve multiplication and division Inequalities and represent the solution using a number line. Lesson 53 Solving Inequalities Part 3 Objective: The student will be able to solve two-step inequalities and graph the solution on a number line. Lesson 54 Equations and Inequalities Review Objective: The student will be able to review the skills learned throughout the Lessons teaching how to solve equations and solve and graph inequalities. Lesson 55 Equations and Inequalities Assessment Objective: The student will be able to display knowledge and understanding of solving equations and inequalities Lesson 56 Geometry Terminology Objective: The student will be able to understand and apply basic geometric vocabulary related to lines and angles. Lesson 57 Angles Objective: The student will be able to use measuring tools to measure angles. Lesson 58 Polygons Objective: The student will be able to classify an angle and polygon by type. Lesson 59 Circles Objective: The student will be able to understand and identify the properties of Circles, and use a compass to draw Circles that illustrate given specific information.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 60 Congruent and Similar Figures Objective: The student will be able to identify two figures as congruent or similar. Lesson 61 Symmetry Objective: The student will be able to draw Lines of Symmetry into a figure, and determine whether a figure has Rotational Symmetry. Lesson 62 Geometry Review and Assessment 1 Objective: The student will be able to review the skills learned in the first Geometry Lessons taught, and successfully complete the Assessment Lesson 63 Introduction to Plane and Solids Figures Objective: The student will be able to make an artistic collage to classify Plane and Solid figures. Lesson 64 Triangles Objective: The student will be able to classify the types of Triangles. Lesson 65 Quadrilaterals Objective: The student will be able to classify the types of Quadrilaterals. Lesson 66 Transformations Objective: The student will be able to understand and use the various types of Transformations. Lesson 67 Understanding Solid Figures Objective: The student will be able to identify Solid Figures. Lesson 68 Geometry Review and Assessment 2 Objective: Students will be able to review the skills learned in this unit regarding Triangles, Quadrilaterals, Polygons, and Transformations. Lesson 69 Measuring Length with the Metric System Objective: The student will be able to understand length in terms of the Metric System. Lesson 70 Length Activity Objective: The student will be able to understand the Metric System as it relates to measuring length.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 71 Metric Conversions Objective: The student will be able to make Conversions using metric units of length. Lesson 72 Customary Conversions Objective: The student will be able to make conversions using customary units of length. Lesson 73 Capacity and Weight Objective: The student will be able to make conversions using customary units of Capacity and Weight. Lesson 74 Capacity and Mass Objective: The student will be able to make conversions using metric units of capacity and mass. Lesson 75 Time Objective: The student will be able to determine elapsed time and make conversions using units of time. Lesson 76 Temperature Objective: The student will be able to make conversions with temperatures. Lesson 77 The Metric System Review Objective: The student will review the skills taught and learned in the previous Lessons on the metric system and conversion of units of measure. Lesson 78 Measurement Assessment Objective: The student will be able to display knowledge attained throughout the Lessons taught on the metric system and conversions. Lesson 79 Measuring Perimeter Objective: The student will be able to use a ruler to measure the Perimeters of various objects in the real world. Lesson 80 Finding Perimeter Objective: The student will be able to find the Perimeter of an object even when not given all of the lengths of the sides of object Lesson 81 Finding Circumference Objective: The student will be able to find the Circumference of a circle.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 82 Circumference and Diameter Objective: The student will be able to understand the relationship between Circumference and Diameter. Lesson 83 Perimeter Review Objective: The student will review finding Perimeter and Circumference in preparation for the Perimeter Assessment. Lesson 84 Perimeter Assessment Objective: The student will be able to display knowledge of finding Perimeter and Circumference by completing the Perimeter Assessment. Lesson 85 What is Area? Objective: The student will be able to use grid paper to estimate Area. Lesson 86 Finding Area Part 1 Objective: The student will be able to find the Area of a rectangle or square. Lesson 87 Area and Perimeter Objective: The student will be able to practice finding Area and Perimeter of squares and rectangles. Lesson 88 Finding Area Part 2 Objective: The student will be able to find the Area of a triangle. Lesson 89 Finding Area Part 3 Objective: The student will be able to find the Area of a parallelogram. Lesson 90 Finding Area Review Objective: The student will be able to practice finding the Area of rectangles, squares, triangles, and parallelograms. Lesson 91 Area Assessment Objective: The student will be able to display knowledge and understanding of finding the Area of squares, rectangles, triangles, and parallelograms. Lesson 92 Surface Area of a Prism Objective: The student will be able to understand how to find the Lateral Area of a prism and use the Lateral Area to find the Surface Area.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 93 Surface Area of a Pyramid Objective: The student will be able to find the Lateral Area and Surface Area of a Pyramid. Lesson 94 Surface Area of a Cylinder Objective: The student will be able to find the Lateral Area and Surface Area of a Cylinder. Lesson 95 Surface Area of a Cone Objective: The student will be able to find the Lateral Area and Surface Area of a Cone. Lesson 96 Volume of a Prism Objective: The student will be able to find the Volume of a Prism. Lesson 97 Volume of a Pyramid Objective: The student will be able to find the Volume of a Pyramid. Lesson 98 Volume of a Cylinder Objective: The student will be able to find the Volume of a Cylinder. Lesson 99 Volume of a Cone Objective: The student will be able to find the Volume of a cone. Lesson 100 Surface Area and Volume Review Objective: The student will review how to find the Surface Area and Volume of a Prism, Pyramid, Cone, and Cylinder in preparation for the Assessment in Lesson 101. Lesson 101 Surface Area and Volume Assessment Objective: The student will be able to display knowledge of how to find the Lateral and Surface Area and Volume of a Prism, Pyramid, Cylinder, and Cone. Lesson 102 Geometry in Art Project Preparation Objective: The student will be given a review of basic geometry concepts and terms needed in order to be prepared for Geometry in Art Project in Lessons 103-114. Lesson 103 Geometry in Art, Project Part 1 Objective: The student will be able to use the various concepts learned about Geometry to apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze the importance of that connection.