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 Note on Materials 16 Manipulatives and Materials Used in This Book 17 Activities for Building Norms 19 Encouraging Good Group Work 19 Paper Folding: Learning to Reason, Convince, and Be Skeptical 21 Big Idea 1: Taking Apart Prisms and Polygons 24 Visualize: How Big Is the Footprint? 26 Play: Shards of a Shape 38 Investigate: Rising from the Footprint 46 Big Idea 2: Folding and Unfolding Objects 57 Visualize: Folding Cubes in Your Mind 60 Play: Folding Nets in Your Mind 70 Investigate: Filling Our Nets 85 Big Idea 3: Expanding the Number Line 92 Visualize: Folding around Zero 94 Play: Bouncing around the Number Line 101 Investigate: Going 2-D 107 Big Idea 4: Finding and Using Unit Rates 116 Visualize: Seeing Unit Rates 118 Play: Seeing the Best Deal 128 Investigate: How Fast Do You Walk? 136 Big Idea 5: Reasoning with Proportions 142 Visualize: Jump! Jump! 144 Play: Seeing Animals in a New Way 149 Investigate: A Seat at the Table 156 Big Idea 6: Visualizing the Center and Spread of Data 164 Visualize: The Shape of Data 167 Play: What Does Mean Mean? 178 Investigate: When Does Mean = Median = Mode = Range? 185 Big Idea 7: Using Symbols to Describe the World 192 Visualize: Cuisenaire Rod Equivalents 195 Play: Math Mobiles 204 Investigate: Radial Patterns 215 Big Idea 8: Generalizing 221 Visualize: Generalizing Number Patterns 223 Play: Generalizing Strategy 230 Investigate: Generalizing Visual Patterns 239 Appendix 246 Centimeter Grid Paper 247 Grid Paper 248 1" Grid Paper 249 Isometric Dot Paper 250 Dot Paper 251 About the Authors 252 Acknowledgments 254 Index 255

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 sixth 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.