Brief Contents - Math Solutionsstore.mathsolutions.com/pub/media/documents/doc/978-1-935099-05-5...Chapter 4: Introducing the Graphing Calculator 19 ... Mental Math Start-up: More

Acknowledgments xvIntroduction xviiConnections to NCTM’s Principles and Standards for School Mathematics xxi

Section I: Teaching Active Algebra 1

Chapter 1: Mathematics Classroom Logistics 3

Chapter 2: Teaching Mental Math 11

Chapter 3: Teaching Using Student Presentations 15

Chapter 4: Introducing the Graphing Calculator 19

Chapter 5: Understanding Slope and Rate of Change 21

Chapter 6: Brain Research and Teaching Mathematics 25

Chapter 7: Mathematics Classroom Management and Discipline 29

Section II: Linear Relations Lessons and Assessments 41

Lesson 1 43

Lesson 2 49

Lesson 3 55

Assessment: Quiz A 63

Lesson 4 67

Lesson 5 73

Lesson 6 79

Lesson 7 87

Assessment: Quiz B 95

Lesson 8 99

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Brief Contents

Frontmatter.indd viiFrontmatter.indd vii 7/7/09 1:57:17 AM7/7/09 1:57:17 AM

Active Algebra: Strategies and Lessons for Successfully Teaching Linear Relationships, Grades 7–10 © 2009 Math Solutions

Lesson 9 105

Lesson 10 109

Section III: Answers and Teaching Insights 117

Lesson 1: Answers and Teaching Insights 119



Assessment: Quiz A Answers 133





Assessment: Quiz B Answers 151




References 163

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i x

Acknowledgments xvIntroduction xvii

Active Learning xviiOverview xviiiActive Algebra Prerequisite Knowledge xviiiActive Algebra: The Teacher’s Role xviiiActive Algebra: The Students’ Role xixAbout the “From the Classroom” Vignettes xixFrom the Classroom: Adolescent Logic xx

Connections to NCTM’s Principles and Standards for School Mathematics xxi

Section I: Teaching Active Algebra 1

Chapter 1: Mathematics Classroom Logistics 3Reproducible A: Seating Chart Grid 1 7Reproducible B: Seating Chart Grid 2 8Reproducible C: Seating Chart Grid 3 9

Chapter 2: Teaching Mental Math 11Teaching Mental Math: Three Steps 12Teaching Mental Math: Variations 13Mental Math Problems: At-a-Glance 13Mental Math: Common Questions and Answers 14

Chapter 3: Teaching Using Student Presentations 15Teaching Using Student Presentations: Five Steps 15From the Classroom: Playing It Fair When Assigning Problems for Presentations 17From the Classroom: Not Fair! Some Groups Work on Presentations While Others Present 18

Chapter 4: Introducing the Graphing Calculator 19Reproducible D: Graphing Calculator Basics 20

Chapter 5: Understanding Slope and Rate of Change 21Slope in the Real World 21Slope in the Mathematical World 22

Chapter 6: Brain Research and Teaching Mathematics 25From the Classroom: The Working Student Brain 27

Chapter 7: Mathematics Classroom Management and Discipline 29Student Dilemmas: A Case-by-Case Reflection 29From the Classroom: Student Dilemmas and Actions 33

Contents

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Classroom Management Forms 35Reproducible E: Classroom Expectations 37Reproducible F: Behavior Self-Evaluation 38Reproducible G: Letter to Parents/Guardians 39

Section II: Linear Relations Lessons and Assessments 41

Lesson 1 43working with y = mx + b • positive rates of changeOverview 43Mental Math Start-up: Figuring 5 Percent, 10 Percent, or 15 Percent of a Number 44Core Problems 45Additional Problems 47

Lesson 2 49more y = mx + b • negative rates of change • using y = mx + b with real data Overview 49Mental Math Start-up: Solving One-Step Equations 50Core Problems 51Additional Problems 53

Lesson 3 55y = mx + b when rate of change is a speedOverview 55Mental Math Start-up: Estimating Sale Prices 56Core Problems 57Additional Problems 59

Assessment: Quiz A 63Mental Math 64Assessing Lessons 1–3 65

Lesson 4 67finding where two lines intersect Overview 67Mental Math Start-up: Figuring Distance, Rate, and Time 68Core Problems 69Additional Problems 71



