Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 2

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, including Mathematical Mindsets, and numerous research articles, she is a regular contributor to news and radio in the United States and England.JEN MUNSON is an assistant professor of 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 1Low-Floor, High-Ceiling Tasks 2Youcubed Summer Camp 3Memorization versus Conceptual Engagement 4Mathematical Thinking, Reasoning, and Convincing 5Big Ideas 9Structure of the Book 9Note on Materials 17Manipulatives and Materials Used in This Book 18Activities for Building Norms 21Encouraging Good Group Work 21How Many Do You See? Learning to Reason, Convince, and Pose Questions 23◼ Big Idea 1: Partitioning Shapes into Equal Parts 31Visualize: Equal or Same? 33Play: Four Fourths 39Investigate: Rows and Columns 44◼ Big Idea 2: Making and Using Equal Groups 53Visualize: The Groups Inside 55Play: Skipping down the Hall 61Investigate: Array Museum 67◼ Big Idea 3: What Is 100? 73Visualize: The Many Ways to See 100 75Play: Scoop and Count 82Investigate: Making a Dollar, Revisited 86◼ Big Idea 4: Composing and Decomposing Numbers 91Visualize: Array Talks 93Play: Which Is More? 103Investigate: Coin Grab 114◼ Big Idea 5: Using Patterns in Place Value 119Visualize: What’s in Your 12? 121Play: Reach for It! 126Investigate: Window Mysteries 136◼ Big Idea 6: Thinking on the Number Line 145Visualize: Long Lives 148Play: Life- Span Puzzles 157Investigate: Living on the Number Line 166◼ Big Idea 7: Rulers and Clocks Are Number Lines 173Visualize: Noticing the Ruler and Clock 175Play: Walking the Clock 181Investigate: A Sea of Sharks 187◼ Big Idea 8: Using Units to Estimate 205Visualize: Foot by Foot 207Play: Length Scavenger Hunt 216Investigate: School- Day Walkabout 222◼ Big Idea 9: Using Data to Visualize and Wonder about Our World 229Visualize: Fruit around the World 231Play: Eat Your Roots 238Investigate: Dear Data 243Appendix 253Grid Paper 254About the Authors 255Acknowledgments 257Index 259