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: Thinking in Cubes 23 Visualize: Solids, Inside and Out 25 Play: City of Cubes 33 Investigate: A Box of Boxes 44 Big Idea 2: Estimating with Fractions 53 Visualize: Making Snowflakes 55 Play: Fraction Blizzard 61 Investigate: Wondering with Fractions 67 Big Idea 3: Using Fraction Equivalence 81 Visualize: Picking Paintings Apart 83 Play: Make a Fake 94 Investigate: Squares with a Difference 101 Big Idea 4: Exploring the Coordinate Plane 115 Visualize: Getting around the Plane 118 Play: Ship Shape 124 Investigate: Table Patterns 133 Big Idea 5: Seeing and Connecting Patterns across Representations 143 Visualize: Two-Pattern Tango 145 Play: Pattern Carnival 153 Investigate: Seeing Growth on a Graph 159 Big Idea 6: Understanding Fraction Multiplication Visually 169 Visualize: Fractions in a Pan 172 Play: Pieces and Parts 180 Investigate: The Sum of the Parts 187 Big Idea 7: What Does It Mean to Divide Fractions? 199 Visualize: Creating Cards 201 Play: Cuisenaire Trains 209 Investigate: Fraction Division Conundrum 217 Big Idea 8: Thinking in Powers of 10 223 Visualize: The Unit You 225 Play: Filling Small and Large 233 Investigate: Museum of the Very Large and Small 239 Big Idea 9: Using Numbers and Symbols Flexibly 247 Visualize: Seeing Expressions 250 Play: Inside Pascal’s Triangle 261 Investigate: The 1492 Problem 268 Appendix 279 Centimeter Dot Paper 280 Isometric Dot Paper 281 About the Authors 283 Acknowledgments 285 Index 287

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 fifth 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.