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 teacher education and mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction and coaching. 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 21Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22Big Idea 1: Connecting 2D and 3D Worlds 27Visualize: Seeing Slices 29Play: Playing with Clay 34Investigate: The Area of Slices 40Big Idea 2: Constructing Figures to Scale 47Visualize: What is Scale? 50Play: A Fishy Image 55Investigate: Magnifying Solids 61Big Idea 3: Seeing Proportional Relationships 69Visualize: Growing Dough 72Play: is It Proportional? 80Investigate: Sizing Up Proportions 86Big Idea 4: Understanding Percents in the World 93Visualize: Painting Percents 95Play: Building Benchmarks 103Investigate: What’s It Going to Cost? 109Big Idea 5: Building Intuition about Probability 119Visualize: is It Fair? 121Play: Fair Sums? 131Investigate: What’s in the Bag? 136Big Idea 6: Modeling Probabilities 145Visualize: What’s the Chance of That? 147Play: Probability Carnival 155Investigate: Go, Go Galton Board! 163Big Idea 7: Sampling to Understand Populations 171Visualize: Sampling Dots and Beads 173Play: Catch and Release 180Investigate: Wildlife Populations 186Big Idea 8: Operating with Opposites 197Visualize: Line Dancing 199Play: Integer Tic-Tac-Toe 207Investigate: Coordinating Multiplication 216Big Idea 9: Using Algebra as a Problem-Solving Tool 225Visualize: Case by Case 228Play: (Non) Linear Pattern Puzzles 237Investigate: Linear Letters 245Big Idea 10: Exploring Circles 251Visualize: Building Hunches about Circumference 253Play: Dissecting Circle Area 260Investigate: Unraveling Circles 267Appendix 273Centimeter Grid Paper 2741" Grid Paper 275Snap Cube Grid Paper 276Isometric Dot Paper 277Dot Paper 278About the Authors 279Acknowledgments 281Index 283

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 teacher education and mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction and coaching. 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 21Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22Big Idea 1: Connecting 2D and 3D Worlds 27Visualize: Seeing Slices 29Play: Playing with Clay 34Investigate: The Area of Slices 40Big Idea 2: Constructing Figures to Scale 47Visualize: What is Scale? 50Play: A Fishy Image 55Investigate: Magnifying Solids 61Big Idea 3: Seeing Proportional Relationships 69Visualize: Growing Dough 72Play: is It Proportional? 80Investigate: Sizing Up Proportions 86Big Idea 4: Understanding Percents in the World 93Visualize: Painting Percents 95Play: Building Benchmarks 103Investigate: What’s It Going to Cost? 109Big Idea 5: Building Intuition about Probability 119Visualize: is It Fair? 121Play: Fair Sums? 131Investigate: What’s in the Bag? 136Big Idea 6: Modeling Probabilities 145Visualize: What’s the Chance of That? 147Play: Probability Carnival 155Investigate: Go, Go Galton Board! 163Big Idea 7: Sampling to Understand Populations 171Visualize: Sampling Dots and Beads 173Play: Catch and Release 180Investigate: Wildlife Populations 186Big Idea 8: Operating with Opposites 197Visualize: Line Dancing 199Play: Integer Tic-Tac-Toe 207Investigate: Coordinating Multiplication 216Big Idea 9: Using Algebra as a Problem-Solving Tool 225Visualize: Case by Case 228Play: (Non) Linear Pattern Puzzles 237Investigate: Linear Letters 245Big Idea 10: Exploring Circles 251Visualize: Building Hunches about Circumference 253Play: Dissecting Circle Area 260Investigate: Unraveling Circles 267Appendix 273Centimeter Grid Paper 2741" Grid Paper 275Snap Cube Grid Paper 276Isometric Dot Paper 277Dot Paper 278About the Authors 279Acknowledgments 281Index 283