Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

Beyond Invert & Multiply builds on the foundational understandings that are described in Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Second Edition, and applies them to situations involving fraction computation. You’ll find:
Classroom Scenarios that address common challenges students (and teachers!) encounter as they learn to operate with fractions;
What’s the Math? sections intended to clarify the mathematics;
What’s the Research? insights that show why “that’s the way we’ve always done things” might not be the most successful approach;
Classroom Activities with friendly, step-by-step instructions and video clips demonstrating how to teach the concepts;
Reproducibles that are also available in a downloadable, printable format at www.mathsolutions.com/beyondinvertandmultiplyreproducibles;
Study Questions at the end of each chapter that encourage readers to set concrete goals for implementing what they’ve read; and
Connections to the Common Core for those states implementing the Common Core State Standards for Mathematics.
 
This resource features more than 30 online video clips filmed in actual classrooms. Clips range from 1 minute to 6 minutes in length with a total viewing time of approximately 70 minutes.
 
1121066177
Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

Beyond Invert & Multiply builds on the foundational understandings that are described in Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Second Edition, and applies them to situations involving fraction computation. You’ll find:
Classroom Scenarios that address common challenges students (and teachers!) encounter as they learn to operate with fractions;
What’s the Math? sections intended to clarify the mathematics;
What’s the Research? insights that show why “that’s the way we’ve always done things” might not be the most successful approach;
Classroom Activities with friendly, step-by-step instructions and video clips demonstrating how to teach the concepts;
Reproducibles that are also available in a downloadable, printable format at www.mathsolutions.com/beyondinvertandmultiplyreproducibles;
Study Questions at the end of each chapter that encourage readers to set concrete goals for implementing what they’ve read; and
Connections to the Common Core for those states implementing the Common Core State Standards for Mathematics.
 
This resource features more than 30 online video clips filmed in actual classrooms. Clips range from 1 minute to 6 minutes in length with a total viewing time of approximately 70 minutes.
 
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Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

by Julie McNamara
Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

Beyond Invert and Multiply, Grades 3-6: Making Sense of Fraction Computation

by Julie McNamara

(First Edition, None)

$61.95 
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Overview


Beyond Invert & Multiply builds on the foundational understandings that are described in Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Second Edition, and applies them to situations involving fraction computation. You’ll find:
Classroom Scenarios that address common challenges students (and teachers!) encounter as they learn to operate with fractions;
What’s the Math? sections intended to clarify the mathematics;
What’s the Research? insights that show why “that’s the way we’ve always done things” might not be the most successful approach;
Classroom Activities with friendly, step-by-step instructions and video clips demonstrating how to teach the concepts;
Reproducibles that are also available in a downloadable, printable format at www.mathsolutions.com/beyondinvertandmultiplyreproducibles;
Study Questions at the end of each chapter that encourage readers to set concrete goals for implementing what they’ve read; and
Connections to the Common Core for those states implementing the Common Core State Standards for Mathematics.
 
This resource features more than 30 online video clips filmed in actual classrooms. Clips range from 1 minute to 6 minutes in length with a total viewing time of approximately 70 minutes.
 

Product Details

ISBN-13: 9781935099574
Publisher: Houghton Mifflin Harcourt
Publication date: 01/05/2015
Edition description: First Edition, None
Pages: 240
Sales rank: 200,567
Product dimensions: 7.30(w) x 9.10(h) x 0.60(d)
Age Range: 4 - 18 Years

About the Author



Julie McNamara is an Assistant Professor of Mathematics Education at California State University, East Bay, in Hayward, California. She also provides professional development and classroom coaching to teachers in the San Francisco Bay Area. Before receiving a PhD in mathematics education from the University of California, Berkeley, she was a classroom teacher in local public schools. Julie is also the coauthor (with Meghan M. Shaughnessy) of Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Grades 3–5, Second Edition (Math Solutions, 2015).
 

