Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 2

Engage students in mathematics using growth mindset techniques

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low-floor, high-ceiling tasks that will help you do just that, by looking at the big ideas in second grade through visualization, play, and investigation.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same messagethat they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So, the authors designedMindset Mathematics around the principle of active student inquiry, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to support student learning, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks inMindset Mathematics reflect the lessons from brain science that:

• There is no such thing as a math person and anyone can learn mathematics to high levels.
• Mistakes, struggle, and challenge are opportunities for brain growth.
• Speed is unimportant, and even counterproductive, in mathematics.
• Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.

With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics,Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

JO BOALER is a professor of mathematics education at Stanford University and co-founder and faculty director of youcubed. She serves as an advisor to several Silicon Valley companies and is a White House presenter on girls and STEM (Science, Technology, Engineering, and Math). The author of seven books, includingMathematical Mindsets, and numerous research articles, she is a regular contributor to news and radio in the United States and England.

JEN MUNSONis an assistant professorof learning sciences at Northwestern University, a professional developer, and a former classroom teacher. She received her PhD in mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction.

CATHY WILLIAMS is the co-founder and the executive director of youcubed at Stanford University. Before working at youcubed, she was a high school math teacher and worked in mathematics curriculum and administration at the county and district levels in California.

Introduction 1

Low-Floor, High-Ceiling Tasks 2

Youcubed Summer Camp 3

Memorization versus Conceptual Engagement 4

Mathematical Thinking, Reasoning, and Convincing 5

Big Ideas 9

Structure of the Book 9

Note on Materials 17

Manipulatives and Materials Used in This Book 18

Activities for Building Norms 21

Encouraging Good Group Work 21

How Many Do You See? Learning to Reason, Convince, and Pose Questions 23

Big Idea 1: Partitioning Shapes into Equal Parts 31

Visualize: Equal or Same? 33

Play: Four Fourths 39

Investigate: Rows and Columns 44

Big Idea 2: Making and Using Equal Groups 53

Visualize: The Groups Inside 55

Play: Skipping down the Hall 61

Investigate: Array Museum 67

Big Idea 3: What Is 100? 73

Visualize: The Many Ways to See 100 75

Play: Scoop and Count 82

Investigate: Making a Dollar, Revisited 86

Big Idea 4: Composing and Decomposing Numbers 91

Visualize: Array Talks 93

Play: Which Is More? 103

Investigate: Coin Grab 114

Big Idea 5: Using Patterns in Place Value 119

Visualize: Whats in Your 12? 121

Play: Reach for It! 126

Investigate: Window Mysteries 136

Big Idea 6: Thinking on the Number Line 145

Visualize: Long Lives 148

Play: Life- Span Puzzles 157

Investigate: Living on the Number Line 166

Big Idea 7: Rulers and Clocks Are Number Lines 173

Visualize: Noticing the Ruler and Clock 175

Play: Walking the Clock 181

Investigate: A Sea of Sharks 187

Big Idea 8: Using Units to Estimate 205

Visualize: Foot by Foot 207

Play: Length Scavenger Hunt 216

Investigate: School- Day Walkabout 222

Big Idea 9: Using Data to Visualize and Wonder about Our World 229

Visualize: Fruit around the World 231

Play: Eat Your Roots 238

Investigate: Dear Data 243

Appendix 253

Grid Paper 254

About the Authors 255

Acknowledgments 257

Index 259