Common Core State Standards for Mathematics
The Common Core State Standards for Mathematics (CCSSM) define what students should understand at each grade level. Browse every standard below with links to free practice and worked examples.
Kindergarten
0–20 (counting to 100)▶
Kindergarten
0–20 (counting to 100)- Counting — Count 100Count to 100 by ones and by tens
- Counting — WriteWrite numbers 0–20; represent quantities
- Counting — Compare OrderCount to determine how many; compare groups
- AddSub — Within 10Represent addition/subtraction with objects and equations
- AddSub — Fluency 5Fluently add and subtract within 5
- AddSub — DecomposeDecompose numbers ≤10 into pairs
- PlaceValue — Teen NumbersCompose and decompose 11–19 as ten and ones
- Measurement — CompareDescribe and compare measurable attributes
- Statistics — ClassifyClassify objects into categories; count each
- Geometry2d — Shapes BasicIdentify and describe 2D and 3D shapes; positions
Grade 1
0–120▶
Grade 1
0–120- AddSub — Within 20Add and subtract within 20; word problems
- AddSub — Three AddendsAdd three whole numbers whose sum ≤ 20
- AddSub — PropertiesApply commutative and associative properties
- AddSub — InverseSubtraction as unknown-addend
- AddSub — Fluency 10Fluently add/subtract within 10
- Expressions — EqualityMeaning of equals sign; true/false equations
- Expressions — Missing NumberFind unknown in equation
- Counting — To 120Count to 120; read and write numerals
- PlaceValue — Tens OnesTwo-digit numbers as tens and ones
- PlaceValue — CompareCompare two two-digit numbers using >, =, <
- AddSub — Within 100Add within 100
- Measurement — Length NonstandardOrder objects by length; measure using non-standard units
- Measurement — Time BasicTell time to hour and half-hour
- Geometry2d — Shapes BasicDistinguish between defining/non-defining attributes
- Fractions — Intro ShapesPartition circles and rectangles into halves/fourths
Grade 2
0–1000▶
Grade 2
0–1000- AddSub — Within 100Fluently add/subtract within 100
- AddSub — Two StepSolve two-step word problems
- Counting — Even OddDetermine even/odd; write equations for even numbers
- PlaceValue — HundredsThree-digit place value
- Counting — Skip CountSkip count by 5s, 10s, 100s
- PlaceValue — CompareCompare three-digit numbers
- AddSub — Within 1000Add/subtract within 1,000
- Measurement — Length StandardMeasure in inches, feet, cm, meters
- Measurement — Time 5minTell time to 5 minutes
- Measurement — MoneySolve word problems involving money
- Statistics — Line PlotGenerate measurement data; line plots
- Geometry2d — Shapes BasicRecognise and draw shapes; identify faces
- Fractions — Intro ShapesPartition shapes into halves, thirds, fourths
Grade 3
0–10,000; fractions introduced▶
Grade 3
0–10,000; fractions introduced- MulDiv — ConceptInterpret products of whole numbers
- MulDiv — InverseDivision as unknown factor
- MulDiv — Word ProblemsSolve multiplication/division word problems
- MulDiv — TablesFluently multiply/divide within 100
- MulDiv — PropertiesApply commutative, associative, distributive properties
- Expressions — PatternsIdentify arithmetic patterns
- PlaceValue — RoundingRound whole numbers to nearest 10 or 100
- AddSub — AlgorithmFluently add/subtract within 1,000 using strategies
- Fractions — RepresentationsUnderstand fractions as numbers
- Fractions — Number LineRepresent fractions on number line
- Fractions — Equivalent BasicExplain equivalent fractions; compare fractions
- Measurement — TimeTell time to nearest minute; elapsed time
- Measurement — Mass CapacityMeasure mass and capacity (g, kg, L)
- Geometry2d — Area IntroUnderstand area; measure by counting unit squares
- Geometry2d — PerimeterSolve perimeter problems
- Geometry2d — ClassifyUnderstand shapes belong to categories
Grade 4
0–1,000,000; fractions with denominators 2–12▶
Grade 4
0–1,000,000; fractions with denominators 2–12- MulDiv — Multi DigitMultiply up to 4-digit by 1-digit
- MulDiv — Long Division IntroDivide with remainders (1-digit divisor)
- Expressions — Factors PrimesFind factor pairs; identify prime/composite
- Expressions — PatternsGenerate and analyse number patterns
- PlaceValue — MillionsRead/write multi-digit whole numbers
- PlaceValue — CompareCompare multi-digit numbers
- PlaceValue — RoundingRound to any place
- AddSub — AlgorithmFluently add/subtract using standard algorithm
- Fractions — EquivalentExplain and generate equivalent fractions