Table of Contents

Foreword Deborah Loewenberg Ball xvii

How to Use This Resource xix

The Common Core State Standards

A Letter from Math Coach Lori MacDonald xxiii

Summary of Connections with the Common Core State Standards xxv

Video Clips by Chapter xxix

Video Clips by Grade, Including Demographics xxxi

Part I What Is a Fraction? 1

Chapter 1 Making Sense: Fractions as Numbers 3

Classroom Scenario 4

What's the Math? 7

What's the Research? 9

Classroom Activities 11

Video Clip 1a Placing ½ on the Number Line 16

Video Clip 1b Using Cuisenaire Rods to Place $$$ on the Number Line 17

Video Clip 1c Using Cuisenaire Rods to Place $$$ on the Number Line 18

Video Clip 1d Deciding Where to Place $$$ on the Number Line 19

Wrapping It Up 24

Part II Addition and Subtraction with Fractions 25

Chapter 2 Developing Awareness: Addition and Subtraction Problem Types 27

What's the Context? 28

What's the Research? 30

Wrapping It Up 35

Chapter 3 Making Sense: Addition with Fractions 37

Classroom Scenario 38

What's the Math? 40

What's the Research? 42

Classroom Activities 43

Video Clip 3a Reviewing the "Make a 10" Strategy 51

Video Clip 3b Introducing "Get to the Whole" 52

Video Clip 3c ¾ + ¾: Will's Strategy 53

Video Clip 3d ¾ + ¾: Belen's Strategy 53

Video Clip 3e $$$ + $$$: Malaya's Strategy 54

Video Clip 3f $$$ + $$$: Yuli's Use of Academic Language 54

Wrapping It Up 60

Chapter 4 Making Sense: Subtraction with Fractions 61

Classroom Scenario 62

What's the Math? 64

What's the Research? 65

Classroom Activities 67

Wrapping It Up 76

Part III Multiplication and Division with Fractions 77

Chapter 5 Developing Awareness: Multiplication and Division Problem Types 79

What's the Context? 80

What's the Research? 81

Wrapping It Up 85

Chapter 6 Making Sense: Multiplication with Fractions 87

Classroom Scenario 88

What's the Math? 90

What's the Research? 95

Classroom Activities 96

Video Clip 6a Introducing Activity 6.1: Multiplication Patterns 96

Video Clip 6b Noticing Patterns in Factors and Products 97

Video Clip 6c Moving from Additive to Multiplicative Language 97

Video Clip 6d What Number Is ½ of 1? 98

Video Clip 6e Multiplication as Repeated Addition 99

Video Clip 6f What Do We Know About 6 × 2½? 104

Video Clip 6g "6 × 2½ Has to Be Greater Than 2½" 104

Video Clip 6h Applying the Distributive Property to Reason About the Product of 6 × 2½ 105

Video Clip 6i 4½ Is More Than 4 But Less Than 5 105

Wrapping It Up 114

Chapter 7 Making Sense: Division with Fractions 115

Classroom Scenario 116

What's the Math? 119

What's the Research? 124

Classroom Activities 126

Video Clip 7a Introducing Activity 7.2: How Long? How Far? 128

Video Clip 7b Comparing the Two Jogging Experiences 128

Video Clip 7c How Many ¼s Are in 1? 130

Video Clip 7d How Many ¼s Are in 2? 131

Video Clip 7e How Many $$$s Are in 2? 131

Wrapping It Up 138

Part IV Discourse with Fractions 139

Chapter 8 Developing Awareness: Six Strategies for Fostering Student Talk About Fractions 141

Conference Scenario 142

Strategy 1 Using Strategic Tasks 143

Video Clip 8a Multiplication Patterns 143

Strategy 2 Creating Records of Thinking 144

Video Clip 8b Muhammad's Strategy for Adding $$$ and $$$ 144

Strategy 3 Building Visual Models 145

Video Clip 8c Using the Cuisenaire Rods to Explain Equivalent Fractions 145

Strategy 4 Reasoning with Benchmarks and the Number Line 146

Video Clip 8d What Do You Notice About the Numerators and Denominators of Fractions Equal to ½? 146

Strategy 5 Using Talk Moves 147

Video Clip 8e Ms. Lee Revoices Ashley's Justification 147

Video Clip 8f Julian Restates Carlos's Answer 148

Video Clip 8g Multiple Students Share Their Reasoning About Placing ½ on the Number Line 149

Video Clip 8h "Tell Us More About That" 150

Video Clip 8i Posing a "Thinking Question" 151

Strategy 6 Asking Students to Turn and Talk 152

Video Clips 6d, 6f, 7d, and 7e Teachers' Use of Turn and Talk 152

Wrapping It Up 153

Acknowledgments 155

Reproducibles 157

Appendix: Author's Video Reflections 185

References 199

Index 203

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