The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the seventh-grade level through visualization, play, and investigation.
During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message - that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:
- There is no such thing as a math person - anyone can learn mathematics to high levels.
- Mistakes, struggle and challenge are the most important times for brain growth.
- Speed is unimportant in mathematics.
- Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.
With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.
Table of Contents
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: Connecting 2D and 3D Worlds 27
Visualize: Seeing Slices 29
Play: Playing with Clay 34
Investigate: The Area of Slices 40
Big Idea 2: Constructing Figures to Scale 47
Visualize: What is Scale? 50
Play: A Fishy Image 55
Investigate: Magnifying Solids 61
Big Idea 3: Seeing Proportional Relationships 69
Visualize: Growing Dough 72
Play: is It Proportional? 80
Investigate: Sizing Up Proportions 86
Big Idea 4: Understanding Percents in the World 93
Visualize: Painting Percents 95
Play: Building Benchmarks 103
Investigate: What’s It Going to Cost? 109
Big Idea 5: Building Intuition about Probability 119
Visualize: is It Fair? 121
Play: Fair Sums? 131
Investigate: What’s in the Bag? 136
Big Idea 6: Modeling Probabilities 145
Visualize: What’s the Chance of That? 147
Play: Probability Carnival 155
Investigate: Go, Go Galton Board! 163
Big Idea 7: Sampling to Understand Populations 171
Visualize: Sampling Dots and Beads 173
Play: Catch and Release 180
Investigate: Wildlife Populations 186
Big Idea 8: Operating with Opposites 197
Visualize: Line Dancing 199
Play: Integer Tic-Tac-Toe 207
Investigate: Coordinating Multiplication 216
Big Idea 9: Using Algebra as a Problem-Solving Tool 225
Visualize: Case by Case 228
Play: (Non) Linear Pattern Puzzles 237
Investigate: Linear Letters 245
Big Idea 10: Exploring Circles 251
Visualize: Building Hunches about Circumference 253
Play: Dissecting Circle Area 260
Investigate: Unraveling Circles 267
Appendix 273
Centimeter Grid Paper 274
1" Grid Paper 275
Snap Cube Grid Paper 276
Isometric Dot Paper 277
Dot Paper 278
About the Authors 279
Acknowledgments 281
Index 283
