Introduction

Problem Solving

Problem or Exercise?

Problem Solving Strategies

Beware of Patterns!

Problem Bank

Careful Use of Language in Mathematics

Explaining Your Work

The Last Step

Place Value

Dots and Boxes

Other Rules

Binary Numbers

Other Bases

Number Systems

Even Numbers

Exploration

Number and Operations

Addition: Dots and Boxes

Subtraction: Dots and Boxes

Multiplication: Dots and Boxes

Division: Dots and Boxes

Number Line Model

Area Model for Multiplication

Properties of Operations

Division Explorations

Fractions

What is a Fraction?

The Key Fraction Rule

Adding and Subtracting Fractions

What is a Fraction? Revisited

Multiplying Fractions

Dividing Fractions: Meaning

Dividing Fractions: Invert and Multiply

Dividing Fractions: Problems

Fractions involving zero

Egyptian Fractions

Algebra Connections

What is a Fraction? Part 3

Patterns and Algebraic Thinking

Borders on a Square

Careful Use of Language in Mathematics: =

Growing Patterns

Matching Game

Structural and Procedural Algebra

Place Value and Decimals

Review of Dots & Boxes Model

Decimals

x-mals

Division and Decimals

More x -mals

Terminating or Repeating?

Operations on Decimals

Orders of Magnitude

Geometry

Tangrams

Triangles and Quadrilaterals

Polygons

Platonic Solids

Painted Cubes

Symmetry

Geometry in Art and Science

Voyaging on Hōkūle`a

Hōkūle`a

Worldwide Voyage

Navigation

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Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

-Paul Lockhart

Mathematics for Elementary Teachers by Michelle Manes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.