Table of contents
Low-Floor, High-Ceiling Tasks
Youcubed Summer Camp
Memorization versus Conceptual Engagement
Mathematical Thinking, Reasoning, and Convincing
Structure of the Book
Note on Materials
Activities for Building Norms
Encouraging Good Group Work
Paper Folding: Learning to Reason, Convince, and Be a Skeptic
Big Idea 1: Connecting 2D & 3D Worlds
Visualize: Seeing Slices
Play: Playing with Clay
Investigate: The Area of Slices
Big Idea 2: Constructing Figures to Scale
Visualize: What is Scale?
Play: A Fishy Image
Investigate: Magnifying Solids
Big Idea 3: Seeing Proportional Relationships
Visualize: Growing Dough
Play: Is It Proportional?
Investigate: Sizing Up Proportions
Big Idea 4: Understanding Percents in the World
Visualize: Painting Percents
Play: Building Benchmarks
Investigate: What’s It Going to Cost?
Big Idea 5: Building Intuition about Probability
Visualize: Is It Fair?
Play: Fair Sums?
Investigate: What’s in the Bag?
Big Idea 6: Modeling Probabilities
Visualize: What’s the Chance of That?
Play: Probability Carnival
Investigate: Go, Go Galton Board!
Big Idea 7: Sampling to Understand Populations
Visualize: Sampling Dots and Beads
Play: Catch and Release
Investigate: Wildlife Populations
Big Idea 8: Operating with Opposites
Visualize: Line Dancing
Play: Integer Tic-Tac-Toe
Investigate: Coordinating Multiplication
Big Idea 9: Using Algebra as a Problem-Solving Tool
Visualize: Case by Case
Play: (Non) Linear Pattern Puzzles
Investigate: Linear Letters
Big Idea 10: Exploring Circles
Visualize: Building Hunches about Circumference
Play: Dissecting Circle Area
Investigate: Unraveling Circles
Centimeter Grid Paper
1” Grid Paper
Snap Cube Grid Paper
Isometric Dot paper
About the Authors