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 fifth-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 mathematics 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 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
