How math skills build on each other
Find the ideas that come before a skill, see how the work develops, and choose a useful next step. Grade labels show our worksheet organization; school sequences can differ.
Counting and number sense
Connect number words, written numerals, and quantities before using numbers in calculations.
Place value and number forms
Build numbers from ones, tens, and hundreds, then extend the same structure to large numbers and decimals.
Addition and subtraction
Move from combining and taking away objects to flexible mental strategies and written regrouping.
Multiplication and division
Connect equal groups, arrays, facts, and partial products before moving to larger calculations.
Fractions
Progress from equal shares to fraction size, equivalence, and operations with fractions.
Decimals
Use place value to connect decimal notation with fractions and perform accurate decimal calculations.
Length, time, money, and measurement
Move from comparing objects to reading instruments, using units, and converting measures.
Shapes and angles
Identify shapes by their properties, then reason about lines, angles, and geometric relationships.
Area, perimeter, and volume
Distinguish boundary length, surface coverage, and space filled before using formulas.
Ratios, rates, and percent
Connect equivalent ratios and unit rates to proportional relationships and percent change.
Integers and rational numbers
Extend arithmetic across zero using signed quantities, distances, and consistent operation rules.
Expressions and equations
Translate situations, simplify expressions, and solve equations by preserving equality.
Functions and graphs
Connect inputs and outputs across equations, tables, and graphs, then study transformations and composition.
Exponents and polynomials
Develop exponent rules and polynomial structure to simplify expressions and solve equations.
Triangles and trigonometry
Use triangle properties, similarity, and right-triangle ratios to calculate unknown lengths and angles.
Geometry and transformations
Connect geometric properties with coordinates, transformations, circles, and logical arguments.
Probability and counting outcomes
Build from simple chance events to counting methods, compound probabilities, and probability models.
Data and statistics
Move from reading simple displays to summarizing distributions and interpreting relationships in data.
Sequences, exponential functions, and logarithms
Distinguish additive from multiplicative patterns and connect powers with logarithms.
Limits, derivatives, and integrals
Use nearby behavior, rates of change, and accumulation to extend algebraic and graphical reasoning.