Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

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 teacher education and mathematics education from Stanford University. Her research focuses on responsive, equitable mathematics instruction and coaching. 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.

• Introduction 1Low-Floor, High-Ceiling Tasks 2Youcubed Summer Camp 3Memorization versus Conceptual Engagement 4Mathematical Thinking, Reasoning, and Convincing 5Big Ideas 9Structure of the Book 9Note on Materials 17Manipulatives and Materials Used in This Book 18Activities for Building Norms 21Encouraging Good Group Work 21Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22Big Idea 1: Moving Shapes 27Visualize: What Does It Mean to Be the Same? 29Play: Pixel Puzzles 35Investigate: Slide It, Flip It, Turn It 45Big Idea 2: Zooming In and Out 53Visualize: What is Similarity? 55Play: Find the Fakes 60Investigate: Growing on a Grid 65Big Idea 3: Analyzing Proportional Relationships 71Visualize: Dropping the Altitude 73Play: Seeing Triangles under the Line 79Investigate: Stairway to Eleven 85Big Idea 4: Comparing Patterns of Growth 91Visualize: Squared Squares 93Play: Skip-Counting Arrays 100Investigate: Stacking Pennies 107Big Idea 5: The Ins and Outs of Functions 117Visualize: Growing Functions 120Play: Getting Warmer! 134Investigate: The Functions of Near Squares 140Big Idea 6: Finding Patterns in the Clouds 149Visualize: What’s Going On in This Graph? 151Play: What’s the Story Here? 158Investigate: Creating Data Visualizations 166Big Idea 7: Completing the Real Number System 177Visualize: Square Sides 179Play: Between 4 × 4 and 5 × 5 187Investigate: The Hypotenuse Hypothesis 193Big Idea 8: Discovering Pythagoras 201Visualize: Unpacking Pythagoras 204Play: Pythagorean Triples 209Investigate: Approximating Square Roots 214Big Idea 9: Exploring the Geometry of Ice Cream 221Visualize: Building Intuition about Volume 223Play: Comparing Cylinders 227Investigate: Scooping Up Volume 233Appendix 239Centimeter Grid Paper 240Grid Paper 241Isometric Dot Paper 242Dot Paper 243About the Authors 245Acknowledgments 247Index 249

Select Guide Rating