- Fractions — CompareCompare fractions with different numerators/denominators
- Fractions — Add Sub LikeAdd fractions with like denominators
- Fractions — Subtract LikeSubtract fractions with like denominators
- Fractions — Multiply WholeMultiply fraction by whole number
- Decimals — IntroDecimal notation for fractions (tenths/hundredths)
- Decimals — CompareCompare two decimals to hundredths
- Measurement — Convert BasicConvert within measurement system
- Geometry2d — Area PerimeterApply area and perimeter formulas
- Geometry2d — Angles IntroMeasure and classify angles
- Geometry2d — SymmetryIdentify line-symmetric figures
- Geometry2d — LinesDraw and identify lines, angles, rays
Grade 5
0–billions; decimals to thousandths▶
Grade 5
0–billions; decimals to thousandths- Expressions — Order Of OpsEvaluate expressions with parentheses
- Expressions — Two PatternsGenerate and compare two numerical patterns
- PlaceValue — Decimal SystemUnderstand place value system (powers of 10)
- PlaceValue — Multiply Divide PowersMultiply/divide by powers of 10
- MulDiv — Long MultiplicationMultiply multi-digit whole numbers
- MulDiv — Long DivisionDivide by two-digit divisors
- Decimals — ThousandthsRead/write/compare decimals to thousandths
- Decimals — OperationsAdd, subtract, multiply, divide decimals
- Fractions — Add Sub UnlikeAdd fractions with unlike denominators
- Fractions — Subtract UnlikeSubtract fractions with unlike denominators
- Fractions — MultiplyMultiply fractions and mixed numbers
- Fractions — Divide IntroDivide with unit fractions
- Measurement — Convert AdvancedConvert measurement units within a system
- Geometry3d — Volume IntroUnderstand volume; measure by counting cubes
- Geometry3d — Rectangular PrismVolume of rectangular prisms
- Geometry2d — Coordinates BasicGraph points in first quadrant
- Geometry2d — ClassifyClassify 2D shapes in a hierarchy
Grade 6
rational numbers; ratios; expressions▶
Grade 6
rational numbers; ratios; expressions- RatiosProp — IntroUnderstand ratio concepts; use ratio reasoning
- RatiosProp — Unit RateUnit rates; solve problems
- Decimals — PercentFind percent of a quantity
- MulDiv — Long DivisionFluently divide multi-digit numbers
- Fractions — DivideDivide fractions by fractions
- NegNumbers — IntroUnderstand positive and negative numbers
- NegNumbers — CompareOrder and absolute value of rational numbers
- Expressions — EvaluateWrite and evaluate expressions
- Expressions — SimplifyApply properties to generate equivalent expressions
- Expressions — Equations One StepSolve one-variable equations and inequalities
- Expressions — Dependent IndependentRepresent relationships between quantities
- Geometry2d — Area AdvancedArea of triangles, quadrilaterals, polygons
- Geometry3d — Nets Surface AreaSurface area from nets
- Geometry3d — Rectangular PrismVolume with fractional edges
- Statistics — VariabilityStatistical questions; centre and variability
- Statistics — MeasuresMean, median, MAD, IQR
Grade 7
rational numbers; proportional relationships▶
Grade 7
rational numbers; proportional relationships- RatiosProp — ProportionalAnalyse proportional relationships
- RatiosProp — Complex RatesCompute unit rates with fractions
- RatiosProp — Percent ProblemsMulti-step percent problems
- NegNumbers — OperationsAdd, subtract, multiply, divide rational numbers
- Expressions — ManipulateUse properties to rewrite expressions
- Expressions — Equations Two StepSolve multi-step real-life problems
- Expressions — InequalitiesSolve inequalities of the form px + q > r
- Geometry2d — Draw PreciseDraw geometric shapes with given conditions
- Geometry2d — Area AdvancedArea and circumference of circles; angle relationships
- Geometry3d — PrismsVolume and surface area of prisms
- Geometry2d — Cross SectionsDescribe cross-sections of 3D shapes
- Statistics — SamplingUnderstand sampling; draw inferences
- Statistics — CompareCompare two populations
- Probability — TheoreticalDevelop probability models
- Probability — CompoundCompound events; tree diagrams
Grade 8
real numbers; linear equations; functions▶
Grade 8
real numbers; linear equations; functions- Expressions — Exponent RulesKnow and apply properties of integer exponents
- Expressions — RootsSquare root and cube root symbols
- Expressions — Scientific NotationScientific notation; operations
- LinearAlg — Slope IntroGraph proportional relationships; interpret slope
- LinearAlg — SystemsSolve systems of two linear equations
