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 at the third-grade level 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 engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, 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:

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 MUNSON is a postdoctoral fellow 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 10

Activities for Building Norms 17

Encouraging Good Group Work 17

Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21

Big Idea 1: Solving Problems with Data 23

Visualize: Tongues, Tails, and in Between 25

Play: Inspector Graph-It 36

Investigate: Data Tells Us about Ourselves 41

Big Idea 2: Thinking around Shapes 51

Visualize: Get Your Arms around It 53

Play: 36-Unit Walk 59

Investigate: Shapes on a Plane 65

Big Idea 3: Thinking in Equal Groups 75

Visualize: Sharing Crackers 78

Play: Dozens of Dice 85

Investigate: Playing with Pairs 91

Big Idea 4: Tiling to Understand Area 99

Visualize: Cover Up 101

Play: A Whole New Alphabet 111

Investigate: Sharing an Area 119

Big Idea 5: Seeing Multiplication as Area 125

Visualize: Rods Around 127

Play: Squares and Near-Squares 132

Investigate: Connecting Area and Perimeter 142

Big Idea 6: Understanding 1 2 149

Visualize: I Spy 1 2 151

Play: Spotting 1 2 160

Investigate: The Many Shapes of 1 2 171

Big Idea 7: Seeing Fractions: The Parts and the Wholes 183

Visualize: Seeing Parts and Wholes 185

Play: Cover, Cut, and Sort 191

Investigate: Taking a Fractional Walk 202

Big Idea 8: Being Flexible with Numbers 209

Visualize: How Many Do You See? 211

Play: How Close to 100? 217

Investigate: Tile and Table Patterns 222

Appendix 231

Grid Paper 232

Grid Paper 233

1 Grid Paper 234

Dot Paper 235

Centimeter Dot Paper 236

Isometric Dot Paper 237

Hundred Grids 238

About the Authors 239

Acknowledgments 241

Index 243