Eyes on math: a visual approach to teaching math concepts

1. Background

Visualization in Math

Focusing on the Important Math

Building Mathematical Communication

2. Grades K

2

Counting up by 1s

Counting Back by 1s

Counting up by 2s

Counting Back by 2s

Counting up by 5s

Counting Back by 5s

Counting up by 10s

Counting Back by 10s

Comparing Numbers by Matching

Benchmark Numbers: All About 5

Benchmark Numbers: All About 10

Ordinal Numbers

Addition as Combining

Addition to Describe Part-Part-Whole Situations

Adding 0 and Adding 1

Addition: Commutativity

Addition: Changing Addends, But Not the Sum

Adding or Subtracting 10

Subtraction as Taking Away

Subtraction to Compare

Relating Addition and Subtraction

Naming Two-Digit Numbers

Naming Three-Digit Numbers

Place Value: Grouping in Tens

Place Value: Positions

Comparing Sizes of Numbers

Fractions: Halves

Fractions: Quarters

Measurement: meaning the Length.

Contents note continued: Measurement: Effect of Unit Size

Measurement: Standard Units of Length

2-D Shapes Versus 3-D Shapes

Comparing 2-D Shapes

Comparing 3-D Shapes

Composing Shapes

Shape Puzzles

3. Grades 3

5

Multiplication: Equal Groups

Multiplication: Commutativity

Multiplication: The Distributive Principle

Multiplication: 2-Digit by 2-Digit

Division as Equal Groups or Sharing

Division: Remainders

Rounding Numbers

Place Value: Multiplying and Dividing by Powers of 10

Place Value: Renaming Numbers

Factors: What They Are

Factors Come in Pairs

Fractions: Representing

Fractions: Equivalence

Fractions: Comparing

Fractions: Mixed Number/Improper Fraction Relationship

Fractions: Common Denominators

Adding Fractions

Multiplying Fractions

Fractions: Multiplying as Resizing

Fractions as Division

Decimals: Relating Hundredths to Tenths

Decimals: Equivalence

Decimals: Adding and Subtracting.

Contents note continued: Measurement: Time Intervals

Measurement: Area of Rectangles

Perimeter versus Area

Measurement Conversions

Graphs with Scales

Coordinate Grids

Classification of Shapes

Parallel and Perpendicular Lines

Lines of Symmetry

Patterns versus Non-patterns

Algebraic Thinking: Growing Additively

Algebraic Thinking: Shrinking Additively

Algebraic Thinking: Growing Multiplicatively

4. Grades 6

8

Common Factors

Common Multiples

Square Roots

Fraction Division

Ratios: Multiple Ratios Describe Any Situation

Equivalent Ratios

Equivalent Rates

Solving Rate Problems

Describing Percent

Uses of Integers

The Zero Principle

Subtraction of Integers as a Directed Distance

Multiplication and Division of Integers

Area of a Parallelogram

Area of a Triangle

The Pythagorean Theorem

Pi

How Measurements Are and Are Not Related

Mean

Variability

Sampling

Probability: What It Means.

Contents note continued: Unpredictability

Rotations, Reflections, and Translations

Scale Drawings

Dilatations

Angles with Parallel Lines

Equivalent Expressions

Equation as a Balance

Different Types of Equations

What Is Linear?

Role of the Slope in the Equation of a Line

Systems of Equations

Function Rules.