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 104 Geometry in Art, Project Part 2 Objective: The student will be able to use the various concepts learned about Geometry to apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze its importance. Lesson 105 Geometry in Art, Project Part 3 Objective: The student will be able to use the various concepts learned about Geometry to apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze its importance. Lesson 106 Geometry in Art, Project Part 4 Objective: The student will be able to use the various concepts learned about Geometry and apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze its importance. Lesson 107 Geometry in Art, Project Part 5 Objective: The student will be able to use the various concepts learned about Geometry to apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze its importance. Lesson 108 Geometry in Art, Project Part 6 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries using a Venn diagram. Lesson 109 Geometry in Art, Project Part 7 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in the first draft of a well-written 5-paragraph essay. Lesson 110 Geometry in Art, Project Part 8 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in a well-written 5-paragraph essay. Lesson 111 Geometry in Art, Project Part 9 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in a well-written 5-paragraph essay. Lesson 112 Geometry in Art, Project Part 10 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in a slide show using presentation software.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 113 Geometry in Art, Project Part 11 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in a slide show using presentation software. Lesson 114 Geometry in Art, Project Part 12 Objective: The student will be able to compare and contrast the Art of the Renaissance period with Art of the 20th and 21st centuries in a well-written 5-paragraph essay. Lesson 115 Ratios Objective: The student will learn how to write Ratios. Lesson 116 Unit Rates Objective: The student will be able to find Unit Rates. Lesson 117 Proportions Objective: The student will be able to write and solve a Proportion. Lesson 118 Scale Objective: The student will be able to use Scale to find the true dimensions of a drawing or object. Lesson 119 Ratio and Proportion Review Objective: The student will review the skills learned in writing and calculating Ratios and Proportions, and using Scale drawings. Lesson 120 Ratio, Proportion and Scale Assessment Objective: The student will be able to display knowledge of Ratios, Proportions and Scale. Lesson 121 Percent Objective: The student will be able to write and compare Percents. Lesson 122 Percents and Decimals Objective: The student will be able to write Percents as Decimals and Decimals as Percents. Lesson 123 Writing Percents from Fractions Objective: The student will be able to write a Percent from a Fraction that does not have a denominator of 100. The student will also be able to write a Fraction from a Percent. Lesson 124 Finding a Percent of a Number Objective: The student will be able to find a Percent of a number.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 125 Discount Objective: The student will be able to solve money problems involving a Discount. Lesson 126 Percent and Discount in the Real World Part 1 Objective: The student will be able to understand how to find a percent of a number and discount in a real-world situation. Lesson 127 Percent and Discount in the Real World Part 2 Objective: The student will be able to understand how percent is used in a real-world situation. Lesson 128 Percent Review Objective: The student will prepare for the Assessment on Percent. Lesson 129 Percent Assessment Objective: The student will be able to display knowledge and understanding of Percent on the Assessment. Lesson 130 Shop ‘til You Drop with $500 – Part 1 Objective: The student will be able to show relationships between fractions, decimals, and percents in a real world situation. The student will also be able to solve problems involving percents. Lesson 131 Shop ‘til You Drop with $500 – Part 2 Objective: The student will be able to show relationships between fractions, decimals, and percents in a real-world situation. The student will also be able to solve problems involving percents. Lesson 132 Shop ‘til You Drop with $500 – Part 3 Objective: The student will be able to show relationships between fractions, decimals, and percents in a real-world situation. The student will also be able to solve problems involving percents. Lesson 133 Math Service Project – Part 1 Objective: The student will creatively apply various 6th grade Math skills. Lesson 134 Math Service Project - Part 2 Objective: The student will creatively apply various 6th grade Math skills.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 135 Math Service Project - Part 3 Objective: The student will creatively apply various 6th grade Math skills. Lesson 136 Math Service Project - Part 4 Objective: The student will creatively apply various 6th grade Math skills. Lesson 137 Math Service Project - Part 5 Objective: The student will creatively apply various 6th grade Math skills. Lesson 138 Theoretical Probability Objective: The student will be able to find the Theoretical Probability of an event. Lesson 139 Experimental Probability Objective: The student will be able to find the Experimental Probability of an Event. Lesson 140 Compound Events and Tree Diagrams Objective: The student will be able to find all possible outcomes for Compound Events. Lesson 141 Compound Events and the Fundamental Counting Principle Objective: The student will be able to find all possible outcomes for Compound Events. Lesson 142 Compound Events in Real Life Objective: The student will be able to see how Compound Events are used in real life. Lesson 143 Independent Events Objective: The student will be able to find the probability of Independent Events. Lesson 144 Dependent Events Objective: The student will be able to find the probability of a Dependent Event. Lesson 145 Probability Review Objective: The student will review the objectives learned regarding Probability. Lesson 146 Probability Assessment Objective: The student will display knowledge and understanding of Probability on the Assessment.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 147 Mean Objective: The student will be able to find the Mean of a set of data.
