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

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 first 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.