Cont ent s x i

Lesson 5 73measuring slopes with ratios • slopes of linear graphs Overview 73Mental Math Start-up: Practicing Percents and One-Step Equations, Estimating Sale Prices, and Figuring Distance, Rate, and Time 74Core Problems 75Additional Problems 78

Lesson 6 79slope in the real worldOverview 79Mental Math Start-up: More Practice with Percents and One-Step Equations, Estimating Sale Prices, and Figuring Distance, Rate, and Time 80Core Problems 81End-of-Unit Project: An Introduction to Your Linear Equation Poster 82Additional Problems 85

Lesson 7 87connecting slope ratio and rate of change • linearity in general Overview 87Mental Math Start-up: More Practice with Percents and One-Step Equations, Estimating Sale Prices, and Figuring Distance, Rate, and Time 88A Note About Slope, Rate of Change, and Linearity 89Core Problems 90End-of-Unit Project: Linear Equation Poster Preparation 92Additional Problems 93

Assessment: Quiz B 95Mental Math 96Assessing Lessons 4–7 97

Lesson 8 99review problems Overview 99Mental Math Start-up: More Practice with Percents and One-Step Equations, Estimating Sale Prices, and Figuring Distance, Rate, and Time 100Core Problems 101End-of-Unit Project: Linear Equation Poster Preparation and Feedback 102Additional Problems 103



Lesson 9 105connecting multiple representations of linear relations: table, graph, equation, and situationOverview 105Mental Math Start-up: More Practice with Percents and One-Step Equations, Estimating Sale Prices, and Figuring Distance, Rate, and Time 106End-of-Unit Project: Linear Equation Poster Completion 107One-Page Unit Summary 107

Lesson 10 109Overview 109End-of-Unit Project: Linear Equation Poster Sharing and Linear Equation Poster Evaluation 110Unit Assessment: Mental Math 112Unit Assessment: Assessing Lessons 1–9 113

Section III: Answers and Teaching Insights 117

Lesson 1: Answers and Teaching Insights 119Mental Math Start-up 119From the Classroom: Mental Math 119Core Problems 120Additional Problems 121

Lesson 2: Answers and Teaching Insights 123Mental Math Start-up 123From the Classroom: Mental Math 123Core Problems 124Additional Problems 126From the Classroom: Scatter Plots 126

Lesson 3: Answers and Teaching Insights 129Mental Math Start-up 129From the Classroom: Mental Math 129Core Problems 130From the Classroom: Constant Rate of Change 131Additional Problems 132

Assessment: Quiz A Answers 133Assessing Lessons 1–3 133



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Lesson 4: Answers and Teaching Insights 135Mental Math Start-up 135From the Classroom: Using Graphing Calculators 135Core Problems 136Additional Problems 137

Lesson 5: Answers and Teaching Insights 139Mental Math Start-up 139From the Classroom: Mental Math 139Core Problems 140From the Classroom: Using Graphing Calculators 141Additional Problems 142

Lesson 6: Answers and Teaching Insights 143Mental Math Start-up 143From the Classroom: Mental Math 143Core Problems 144End-of-Unit Project 145Additional Problems 146

Lesson 7: Answers and Teaching Insights 147Mental Math Start-up 147Core Problems 148End-of-Unit Project 149From the Classroom: Choosing Partners 149Additional Problems 150

Assessment: Quiz B Answers 151Assessing Lessons 4–7 151

Lesson 8: Answers and Teaching Insights 153Mental Math Start-up 153Core Problems 154End-of-Unit Project 155From the Classroom: A Reminder About the Test 155Additional Problems 156

Lesson 9: Answers and Teaching Insights 157Mental Math Start-up 157End-of-Unit Project 158From the Classroom: The Linear Equation Poster 158One-Page Unit Summary 158



Lesson 10: Answers and Teaching Insights 159End-of-Unit Project 159From the Classroom: Poster Presentations 160 Unit Assessment 161

References 163



Documents

Brief Contents - Math Solutionsstore.mathsolutions.com/pub/media/documents/doc/978-1-935099-05-5...Chapter 4: Introducing the Graphing Calculator 19 ... Mental Math Start-up: More