Lesson 148 Median Objective: The student will be able to find the Median of a set of data. Lesson 149 Mode Objective: The student will be able to find the Mode of a set of data. Lesson 150 Creating a Frequency Table Objective: The student will be able to create a Frequency Table to illustrate and display data. Lesson 151 Creating a Line Plot Objective: The student will be able to create a Line Plot as a statistical representation of data. Lesson 152 Stem and Leaf Plot Objective: The student will be able to create a Stem and Leaf Plot to represent data. Lesson 153 Fun with Stem and Leaf and Line Plots Objective: The student will conduct an experiment and display the data in a Stem and Leaf Plot. Lesson 154 Creating a Pie Chart Objective: The student will be able to create a Pie Chart as a data representation. Lesson 155 Creating a Bar Graph Objective: The student will be able to create a Bar Graph to represent data. Lesson 156 Creating a Box and Whisker Plot Objective: The student will be able to create a Box and Whisker Plot to represent data. Lesson 157 Statistics Review Objective: The student will review the skills learned in the Lessons on statistics. Lesson 158 Statistics Assessment Objective: The student will be able to display knowledge and understanding of how to find the measures of central tendency and create the various statistical representations.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 159 Scoring with the Stats - Part 1 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various concepts regarding statistics using this data. Lesson 160 Scoring with the Stats - Part 2 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various concepts regarding statistics using this data. Lesson 161 Scoring with the Stats - Part 3 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 162 Scoring with the Stats - Part 4 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 163 Scoring with the Stats - Part 5 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 164 Scoring with the Stats - Part 6 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 165 Scoring with the Stats - Part 7 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various concepts regarding statistics using this data. Lesson 166 Scoring with the Stats - Part 8 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 167 Scoring with the Stats - Part 9 Objective: In this project, the student will be able to analyze real-world data and display knowledge and understanding of the various statistical concepts using this data. Lesson 168 Graphing 101 Objective: The student will be able to graph a point on a Coordinate Plane. Lesson 169 More Graphing Objective: The student will be continue practicing how to graph on a Coordinate Plane.
TABLE OF CONTENTS AND OBJECTIVES
SIXTH GRADE MATH
Lesson 170 Integers Objective: The student will be able to understand the Number Line and find the Absolute Value of a number. Lesson 171 Comparing Integers Objective: The student will be able to compare Integers with <, >, or =. Lesson 172 Operations with Integers – Addition Objective: The student will be able to add integers. Lesson 173 Operations with Integers – Subtraction Objective: The student will be able to subtract two integers. Lesson 174 Operations with Integers – Multiplication Objective: The student will be able to multiply integers. Lesson 175 Operations with Integers – Division Objective: The student will be able to divide integers. Lesson 176 Integer Review Objective: The student will review the skills he learned throughout the chapter on integers in preparation for the Assessment given on the coordinate plane and integers. Lesson 177 Integer Assessment Objective: The student will be able to display an understanding of integers by taking the Integer Assessment. Lesson 178 Solving Word Problems Objective: The student will be able to solve word problems using the 4-step problem solving method. Lesson 179 More Word Problems Objective: The student will be able to use the 4-step problem solving model to solve word problems. Lesson 180 Math 6 Wrap-Up and Assessment Objective: The student will be able to review all the mathematics concepts introduced, practiced and assessed throughout this 6th Grade Math course.
STUDENT MANUAL
GRADE 6 MATH LESSON 1-1
Lesson 1
Understanding Place Value
Today you are going to work on your understanding of Place Value. To do this, you will examine the number representing the length of Pluto’s orbit, which is: 22,955,012,169 miles. Each of the digits in this number has a specific Place Value, and the value of a digit is determined by the position it holds in the number. For example, the value of the first digit 2 in 22,955,012,169 is 2 x 10,000,000,000 = 20,000,000,000 since it is found in the ten billions place. Examine the following Place Value Chart:
Consider the following points about Place Value. There are three different expanded forms of a number. Standard form: This is the normal form of the number. Ex. 22, 955,012, 169 Expanded form: This form of the number uses the Place Value of each digit. Ex. 20,000,000,000 + 2,000,000,000 + 900,000,000 + 50,000,000 + 5,000,000 + 10,000 + 2,000 + 100 + 60 + 9 Written form: This is the number written out in words. Twenty-two billion, nine hundred, fifty-five million, twelve thousand, one hundred, sixty-nine
STUDENT MANUAL
GRADE 6 MATH LESSON 1-2
Answer the following questions: What would you need to know in order to write a number in expanded form? ___________________________________________________________________________________ What do the 5’s in the number 22, 955,012,169 represent? ___________________________________________________________________________________ ___________________________________________________________________________________
When thinking about place value, what is the relationship of any Place Value in any position of a number to the position on its right? ___________________________________________________________________________________
Work through these examples: Use < or > to compare the following numbers: 537,437, 641
537,438,006
1,359,214
1,359,124
31,012,367
31,021,367
Order the following lists of numbers from least to greatest: 467,703,522
476,703,520
436,703,521
_____________________________________ 24,127,256
24,172,265
24,127,265
_____________________________________ 324,480,125
324,408,127
324,480,521
_____________________________________ Write the Place Value of the bold digit in each number: 37,951,252___________________ 861,740,213,903___________________ 4,350,217___________________ Lesson Wrap-Up: Write in your Math Journal the steps and the process you would use if you were asked to compare a set of numbers.
