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: Building with and Talking about Shapes 31 Visualize: Build(ings) 33 Play: Tangram Puzzles 40 Investigate: Tangram Squares 52 Big Idea 2: Tens and Ones Are Useful Ways to Organize 59 Visualize: Organizing and Counting a Collection 61 Play: How Many Dots? 68 Investigate: Boxes of Pencils 74 Big Idea 3: Representing and Modeling Joining and Separating Situations 81 Visualize: Showing the Story 83 Play: Playing with Problem Types 89 Investigate: Library Wonders 99 Big Idea 4: Using Data to Describe and Wonder about Our World 107 Visualize: Organizing the Natural World 109 Play: Displaying Data 115 Investigate: Our Trash, Ourselves 124 Big Idea 5: Equal Means the Same 133 Visualize: Hungry, Hungry Monsters! 136 Play: True or False? 155 Investigate: Exploring Relations 165 Big Idea 6: Building with Numbers within 20 175 Visualize: Seeing Spots 177 Play: Rolling Ten 186 Investigate: Addition Table Patterns 195 Big Idea 7: Finding Patterns in Numbers 203 Visualize: Patterns in the Hundred Chart 205 Play: Skipping across the Hundred Chart 213 Investigate: Weaving Patterns 220 Big Idea 8: Using Place Value to Add and Subtract 231 Visualize: Recess! 233 Play: Playing with Place Value across Problem Types 243 Investigate: Making a Dollar 251 Big Idea 9: Using Units to Measure Our World 259 Visualize: Which One is Longer? 261 Play: Measuring Our World in Cubes 267 Investigate: Measuring with Cuisenaire Rods 275 Big Idea 10: Partitioning Shapes into Equal Parts 281 Visualize: Half and Half-of-a-Half 283 Play: Analyzing Tangrams 293 Investigate: What's in a Flag? 299 Appendix 313 1" Grid Paper 314 Hundred Chart 315 Grid Paper 316 About the Authors 317 Acknowledgments 319 Index 321
JO BOALER is the Nominelli-Olivier professor at Stanford. Former roles have included being a maths teacher in London schools. She is author of 18 books, numerous articles and a White House presenter on women and girls. She co-founded www.youcubed.org, is a regular contributor to news and radio in the US and was named as one of the 8 educators "changing the face of education" by the BBC. JEN MUNSON is an assistant professor of learning sciences at Northwestern University, a profession- al 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.