Addition & Subtraction of Fractions

Addition & Subtraction Story Problems

Algebraic Equality

Algebraic Equations

Algebraic Expressions

Analyzing Addition & Subtraction Strategies

Angle Measurement

Attributes

Balance Models for Equations

Bar Charts & Pie Charts

Basic Probability

Benchmark Percents & Estimation

Bias in Data Collection

Building Mental Addition Strategies

Building Mental Subtraction Strategies

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

Center, Shape, Spread, & Outliers

Choosing an Appropriate Data Display

Circles

Comparing Alternative Algorithms

Comparing Distributions

Comparing Linear & Nonlinear Patterns

Congruency & Similarity

Connecting Area, Surface Area, & Volume

Connecting Fractions, Decimals, Ratios, & Percents

Connections Between Multiplication & Division

Constant vs. Changing Rate of Change

Conversions

Counting Strategies for Addition & Subtraction

Defining Ratios

Describing Geometry

Describing Geometry Using Precise Mathematical Language

Direct Modeling with Objects & Drawings

Displaying Categorical Data

Displaying Numerical Data

Divisibility & Divisibility Rules

Division Algorithms

Division of Fractions

Division Strategies

Equivalent Fractions

Experimental vs. Theoretical Probability

Experiments & Simulations

Explaining Mathematical Reasoning

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.

Finding Rules in Repetition

Fraction Comparisons

Factors & Prime Factorizations

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

Fractions on the Number Line

Fractions to Decimals

Function Tables

Generalizing a Pattern with Variables

Geometric Patterns

Geometric Problems

Graphing Functions

Greatest Common Factors

Hierarchical Classification of Shapes

Histograms & Dotplots

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

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.

Inputs, Outputs, & Rules

Interior & Exterior Angles

Interpreting Misleading Graphs

Introduction to Fractions

Least Common Multiples

Linear Functions

Lines & Angles

Looking for Structure

Making and Testing Conjectures

Making Friendly Numbers

Making Sense of Division

Meaning of the Equal Sign

Measures of Center

Measures of Spread

Multiple Representations of Functions

Multiplication Algorithms

Multiplication & Division Story Problems

Multiplication of Fractions

Multiplication Strategies

Nets of Three-Dimensional Figures

Number Patterns

Numerical Expressions

Other Functions

Partial Products & Partial Quotients

Percent Increase & Decrease

Perimeter & Area

Polygons

Polyhedra

Population vs. Sample

Prime vs. Composite Numbers

Probability Rules

Properties of Operations as Foundations for Algebra

Properties vs. Definitions

Proportional vs. Nonproportional Relationships

Quadrilaterals

Quartiles & Boxplots

Rates & Unit Rates

Reasoning About Percent

Recursive vs. Explicit Patterns

Relational Thinking

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.

Sample Spaces & Outcomes

Sampling Methods

Scale Factor

Solving Ratios

Standard Deviation

Statistical Questions

Surface Area

Tables, Graphs, & Double Number Lines for Ratios

Transformations & Symmetry

Translations, Rotations, & Reflections

Triangles

True, False, & Open Number Sentences

Types of Data

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

Understanding the Standard Addition Algorithm

Understanding the Standard Subtraction Algorithm

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.

Units & Iteration

Variables as Unknowns, Changing Quantities, & Generalized Numbers

Visual Models for Fraction Operations

Volume

Weighted Averages

What Does Addition Mean?

What Does Subtraction Mean?

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.

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

Why Area Formulas Work

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.

Why Regrouping Works