STUDENT MANUAL
GRADE 6 MATH LESSON 1-3
Worksheet 1 Directions: Compare each set of numbers using <, >, =. 1. 5,048 _______ 6,171 2. 125,394 _______ 195,324 3. 479,361 _______ 473,961 4. 57,541 _______ 575,363 5. 14,753,000 _______ 14,752,418 6. 39,942 _______ 39,942 7. 6,887 _______ 6,907 8. 261,354 _______ 261,334 9. 7,014 _______ 7,015 10. 5,140 _______ 5,132
STUDENT MANUAL
GRADE 6 MATH LESSON 1-4
Directions: Put each of the following sets of numbers in order from least to greatest. 11. 8,919; 8,403; 10,058; 9,449 _____________________________________ 12. 3,805; 3,783; 3,796 _____________________________________ 13. 651; 1,151; 851 _____________________________________ 14. 7,391; 7,630; 6,387; _____________________________________ 15. 86,738; 86,715; 86,734; 86,718 _____________________________________ 16. 5,304; 5,312; 5,298
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17. 986,405; 702,738; 774,643; 764,343 _____________________________________ 18. 440; 627; 645 _____________________________________ 19. 89,319; 119,319; 29,319 _____________________________________ 20. 4,398; 6,110; 6,333; 5,139 _____________________________________ Directions: Identify the Place Value of the underlined digit. 21. 2,038
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22. 868,048,583 __________________________________ 23. 19,764 __________________________________ 24. 55,585,021 __________________________________ 25. 3,202 __________________________________ 26. 23,612 __________________________________ 27. 70,134,704 __________________________________ 28. 982,147 __________________________________ 29. 878,244
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30. 56,043,701 __________________________________ 31. 350 __________________________________ 32. 1,171,386 __________________________________ Print Form
STUDENT MANUAL
GRADE 6 MATH LESSON 2-1
Lesson 2
Estimating with Whole Numbers
The longest throw of a flying disc was about 712 feet, thrown by Christian Voigt in 2001. Do you notice that the distance of the throw is stated as about 712 feet? In today’s Lesson you will be working on estimating with whole numbers. If the following three children each threw a disc as indicated in the chart below, is the sum of all three throws close to Christian Voigt’s record? Name Brandon Kelly Susan
Distance 132 feet 150 feet 183 feet
There are two different methods of Estimation: Clustering: If the numbers you are estimating all cluster around a specific number use that number to estimate the sum or difference. Example Estimate 1,957 + 2,245 + 1,999 Since all three numbers cluster around 2,000, use 2,000 as the estimation for each number and multiply by 3 therefore, the estimation is 6,000.
STUDENT MANUAL
GRADE 6 MATH LESSON 2-2
Rounding: In rounding you have to decide what Place Value you want to round off to, and then look at the digit just to the right of your chosen rounding digit. If the digit to the right is less than 5, do not change the rounding digit itself, just change the numbers to the right of it to 0. If the digit to the right of the rounding digit is 5 or greater, change the rounding digit and all digits to the right to 0. Example Estimate 31,988 – 21,918 by estimating to the nearest thousand or ten thousand. Round each of the numbers to the nearest thousand or ten thousand: 30,000 – 20,000 = 10,000 (nearest ten-thousand) 32,000 – 22,000 = 10,000 (nearest thousand) Example Estimate 5,125 – 1,920 by rounding to the nearest thousand. Round each number to the nearest thousand: 5,000 – 2,000 = 3,000
When you are rounding it is appropriate to use the “approximately equal to” symbol ≈. Example 5,125 – 1,920 ≈ 3,000 The next methods of estimating are underestimation and overestimation. Underestimation: An estimate that is less than the exact answer. Overestimation: An estimate that is greater than the exact answer. Example 366 + 198 = 564 (exact answer) 370 + 200 = 570 (rounded answer = overestimate) Example 144 x 123 = 17,712 (exact answer) 100 x 100 = 10,000 (rounded answer = underestimate)
STUDENT MANUAL
GRADE 6 MATH LESSON 2-3
Consider these real-life examples: There is a school play in the school gym and the students are setting up chairs in 26 rows of 38 chairs each. About how many programs will the school need for each student attending this play? Step 1: Round each number up to the nearest ten (26 up to 30 and 38 up to 40) Step 2: Multiply 30 by 40 = 1,200 Step 3: Answer the question: The school will need about 1,200 programs (note that this is an overestimate because each number is rounded up). Each of the 46 Math students in the Annual Math Competition must complete 25 problems. About how many problems will need to be written? Step 1: Round each number (46 up to 50 and 25 up to 30) Step 2: Multiply 50 by 30 = 1,500 Step 3: Answer the question: The math students of the competition will need to write about 1,500 problems.
Lesson Wrap-Up: Write in your Math Journal two ways to estimate the total mileage walked by 389 students who all completed a 5-mile walk.
