Module 1: Counting & Understanding Quantity

Explore what counting actually means and how numbers communicate quantity. This module develops the ideas behind counting, cardinality, estimation, number representation, and zero.

How Counting Actually Works - Discover why counting is more than simply saying numbers in order. Explore the principles that make counting reliable and meaningful.

Understanding Quantity - Explore how counting connects numbers to actual quantities and why matching one number to one object is fundamental to understanding number.

Representing Numbers in Different Ways - Learn how the same number can be represented using objects, pictures, words, symbols, and expanded forms - and how moving between representations strengthens number sense.

How Big Is It Really? - Develop a sense of how large or small numbers are by comparing quantities, estimating values, and reasoning about numerical magnitude.

Understanding Zero - Explore the many roles of zero: representing no quantity, holding a place in our number system, and acting as an important mathematical identity.

Module 2: Place Value & Number Representation

Investigate how the position of a digit determines its value and how numbers are built within a place-value system. Extend these ideas from whole numbers to decimals, powers of ten, and number systems beyond base ten.

Why Digits Mean What They Mean - Explore why a digit's value depends on where it appears and how the structure of place value makes our number system work.

Building Numbers in Base Ten - Learn how numbers can be built, broken apart, and regrouped using ones, tens, hundreds, and other powers of ten.

Which Number is Really Bigger? - Use place value to read, write, order, and compare numbers while developing strategies for determining their relative size.

Extending Place Value - Extend the place-value system in both directions to understand decimals and the relationships created by multiplying and dividing by powers of ten.

What If We Counted Differently? - Explore number systems that use bases other than ten and discover which features of place value are universal and which depend on the base being used.

Module 3: Meaning of Addition & Subtraction

What Does Addition Mean?

What Does Subtraction Mean?

Addition & Subtraction Story Problems

Direct Modeling with Objects & Drawings

Counting Strategies for Addition & Subtraction

Module 4: Addition & Subtraction Strategies & Algorithms

Building Mental Addition Strategies

Building Mental Subtraction Strategies

Making Friendly Numbers

Understanding the Standard Addition Algorithm

Understanding the Standard Subtraction Algorithm

Why Regrouping Works

Analyzing Addition & Subtraction Strategies

Module 5: Multiplication & Division Concepts

Multiplication & Division Story Problems

Multiplication Strategies

Making Sense of Division

Division Strategies

Connections Between Multiplication & Division

Module 6: Multiplication & Division Algorithms

Multiplication Algorithms

Division Algorithms

Partial Products & Partial Quotients

Comparing Alternative Algorithms

Module 7: Fractions as Numbers

Introduction to Fractions

Equivalent Fractions

Fraction Comparisons

Fractions to Decimals

Fractions on the Number Line

Fractions as Part-Whole, Measure, Quotient, & Operator

Module 8: Fraction Operations

Addition & Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

Visual Models for Fraction Operations

Module 9: Factors & Number Structure

Prime vs. Composite Numbers

Factors & Prime Factorizations

Divisibility & Divisibility Rules

Greatest Common Factors

Least Common Multiples

Module 10: Angles, Lines, & Geometric Language

Angle Measurement

Lines & Angles

Interior & Exterior Angles

Attributes

Describing Geometry Using Precise Mathematical Language

Module 11: Two-Dimensional Shapes

Polygons

Quadrilaterals

Triangles

Circles

Hierarchical Classification of Shapes

Properties vs. Definitions

Module 12: Perimeter, Area, & Measurement

Perimeter & Area

Conversions

Units & Iteration

Why Area Formulas Work

Module 13: Three-Dimensional Geometry

Polyhedra

Surface Area

Volume

Nets of Three-Dimensional Figures

Connecting Area, Surface Area, & Volume

Module 14: Transformations, Congruence, & Similarity

Transformations & Symmetry

Congruency & Similarity

Translations, Rotations, & Reflections

Scale Factor

Module 15: Ratios & Proportional Reasoning

Defining Ratios

Solving Ratios

Rates & Unit Rates

Proportional vs. Nonproportional Relationships

Tables, Graphs, & Double Number Lines for Ratios

Module 16: Percent Reasoning

Reasoning About Percent

Percent Increase & Decrease

Connecting Fractions, Decimals, Ratios, & Percents

Benchmark Percents & Estimation

Module 17: Numerical & Algebraic Expressions

Numerical Expressions

Algebraic Expressions

Variables as Unknowns, Changing Quantities, & Generalized Numbers

Properties of Operations as Foundations for Algebra