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 first-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
How Many Do You See? Learning to Reason, Convince, and Pose Questions 23
Big Idea 1: Building with and Talking about Shapes 31
Visualize: Build(ings) 33
Play: Tangram Puzzles 40
Investigate: Tangram Squares 52
Big Idea 2: Tens and Ones Are Useful Ways to Organize 59
Visualize: Organizing and Counting a Collection 61
Play: How Many Dots? 68
Investigate: Boxes of Pencils 74
Big Idea 3: Representing and Modeling Joining and Separating Situations 81
Visualize: Showing the Story 83
Play: Playing with Problem Types 89
Investigate: Library Wonders 99
Big Idea 4: Using Data to Describe and Wonder about Our World 107
Visualize: Organizing the Natural World 109
Play: Displaying Data 115
Investigate: Our Trash, Ourselves 124
Big Idea 5: Equal Means the Same 133
Visualize: Hungry, Hungry Monsters! 136
Play: True or False? 155
Investigate: Exploring Relations 165
Big Idea 6: Building with Numbers within 20 175
Visualize: Seeing Spots 177
Play: Rolling Ten 186
Investigate: Addition Table Patterns 195
Big Idea 7: Finding Patterns in Numbers 203
Visualize: Patterns in the Hundred Chart 205
Play: Skipping across the Hundred Chart 213
Investigate: Weaving Patterns 220
Big Idea 8: Using Place Value to Add and Subtract 231
Visualize: Recess! 233
Play: Playing with Place Value across Problem Types 243
Investigate: Making a Dollar 251
Big Idea 9: Using Units to Measure Our World 259
Visualize: Which One is Longer? 261
Play: Measuring Our World in Cubes 267
Investigate: Measuring with Cuisenaire Rods 275
Big Idea 10: Partitioning Shapes into Equal Parts 281
Visualize: Half and Half-of-a-Half 283
Play: Analyzing Tangrams 293
Investigate: What’s in a Flag? 299
Appendix 313
1" Grid Paper 314
Hundred Chart 315
Grid Paper 316
About the Authors 317
Acknowledgments 319
Index 321