STUDENT MANUAL
GRADE 6 MATH LESSON 2-4
Worksheet 2 Directions: Estimate each sum or difference. 1. 7,407 + 80,867 + 9,557
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2. 530,637 – 747
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3. 51,141 + 51,165
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4. 7,522,617 - 7,522,583
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5. 898,734 + 218,267
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6. 590 – 578
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7. 1,222,198 - 3,330
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8. 59,241 + 68,983
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9. 481,857 + 481,934
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10. 7,330 + 26,091 + 2,147 _____________________________________ 11. 6,725,800 + 681
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12. 8,943 + 9,027
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13. 58,768 - 19,121
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14. 4,570,007 – 826
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15. 691,449 + 691,515
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16. 7,392 – 900
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17. 412,325 - 412,286
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18. 183 + 1,078 + 792
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19. 1,541,626 + 1,893,188
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20. 39,918 + 220
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STUDENT MANUAL
GRADE 6 MATH LESSON 2-5
Directions: Estimate each product or quotient. 21. 403,522 ÷ 703
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22. 197(25,010)
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23. 73 ÷ 6
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24. 17,135 ÷ 991
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25. 2,392 ÷ 54
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26. 646 × 5
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27. 179 × 400
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28. 672,965 ÷ 8,054
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29. 326(150)
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30. 9,069(8,280)
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31. 262 × 826
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32. 59,049 ÷ 380
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33. 553,575 ÷ 605
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34. 153,202 ÷ 706
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35. 18,333 ÷ 9,382
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36. 5,276 ÷ 92
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37. 9,111(7,497)
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38. 82,386 ÷ 138
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39. 54 ÷ 4
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40. 51 ÷ 9
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STUDENT MANUAL
GRADE 6 MATH LESSON 2-6
Directions: Answer each problem based upon the following chart: Library:
Books:
Harvard University
15,190,704
Yale University
12,976,203
University of Illinois
9,302,755
University of California
8,765,478
University of Texas
7,755,430
About how many more library books does Yale University have than the University of alsj;alja;sfldj Texas? _____________________________________ Estimate the total number of library books at both Harvard University and Yale University. _____________________________________ If the library at the University of Illinois tripled in size, about how many books would it then have? _____________________________________
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STUDENT MANUAL
GRADE 6 MATH LESSON 3-1
Lesson 3
Addition and Subtraction
Today you are going to review rounding numbers to help with addition and subtraction problems. Start with the following examples. Examples Round each number to the nearest thousand: 3,871 rounded to the nearest thousand is 4,000 6,790 rounded to the nearest thousand is 7,000 4,253 rounded to the nearest thousand is 4,000 5,341 rounded to the nearest thousand is 5,000 Add or subtract by rounding to the nearest hundred: 452 + 631 when rounded to the nearest 500 + 600 = 1,100 4,530 – 1,725 when rounded to the nearest 4,500 + 1,700 = 6,200
Answer the questions following this chart, check that your answers are reasonable by estimating. Over the years of exploration and flight into space, the time US astronauts spent in space increased with each new exploration as indicated in the chart below. Space Exploration
Years
Hours in Space
Mercury
1961-1963
54
Gemini
1965-1966
1,940
Apollo
1968-1972
7,506
Skylab
1973-1974
12,352
STUDENT MANUAL
GRADE 6 MATH LESSON 3-2
How many hours did US astronauts spend in space from 1965-1974? _________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________ How many more hours did US astronauts spend in the Apollo exploration than on the Gemini exploration? _____________________________________________________________________________________ _____________________________________________________________________________________ _________________________________________________________________________ Answer the following questions with your teacher: How do you know whether to add or subtract when solving a word problem? Why is it a good idea to find an estimate before or after you find the exact answer to a problem? How do you decide if your answer is a reasonable answer to a problem? Lesson Wrap-Up: What are some other things a person estimates or are estimated in real life?
STUDENT MANUAL
GRADE 6 MATH LESSON 3-3
Worksheet 3 Directions: Solve each word problem. Then, estimate to check your answer. 1. Nicole wrote a report about some of the Native American foods of long ago. She wrote about Indian pudding, wild nut soup, berries and wild rice, and feast day puffs. To get information she spent 3 hours and 33 minutes doing research online and 1 hour and 21 minutes doing research at the library. It took her 1 hour and 39 minutes to write her rough draft and another thirty-eight minutes to write her final draft. How long did it take Nicole to research and write her report? _________________________________________________________________________________ 2. It’s harvest time. On Tuesday, Darlene took twelve truck loads of grain to the elevator, and Shannon took eleven truck loads. On Wednesday, Darlene took six loads, and Shannon took eight. How many truck loads went to the grain elevator on Tuesday and Wednesday? How many more loads did they get on Tuesday than Wednesday? _________________________________________________________________________________ 3. The one hundred nine students in fourth grade at Tallassee School were trying to learn to say, “Hello” in five different languages for World Hello Day. If thirty-five students learned to say “Hello” in all five languages, twenty-nine students learned to say it in just four languages, twenty-four learned to say it in just three languages, and the rest of the students learned to say it in just two languages, how many students learned to say “Hello” in just two languages? _________________________________________________________________________________ 4. If Egypt has seventy-one airports with paved runways and fifteen airports with unpaved runways, how many airports does Egypt have altogether? _________________________________________________________________________________ 5. Courtney and Victoria looked for shells on the beach. They found a total of twenty-two shells. If Victoria found six more shells than Courtney, how many shells did Victoria find? _________________________________________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 3-4
