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 kindergarten-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 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 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

A Note on the Structure of Kindergarten 15

Note on Materials 17

Manipulatives and Materials Used in This Book 17

Big Idea 1: Understanding the Physical Quantity of Number 21

Count a Collection 23

How Many Do You See? 30

Making a Counting Book 40

Big Idea 2: Using Fingers as Numbers 47

Feeling Fingers 49

Show Me with Your Fingers 64

Hand Mirrors 70

Big Idea 3: Talking about and Making Shapes 77

Talking about Shapes 79

Make a Shape 93

Building Blocks 97

Big Idea 4: Seeing Numbers inside of Numbers 103

Dot Talks 105

Snap It! 118

Which is More? 123

Big Idea 5: Putting Numbers Together 135

Growing Bigger and Bigger 137

Roll the Dice 144

Foot Parade 151

Big Idea 6: Describing and Sorting Objects 159

Sorting Supplies 161

Sorting Emojis 168

Sorting Buttons 174

Big Idea 7: Seeing and Making Patterns Everywhere 181

A World of Patterns 184

DIY Patterns 195

Kinder Dance Party 200

Big Idea 8: Stretching Counting toward 100 205

Counting Larger Collections 207

Making a Collection 213

Hundred Chart Patterns 219

Appendix 231

About the Authors 235

Acknowledgments 237

Index 239