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 Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22 Big Idea 1: Moving Shapes 27 Visualize: What Does It Mean to Be the Same? 29 Play: Pixel Puzzles 35 Investigate: Slide It, Flip It, Turn It 45 Big Idea 2: Zooming In and Out 53 Visualize: What is Similarity? 55 Play: Find the Fakes 60 Investigate: Growing on a Grid 65 Big Idea 3: Analyzing Proportional Relationships 71 Visualize: Dropping the Altitude 73 Play: Seeing Triangles under the Line 79 Investigate: Stairway to Eleven 85 Big Idea 4: Comparing Patterns of Growth 91 Visualize: Squared Squares 93 Play: Skip-Counting Arrays 100 Investigate: Stacking Pennies 107 Big Idea 5: The Ins and Outs of Functions 117 Visualize: Growing Functions 120 Play: Getting Warmer! 134 Investigate: The Functions of Near Squares 140 Big Idea 6: Finding Patterns in the Clouds 149 Visualize: What’s Going On in This Graph? 151 Play: What’s the Story Here? 158 Investigate: Creating Data Visualizations 166 Big Idea 7: Completing the Real Number System 177 Visualize: Square Sides 179 Play: Between 4 × 4 and 5 × 5 187 Investigate: The Hypotenuse Hypothesis 193 Big Idea 8: Discovering Pythagoras 201 Visualize: Unpacking Pythagoras 204 Play: Pythagorean Triples 209 Investigate: Approximating Square Roots 214 Big Idea 9: Exploring the Geometry of Ice Cream 221 Visualize: Building Intuition about Volume 223 Play: Comparing Cylinders 227 Investigate: Scooping Up Volume 233 Appendix 239 Centimeter Grid Paper 240 Grid Paper 241 Isometric Dot Paper 242 Dot Paper 243 About the Authors 245 Acknowledgments 247 Index 249

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 eighth 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.