- LinearAlg — Function ConceptDefine, evaluate, compare functions
- LinearAlg — Slope InterceptUse functions to model linear relationships
- LinearAlg — Linear Vs NonlinearDistinguish linear from nonlinear
- Geometry2d — Transformations BasicUnderstand congruence via transformations
- Geometry2d — CongruenceUnderstand congruence and similarity
- Geometry2d — PythagorasExplain and apply Pythagorean theorem
- Geometry2d — Distance FormulaApply Pythagorean theorem to find distance
- Geometry3d — Curved VolumesVolume of cylinders, cones, spheres
- Statistics — Scatter PlotConstruct and interpret scatter plots
- Statistics — Line Of FitUse line of best fit; interpret slope/intercept
Algebra I
real numbers; polynomials; quadratics▶
Algebra I
real numbers; polynomials; quadratics- Expressions — StructureInterpret the structure of expressions
- Expressions — ManipulateRewrite expressions in equivalent forms
- Quadratics — FactorFactor quadratic expressions
- Expressions — Equations AdvancedCreate equations in one variable
- LinearAlg — Create SystemsCreate equations in two variables
- Expressions — Equations SolveSolve linear equations and inequalities
- LinearAlg — SystemsSolve systems of equations
- Quadratics — SolveSolve quadratic equations
- LinearAlg — Function NotationUnderstand function notation
- LinearAlg — Graph AnalysisInterpret key features of graphs
- LinearAlg — Build FunctionWrite function from relationships
- LinearAlg — Linear Vs ExponentialDistinguish linear and exponential
- Statistics — BivariateSummarise and interpret bivariate data
Geometry
geometric reasoning; proofs▶
Geometry
geometric reasoning; proofs- Geometry2d — Transformations FormalRepresent transformations in the plane
- Geometry2d — Congruence ProofProve geometric theorems
- Geometry2d — Similarity FormalUnderstand similarity via transformations
- Trigonometry — Right TriangleDefine trig ratios; solve problems
- Geometry2d — Circles TheoremsUnderstand and apply circle theorems
- Geometry2d — Circles EquationsDerive circle equation; complete the square
- Geometry2d — Coordinate ProofsUse coordinates to prove theorems
- Geometry3d — Cross SectionsIdentify cross-sections of 3D objects
- Geometry3d — All VolumesUse volume formulas
- Geometry2d — ProofsApply geometric concepts in modelling
- Probability — ConditionalUnderstand conditional probability
- Probability — CombinatoricsCounting principles; permutations; combinations
Algebra II
complex numbers; polynomials; exponentials; logarithms▶
Algebra II
complex numbers; polynomials; exponentials; logarithms- Expressions — Complex IntroPerform operations with complex numbers
- Quadratics — Polynomial OpsAdd, subtract, multiply polynomials
- Quadratics — Polynomial DivisionPolynomial long division; remainder theorem
- Quadratics — Zeros GraphIdentify zeros; construct rough graph
- Expressions — Rational RadicalSolve simple rational and radical equations
- LinearAlg — Compare FunctionsCompare properties of functions
- Expressions — LogarithmsLogarithmic functions
- Expressions — Composition InverseFunction composition and inverses
- LinearAlg — Linear Vs ExponentialConstruct exponential models
- Trigonometry — Unit CircleExtend trig to unit circle
- Trigonometry — ModellingModel periodic phenomena
- Statistics — Inference IntroUnderstand statistical inference
- Probability — Expected ValueCalculate expected values; use in decisions
Pre-Calculus / AP
limits; advanced functions; series▶
Pre-Calculus / AP
limits; advanced functions; series- Calculus — LimitsLimits and continuity
- Calculus — DerivativesDifferentiation rules and applications
- Calculus — IntegralsIntegration and applications
- Expressions — SeriesArithmetic and geometric series
- Quadratics — ConicsConic sections
- Trigonometry — IdentitiesProve and use trig identities
- Trigonometry — EquationsSolve trig equations
- Expressions — Advanced FunctionsAnalyse polynomial, rational, exponential, log functions
- LinearAlg — Model ComparisonCompare linear, quadratic, exponential models
- Vectors — IntroVectors: magnitude, direction, addition, scalar multiplication
- Vectors — AdvancedVectors: dot product, cross product, 3D operations
- Statistics — Hypothesis TestingHypothesis testing and significance
- Probability — NormalNormal distribution and z-scores
- Probability — BinomialBinomial probability distributions
- Probability — CombinatoricsPermutations, combinations, and counting principles