Big ideas. Your own starting point.
Explore 33 mathematics topics for grades 4–8, with room to strengthen the foundations. Follow your curiosity.
33 topics to explore
Learn your way.Number Foundations
Big understanding starts with the basics.
Whole-Number Place Value
Understand the value of each digit and how numbers are organized.
Addition and Subtraction
Build confident strategies for combining and comparing whole numbers.
Multiplication Facts and Models
Connect equal groups, arrays, and multiplication facts.
Multi-Digit Multiplication
Use place value and area models to multiply larger numbers.
Division and Remainders
Share quantities equally and interpret what is left over.
Factors and Multiples
Explore divisibility, prime numbers, and common factors.
Fractions and Decimals
Make sense of the parts and the whole.
Fractions
Understand, compare, and calculate with parts of a whole.
Decimal Place Value
Connect tenths, hundredths, and thousandths to familiar quantities.
Decimal Operations
Add, subtract, multiply, and divide decimals with understanding.
Fractions, Decimals, and Percentages
Translate between different ways of representing the same amount.
Ratios and Rational Numbers
Discover how quantities relate.
Ratios
Describe and compare relationships between quantities.
Unit Rates
Find the amount per one and make meaningful comparisons.
Proportional Relationships and Percent Problems
Explore proportional reasoning, percentages, and real-world changes.
Signed Numbers
Make sense of positive and negative numbers and their order.
Rational-Number Operations
Calculate with positive and negative fractions and decimals.
Exponents and Scientific Notation
Use powers to describe repeated multiplication and very large or small numbers.
Algebra
Find patterns. Uncover possibilities.
Patterns and Expressions
Describe patterns and represent relationships using variables.
Equations
Use balance and reasoning to solve for unknown values.
Inequalities
Represent and solve relationships involving greater or lesser values.
Coordinate Plane
Locate points and connect ordered pairs to visual relationships.
Linear Relationships and Functions
Explore slope, change, and how inputs connect to outputs.
Geometry and Measurement
See mathematics in every dimension.
Measurement and Unit Conversion
Measure quantities and convert between related units.
Angles and Two-Dimensional Figures
Investigate angles, polygons, and their defining properties.
Perimeter and Area
Reason about distances around shapes and the space inside them.
Surface Area and Volume
Explore the outside and inside of three-dimensional objects.
Transformations
Translate, reflect, and rotate figures on a plane.
Similarity and Congruence
Compare shapes using scale, corresponding sides, and angles.
Pythagorean Theorem
Discover the relationship between the sides of a right triangle.
Data and Applications
Turn information into understanding.
Tables and Graphs
Organize information and interpret visual representations.
Data Distributions and Summary Measures
Describe data using shape, center, and variability.
Probability
Reason about chance and the likelihood of events.
Sampling and Inference
Use samples to ask questions and draw careful conclusions.
Mathematical Modeling and Multi-Step Problems
Connect mathematical ideas to meaningful real-world problems.