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Engage Your Students in Visual, Creative Explorations of the Big Ideas in Mathematics The Mindset Mathematics series offers a unique, research-based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. This hands-on resource is for any teacher who wants to engage their second grade students in reasoning and persisting through problems, and provides activities that will engage students' interest and show them the many ways that mathematics is important in their lives. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much-needed volume, the authors clearly show what the big ideas are at this grade level, why they are important to know, and how students can best learn those big ideas. Filled with engaging questions, open-ended tasks, and four-color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.

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Engage Your Students in Visual, Creative Explorations of the Big Ideas in Mathematics The Mindset Mathematics series offers a unique, research-based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. This hands-on resource is for any teacher who wants to engage their second grade students in reasoning and persisting through problems, and provides activities that will engage students' interest and show them the many ways that mathematics is important in their lives. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much-needed volume, the authors clearly show what the big ideas are at this grade level, why they are important to know, and how students can best learn those big ideas. Filled with engaging questions, open-ended tasks, and four-color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.

Author Biography

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 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.

Table of Contents

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: Partitioning Shapes into Equal Parts 31 Visualize: Equal or Same? 33 Play: Four Fourths 39 Investigate: Rows and Columns 44 — Big Idea 2: Making and Using Equal Groups 53 Visualize: The Groups Inside 55 Play: Skipping down the Hall 61 Investigate: Array Museum 67 — Big Idea 3: What Is 100? 73 Visualize: The Many Ways to See 100 75 Play: Scoop and Count 82 Investigate: Making a Dollar, Revisited 86 — Big Idea 4: Composing and Decomposing Numbers 91 Visualize: Array Talks 93 Play: Which Is More? 103 Investigate: Coin Grab 114 — Big Idea 5: Using Patterns in Place Value 119 Visualize: What's in Your 12? 121 Play: Reach for It! 126 Investigate: Window Mysteries 136 — Big Idea 6: Thinking on the Number Line 145 Visualize: Long Lives 148 Play: Life- Span Puzzles 157 Investigate: Living on the Number Line 166 — Big Idea 7: Rulers and Clocks Are Number Lines 173 Visualize: Noticing the Ruler and Clock 175 Play: Walking the Clock 181 Investigate: A Sea of Sharks 187 — Big Idea 8: Using Units to Estimate 205 Visualize: Foot by Foot 207 Play: Length Scavenger Hunt 216 Investigate: School- Day Walkabout 222 — Big Idea 9: Using Data to Visualize and Wonder about Our World 229 Visualize: Fruit around the World 231 Play: Eat Your Roots 238 Investigate: Dear Data 243 Appendix 253 Grid Paper 254 About the Authors 255 Acknowledgments 257 Index 259

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