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.

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• 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 23Big Idea 1: Building with and Talking about Shapes 31Visualize: Build(ings) 33Play: Tangram Puzzles 40Investigate: Tangram Squares 52Big Idea 2: Tens and Ones Are Useful Ways to Organize 59Visualize: Organizing and Counting a Collection 61Play: How Many Dots? 68Investigate: Boxes of Pencils 74Big Idea 3: Representing and Modeling Joining and Separating Situations 81Visualize: Showing the Story 83Play: Playing with Problem Types 89Investigate: Library Wonders 99Big Idea 4: Using Data to Describe and Wonder about Our World 107Visualize: Organizing the Natural World 109Play: Displaying Data 115Investigate: Our Trash, Ourselves 124Big Idea 5: Equal Means the Same 133Visualize: Hungry, Hungry Monsters! 136Play: True or False? 155Investigate: Exploring Relations 165Big Idea 6: Building with Numbers within 20 175Visualize: Seeing Spots 177Play: Rolling Ten 186Investigate: Addition Table Patterns 195Big Idea 7: Finding Patterns in Numbers 203Visualize: Patterns in the Hundred Chart 205Play: Skipping across the Hundred Chart 213Investigate: Weaving Patterns 220Big Idea 8: Using Place Value to Add and Subtract 231Visualize: Recess! 233Play: Playing with Place Value across Problem Types 243Investigate: Making a Dollar 251Big Idea 9: Using Units to Measure Our World 259Visualize: Which One is Longer? 261Play: Measuring Our World in Cubes 267Investigate: Measuring with Cuisenaire Rods 275Big Idea 10: Partitioning Shapes into Equal Parts 281Visualize: Half and Half-of-a-Half 283Play: Analyzing Tangrams 293Investigate: What’s in a Flag? 299Appendix 3131" Grid Paper 314Hundred Chart 315Grid Paper 316About the Authors 317Acknowledgments 319Index 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.

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• 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 23Big Idea 1: Building with and Talking about Shapes 31Visualize: Build(ings) 33Play: Tangram Puzzles 40Investigate: Tangram Squares 52Big Idea 2: Tens and Ones Are Useful Ways to Organize 59Visualize: Organizing and Counting a Collection 61Play: How Many Dots? 68Investigate: Boxes of Pencils 74Big Idea 3: Representing and Modeling Joining and Separating Situations 81Visualize: Showing the Story 83Play: Playing with Problem Types 89Investigate: Library Wonders 99Big Idea 4: Using Data to Describe and Wonder about Our World 107Visualize: Organizing the Natural World 109Play: Displaying Data 115Investigate: Our Trash, Ourselves 124Big Idea 5: Equal Means the Same 133Visualize: Hungry, Hungry Monsters! 136Play: True or False? 155Investigate: Exploring Relations 165Big Idea 6: Building with Numbers within 20 175Visualize: Seeing Spots 177Play: Rolling Ten 186Investigate: Addition Table Patterns 195Big Idea 7: Finding Patterns in Numbers 203Visualize: Patterns in the Hundred Chart 205Play: Skipping across the Hundred Chart 213Investigate: Weaving Patterns 220Big Idea 8: Using Place Value to Add and Subtract 231Visualize: Recess! 233Play: Playing with Place Value across Problem Types 243Investigate: Making a Dollar 251Big Idea 9: Using Units to Measure Our World 259Visualize: Which One is Longer? 261Play: Measuring Our World in Cubes 267Investigate: Measuring with Cuisenaire Rods 275Big Idea 10: Partitioning Shapes into Equal Parts 281Visualize: Half and Half-of-a-Half 283Play: Analyzing Tangrams 293Investigate: What’s in a Flag? 299Appendix 3131" Grid Paper 314Hundred Chart 315Grid Paper 316About the Authors 317Acknowledgments 319Index 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.

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• 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 23Big Idea 1: Building with and Talking about Shapes 31Visualize: Build(ings) 33Play: Tangram Puzzles 40Investigate: Tangram Squares 52Big Idea 2: Tens and Ones Are Useful Ways to Organize 59Visualize: Organizing and Counting a Collection 61Play: How Many Dots? 68Investigate: Boxes of Pencils 74Big Idea 3: Representing and Modeling Joining and Separating Situations 81Visualize: Showing the Story 83Play: Playing with Problem Types 89Investigate: Library Wonders 99Big Idea 4: Using Data to Describe and Wonder about Our World 107Visualize: Organizing the Natural World 109Play: Displaying Data 115Investigate: Our Trash, Ourselves 124Big Idea 5: Equal Means the Same 133Visualize: Hungry, Hungry Monsters! 136Play: True or False? 155Investigate: Exploring Relations 165Big Idea 6: Building with Numbers within 20 175Visualize: Seeing Spots 177Play: Rolling Ten 186Investigate: Addition Table Patterns 195Big Idea 7: Finding Patterns in Numbers 203Visualize: Patterns in the Hundred Chart 205Play: Skipping across the Hundred Chart 213Investigate: Weaving Patterns 220Big Idea 8: Using Place Value to Add and Subtract 231Visualize: Recess! 233Play: Playing with Place Value across Problem Types 243Investigate: Making a Dollar 251Big Idea 9: Using Units to Measure Our World 259Visualize: Which One is Longer? 261Play: Measuring Our World in Cubes 267Investigate: Measuring with Cuisenaire Rods 275Big Idea 10: Partitioning Shapes into Equal Parts 281Visualize: Half and Half-of-a-Half 283Play: Analyzing Tangrams 293Investigate: What’s in a Flag? 299Appendix 3131" Grid Paper 314Hundred Chart 315Grid Paper 316About the Authors 317Acknowledgments 319Index 321