Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6 (Paperback)

Introduction

Low-Floor, High-Ceiling Tasks

Youcubed Summer Camp

Memorization versus Conceptual Engagement

Mathematical Thinking, Reasoning, and Convincing

Big Ideas

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: Taking apart prisms & polygons

Visualize: How Big is the Footprint?

Play: Shards of a Shape

Investigate: Rising from the Footprint

Big Idea 2: Folding and unfolding objects

Visualize: Folding Cubes in Your Mind

Play: Folding Nets in Your Mind

Investigate: Filling Our Nets

Big Idea 3: Expanding the number line

Visualize: Folding around Zero

Play: Bouncing around the Number Line

Investigate: Going 2D

Big Idea 4: Finding and using unit rates

Visualize: Seeing Unit Rates

Play: Seeing the Best Deal

Investigate: How Fast Do You Walk?

Big Idea 5: Reasoning with proportions

Visualize: Jump! Jump!

Play: Seeing Animals in a New Way

Investigate: A Seat at the Table

Big Idea 6: Visualizing the center and spread of data

Visualize: The Shape of Data

Play: What Does Mean Mean?

Investigate: When Does Mean = Median = Mode = Range?

Big Idea 7: Using symbols to describe the world

Visualize: Cuisenaire Rod Equivalents

Play: Math Mobiles

Investigate: Radial Patterns

Big Idea 8: Generalizing

Visualize: Generalizing Number Patterns

Play: Generalizing Strategy

Investigate: Generalizing Visual Patterns

Appendix

Centimeter grid paper

Grid paper

1” Grid Paper

Isometric Dot paper

Dot Paper

Index