6. Mom likes to whistle while she cleans the house. It took her 40 minutes to clean the bathroom, 13 minutes to do the dishes, 11 minutes to vacuum the house, and half an hour to clean the bedroom. How long did Mom spend cleaning the house? _________________________________________________________________________________ 7. Idaho’s highest elevation is Borah Peak at 12,662 feet above sea level. The lowest elevation is found at the Snake River in Lewiston, measuring 710 feet above sea level. What is the difference between the highest elevation and the lowest elevation? _________________________________________________________________________________ 8. Christine is learning about her family history. She found out that after a potato famine struck Ireland an ancestor of hers came to New York City in 1848. At that time, her relative was ten years old. In what year was her relative born? _________________________________________________________________________________
9. Jordan’s pet is a king snake named Mick. Mick is still very young, so he is only eighteen inches long. When he is grown, he will be forty-seven inches long. How much longer will he be when he is grown than he is now? Oh, by the way, Mick refused to be dressed up as anything! _________________________________________________________________________________
10. In 2009, our neighbor Mrs. Anderson said her family originally immigrated to Canada in 1867. How many years ago did her family immigrate to Canada? _________________________________________________________________________________ 11. Kyle wants to be an actor when he is older. He has a good voice and already has a part in the school play. It is an important part and he has many lines to learn. Samantha is helping him learn his part. He has one hundred nineteen lines to learn and he has memorized thirty-nine of them. How many more lines does he have to learn? _________________________________________________________________________________
12. Brandon has trained to be part of the police department’s bomb squad. In his city there were fifty-one thousand, eighty-nine crimes reported last year. There were fortyeight thousand, one hundred five non-violent crimes. How many violent crimes were there? ________________________________________________________________________________
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STUDENT MANUAL
GRADE 6 MATH LESSON 4-1
Lesson 4
Multiplication and Division
Today you are going to review the ways to tell if an answer to a multiplication or division problem is reasonable. After you finish this Lesson, you will complete the Assessment of what you have learned in the past few Lessons. Examine the following example word problems, solve the problems and check your answers by estimating an answer using rounded numbers. A warehouse has 831 shelves. How many boxes are in the warehouse if each shelf holds 34 boxes? _________________________________________________________________________________ _________________________________________________________________________________ A monthly monorail ticket costs $140. How much will the rail company receive if they sell 12,456 tickets? _________________________________________________________________________________ _________________________________________________________________________________
If a cafeteria table can seat 12 students, and there are 368 students total, how many cafeteria tables are needed? _________________________________________________________________________________ _________________________________________________________________________________ The preschool arts and crafts group is making houses out of craft sticks. Each house uses 1,397 sticks and there are 10,500 sticks in the box. How many houses can they build with one box of sticks? _________________________________________________________________________________ _________________________________________________________________________________
If you had problems with any of the material in Lessons 1-4, review them with your teacher before taking the Lessons 1-4 Assessment. Lesson Wrap-Up: What is the value of estimating an answer to a word problem when solving word problems? Write your answer in your Math Journal.
STUDENT MANUAL
GRADE 6 MATH LESSON 4-2
Worksheet 4 Directions: Solve each word problem. Then, estimate to check your answer. 1. Wei’s school has three school buses to carry one hundred fourteen students to and from school. If the same number of children rides each bus, how many children ride each bus? _________________________________________________________________________________ 2. The Mountain Springs library is open from 8 a.m. until 9 p.m. on Monday through Friday, and from 11 a.m. until 3 p.m. on Saturday. It is closed on Sunday. How many hours is the library open each week? _________________________________________________________________________________
3. Anthony’s family strings popcorn and cranberries to put on their Christmas tree. They made five strings of popcorn and cranberries. Each string was four feet long. How long were the strings all together? _________________________________________________________________________________
4. Grandma has been sick, but the doctor says that she is making progress. She has to take five pills, three times a day. How many pills does she take in one day? _________________________________________________________________________________ 5. The lines at the amusement park were awful. It took us an hour just to get on one ride. The ride has four cars, which hold twelve people each. How many people can go on the ride at once? _________________________________________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 4-3
6. Jasmine cannot finish baking the cookies on time if she does not hurry. She has baked 2 dozen chocolate chip cookies, 3 dozen chocolate chunk cookies, 2 dozen sugar cookies, and 3 dozen sweet oatmeal cookies. How many cookies has Jasmine baked in all? _________________________________________________________________________________ 7. Using the following price list, find out how much Mackenzie spent on school supplies. She bought a notebook, two pocket folders, seventeen pencils, three erasers, a pair of scissors, a box of colored pencils, two black pens, eight blue pens, one ruler, and four packages of paper. Paper $1.29/package Rulers $0.99 each Pens $0.73 each Colored Pencils $3.43/box Scissors $4.42/pair Erasers $0.15 each Pencils $0.16 each Pocket Folders $0.32 each Notebook $4.41 each _________________________________________________________________________________ 8. Jonathan’s brother Austin is entering Mountain Community College this year. When he registered, he was told he could pay for his meals in cash, or he could buy a meal ticket for the whole year. If he pays cash, each meal he eats will cost $5.62. A meal ticket for the year pays for two meals per day for one hundred sixty-eight days and costs $1,596.08. If Austin eats 2 meals per day for one hundred sixty-eight days, how much would he save if he bought the meal ticket instead of paying for his meals in cash?
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STUDENT MANUAL
GRADE 6 MATH LESSON 4-4
9. It was my fault that we arrived at the musical later than we had expected. I had to stop to get gas. I put seven gallons of gas in my car. Each gallon cost me $1.76. How much did I spend on gas? _________________________________________________________________________________
10. Victoria’s Chihuahua had six puppies. When the puppies were old enough, she asked the pet store to help her find homes for them. The owner of the pet store said he would sell the puppies for $66 each and give 23% of the money to her. If the pet store owner sells all six puppies, how much money will Victoria make? _________________________________________________________________________________
11. Jason’s cow is very fragile, but she still gives about 10.9 gallons of milk a day. How many gallons does she give in one hundred twenty-one days? _________________________________________________________________________________
12. Morgan was hungry. She looked in the pantry but there was no food. There was no food in the refrigerator. She looked under her bed where she often kept cookies but only found one empty cookie jar. Well, she would have to buy something. She took $2.64 out of her hiding place and walked to the store. She wanted as many forty-four cent candy bars as she could get. How many candy bars can she buy? _________________________________________________________________________________
13. There are approximately fifty million metric tons of apples grown each year. It has been estimated that half of all the apples grown are eaten fresh. Approximately how many metric tons of apples are eaten fresh? _________________________________________________________________________________ 14. Nathan is making caramel apples for the Halloween Carnival. His recipe makes eleven caramel apples, but he wants to make 33 caramel apples. How many times will he have to make his recipe to have thirty-three caramel apples? _________________________________________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 4-5
15. Zachary and Robert bought a box of apples and divided the cost equally. The box of apples cost $9. How much did each boy have to pay for his half of the box of apples? _________________________________________________________________________________ 16. Nicholas was given the job of making sure there was enough water for his family’s nine cows. Because a dairy cow requires ten to thirty gallons of water each day, it was a very big job. The bucket Nicholas used only held three gallons of water. How many times would he have to take water to the drinking trough each day if each cow drank nineteen gallons of water? _________________________________________________________________________________ 17. My grandma loves to feel soft, clean towels. She put the towels in the dryer for fiftyeight minutes, but they did not get completely dry. She put them back in for half that time. How long were the towels in the dryer? _________________________________________________________________________________
18. Mr. Walker, the band director, decided to teach his band members to play the kazoo. He thought it would be a good way for them to relax and have some fun. The Band Boosters Club gave him $90 to buy kazoos. At $4 each, how many kazoos can he buy? Will there be any money left over? _________________________________________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 4-6
Assessment for Lessons 1-4 Directions: Compare each pair of Whole Numbers using <, >, or =. 1. 2,015,686 _______ 2,015,694 2. 6,198 _______ 6,918 3. 5,654,642 _______ 5,654,633 4. 4,862 _______ 4,682 5. 3,206,300 _______ 3,206,154 6. 52,624 _______ 91,821 Directions: Put each set of numbers in order from least to greatest. 7. 66,890; 38,839; 89,066
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8. 2,537; 2,466; 2,421; 2,437 9. 7,919; 7,908; 7,893
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10. 1,911,459; 1,511,459; 811,459; 311,459 ___________________________ 11. 3,035; 7; 163; 61
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12. 3,833; 3,847; 3,865; 3,816
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STUDENT MANUAL
GRADE 6 MATH LESSON 4-7
Directions: Tell the Place Value of each underlined number. 13. 34,320,223
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14. 32,530,212
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15. 910
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16. 868,411,254
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Directions: Estimate the answer to each problem. 17. 2,961 + 918 ________________ 18. 98 + 442 ________________ 19. 11 + 44 20. 895 – 352
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21. 8,319 - 4,119 ________________ 22. 241 – 226
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23. 79 x 95
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24. 8 x 50
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25. 15 x 14
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26. 448 ÷ 7
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27. 348 ÷ 5
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28. 45 ÷ 9
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Directions: Solve each word problem. 29. Mom offered to mend all of my torn socks. I found two in my closet, nine in the dirty laundry, six on the rug, and one in the dryer. How many torn socks did I have? _____________________________________________________ 30. Maybe the wind will blow enough today for the kite competition. There are twelve red kites, eleven yellow kites, eleven blue kites, and five green kites in the competition. How many kites are in the competition? _____________________________________________________ 31. Grace, Alexis, and Destiny had a contest. They wanted to find out who could hear a bell from the longest distance. Grace could hear it from eight feet. Alexis could hear it from seventeen feet. Destiny could hear it from twenty-six feet. How many feet further could Destiny hear it than Alexis? _____________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 4-8
32. Mrs. Harris drives a mail truck. She brings the mail to the houses on our street. Today she brought thirty-one letters to the houses on our street. She brought fifty letters to the houses on Elm Street. How many more letters did she bring to the houses on Elm Street? _____________________________________________________ 33. Samuel promised he would attempt to clean his room later this week. His mother’s scowl was a clue that he should get busy! He decided he would work for thirty-eight minutes each day until it was finished. It took him five days to get his room cleaned! How much time did he spend cleaning? _____________________________________________________ 34. A groundhog is a true hibernator. When it hibernates, its heart rate can drop from seventy-four beats per minute to five beats per minute. In three hours, how many fewer heartbeats will a hibernating groundhog have than a groundhog not hibernating? _____________________________________________________ 35. The pet shelter had a “dog wash” to raise money to take care of the animals at the shelter. They charged $4 per dog. If they made $204, how many dogs did they wash? _____________________________________________________ 36. Hailey and Justin are planning a garden. Hailey said if they make the garden round it will look better. Justin said if they make the garden square they will be able to plant more. They have enough space to make a round garden with a diameter of nineteen feet or a square garden with each side being nineteen feet. If they put five plants in each square foot of ground, how many more plants will they be able to plant in the square garden than they could plant in the round garden? _____________________________________________________ 37. Kayla began to take sign language classes so she could become an interpreter for the deaf people in her community. On her first seven assignments, her scores were: 80, 98, 89, 90, 97, 84, and 95. What was her average grade for these assignments; round your answer to the nearest whole point? _____________________________________________________
STUDENT MANUAL
GRADE 6 MATH LESSON 4-9
38. When Mrs. Garcia told her class about National Play-Dough Day, she was surprised to find out that some of her students had never heard of play-dough. There are twenty-four students in her class and a third of them owned cans of play-dough, three of them didn’t have any play- dough, but knew what it was, and the rest hadn’t even heard of playdough. How many of Mrs. Thomas’ students had never heard of play-dough? _____________________________________________________ 39. Steven made a basket of fire starters for his father. He made them by dipping pinecones in wax. The wax was different colors. When he finished he put them in a pretty basket with a big red bow on it. He made twelve fire starters. A third of them were red and the rest of them were green. How many were green? _____________________________________________________ 40. Stephanie wanted to make a chart illustrating the effects of static electricity. She used a sheet of poster board that was 30 inches wide and 48 inches long. She divided the poster board into six equal sections. What was the area of each section? _____________________________________________________
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STUDENT MANUAL
GRADE 6 MATH LESSON 5-1
Lesson 5
Algebraic Expressions
In today’s Lesson, you are going to learn about Algebraic Expressions. You will need to be familiar with the following phrases and terms in order to understand this Lesson: Numerical Expression: A mathematical phrase that includes only numbers and operation symbols. Variable: A letter or a symbol used to represent one or more numbers. Algebraic Expression: An expression that contains at least one variable. Evaluate: To find the value of a numerical expression. Consider this example of a Numerical Expression: In a football game, a team scored 21 points in the first half and 14 points in the second half. To represent the total points the team scored, you can use a Numerical Expression: Total points scored = 21 + 14 Give some examples of other Numerical Expressions. If you did not know how many points the football team scored in the second half, you could use a variable to represent the points. You can use any letter of the alphabet as a variable, although it is common to use a letter, which corresponds to the piece of information it will represent. For example, to represent the total points scored in the second half of the football game it makes sense to use P. The Algebraic Expression that would represent the total points scored in the game would be 21 + P.
STUDENT MANUAL
GRADE 6 MATH LESSON 5-2
When writing an expression, it is helpful to understand all of the various words and phrases that indicate addition, subtraction, multiplication, and division: Addition Sum Increase More than Plus Greater than
Subtraction Difference Decrease Less than Minus Fewer than
Multiplication Product Factors Twice Times Multiplied by
Division Quotient Equally divided Divided by
There are many different ways to represent multiplication in an expression. For example, 7 x B could be written in the following ways: 7B, 7(B), B x 7, or 7∙ B. Practice with these additional examples of expressions: Write a numerical expression for each word expression: $9.00 less than $12.00 Q divided by S Three times a distance, D
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The number of slices of 2 dozen apples, each of which has 5 slices ______________________________________ Evaluate each expression below: X + 125 for X = 12
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G / 10 for G = 140
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5R – 6 for R = 3
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A – 2B for A = 8 and B = 4
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Lesson Wrap-Up: In your Math Journal, write three expressions in words. If you have a partner trade journals and ask your partner to rewrite the expressions algebraically. If you do not have a partner, re-write your expressions algebraically in your Journal.
STUDENT MANUAL
GRADE 6 MATH LESSON 5-3
Worksheet 5 Directions: Re-write each of the following as an algebraic expression. 1. a number s minus 20
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2. 18 divided by a number j
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3. subtract a number v from 48
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4. product of a number k and 46
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5. a number q plus 34
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6. a number n decreased by 13
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7. quotient of 12 by a number r
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8. 37 less a number t
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9. a number p increased by 31 10. add 5 to a number a
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11. take away a number d from 36
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12. 32 multiplied by a number b
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13. 2 more than a number m
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14. 17 divided into a number x
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15. a number u less than 30
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16. difference of a number y and 49 17. sum of 15 and a number z 18. a number c times 33
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19. take away 8 from a number f
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20. 14 less than a number w
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STUDENT MANUAL
GRADE 6 MATH LESSON 5-4
Directions: Evaluate each expression for the given variables. 21. (19 - r) + r = _________ for r = 10 22. 11j = _________ for j = 32 23. 5a + 4a = _________ for a = 8 24. 10 + c =_________ for c = 59 25. 32s ÷ 4 = _________ for s = 36 26. 9d + 4 = _________ for d = 5 27. x/3 = _________
Print Form
for x = 21 28. 4y + 17 = _________ for y = 33 29. r + 8r + 3 = _________ for r = 6 30. 3z – z = _________ for z = 10 31. 3q – 88 = _________ for q = 69 32. 5h + 18 = _________ for h = 56
