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)- Skip CountingCount to 100 by ones and by tens
- Represent NumbersWrite numbers 0–20; represent quantities
- Compare & Order NumbersCount to determine how many; compare groups
- AdditionRepresent addition/subtraction with objects and equations
- AdditionFluently add and subtract within 5
- AdditionDecompose numbers ≤10 into pairs
- Tens & OnesCompose and decompose 11–19 as ten and ones
- Compare MeasurementsDescribe and compare measurable attributes
- Representing DataClassify objects into categories; count each
- Recognising 2D ShapesIdentify and describe 2D and 3D shapes; positions
Grade 1
0–120▶
Grade 1
0–120- AdditionAdd and subtract within 20; word problems
- AdditionAdd three whole numbers whose sum ≤ 20
- Addition PropertiesApply commutative and associative properties
- SubtractionSubtraction as unknown-addend
- AdditionFluently add/subtract within 10
- Equality & InequalityMeaning of equals sign; true/false equations
- Missing NumberFind unknown in equation
- Skip CountingCount to 120; read and write numerals
- Tens & OnesTwo-digit numbers as tens and ones
- Tens & OnesCompare two two-digit numbers using >, =, <
- AdditionAdd within 100
- Compare MeasurementsOrder objects by length; measure using non-standard units
- TimeTell time to hour and half-hour
- Recognising 2D ShapesDistinguish between defining/non-defining attributes
- Introduction to FractionsPartition circles and rectangles into halves/fourths
Grade 2
0–1000▶
Grade 2
0–1000- AdditionFluently add/subtract within 100
- AdditionSolve two-step word problems
- Even & Odd NumbersDetermine even/odd; write equations for even numbers
- Tens & OnesThree-digit place value
- Skip CountingSkip count by 5s, 10s, 100s
- Tens & OnesCompare three-digit numbers
- AdditionAdd/subtract within 1,000
- Basic UnitsMeasure in inches, feet, cm, meters
- TimeTell time to 5 minutes
- Decimal ArithmeticSolve word problems involving money
- Representing DataGenerate measurement data; line plots
- Recognising 2D ShapesRecognise and draw shapes; identify faces
- Introduction to FractionsPartition shapes into halves, thirds, fourths
Grade 3
0–10,000; fractions introduced▶
Grade 3
0–10,000; fractions introduced- MultiplicationInterpret products of whole numbers
- Long DivisionDivision as unknown factor
- MultiplicationSolve multiplication/division word problems
- MultiplicationFluently multiply/divide within 100
- Multiplication PropertiesApply commutative, associative, distributive properties
- Algebraic PatternsIdentify arithmetic patterns
- Rounding & EstimationRound whole numbers to nearest 10 or 100
- AdditionFluently add/subtract within 1,000 using strategies
- Fraction RepresentationsUnderstand fractions as numbers
- Fraction RepresentationsRepresent fractions on number line
- Fraction RepresentationsExplain equivalent fractions; compare fractions
- TimeTell time to nearest minute; elapsed time
- Basic UnitsMeasure mass and capacity (g, kg, L)
- Area & PerimeterUnderstand area; measure by counting unit squares
- Area & PerimeterSolve perimeter problems
- Classify Triangles & QuadrilateralsUnderstand 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- MultiplicationMultiply up to 4-digit by 1-digit
- Long DivisionDivide with remainders (1-digit divisor)
- Factors, GCF & LCMFind factor pairs; identify prime/composite
- Algebraic PatternsGenerate and analyse number patterns
- Tens & OnesRead/write multi-digit whole numbers
- Tens & OnesCompare multi-digit numbers
- Rounding & EstimationRound to any place
- AdditionFluently add/subtract using standard algorithm
- Fraction RepresentationsExplain and generate equivalent fractions
- Fraction RepresentationsCompare fractions with different numerators/denominators
- Adding FractionsAdd fractions with like denominators
- Subtracting FractionsSubtract fractions with like denominators
- Multiplying FractionsMultiply fraction by whole number
- Decimal ArithmeticDecimal notation for fractions (tenths/hundredths)
- Decimal ArithmeticCompare two decimals to hundredths
- Basic ConversionsConvert within measurement system
- Area & PerimeterApply area and perimeter formulas
- AnglesMeasure and classify angles
- SymmetryIdentify line-symmetric figures
- Shape PropertiesDraw and identify lines, angles, rays
Grade 5
0–billions; decimals to thousandths▶
Grade 5
0–billions; decimals to thousandths- Order of OperationsEvaluate expressions with parentheses
- Algebraic PatternsGenerate and compare two numerical patterns
- Tens & OnesUnderstand place value system (powers of 10)
- Tens & OnesMultiply/divide by powers of 10
- MultiplicationMultiply multi-digit whole numbers
- Long DivisionDivide by two-digit divisors
- Decimal ArithmeticRead/write/compare decimals to thousandths
- Decimal ArithmeticAdd, subtract, multiply, divide decimals
- Adding FractionsAdd fractions with unlike denominators
- Subtracting FractionsSubtract fractions with unlike denominators
- Multiplying FractionsMultiply fractions and mixed numbers
- Dividing FractionsDivide with unit fractions
- Advanced ConversionsConvert measurement units within a system
- VolumeUnderstand volume; measure by counting cubes
- VolumeVolume of rectangular prisms
- Coordinates (First Quadrant)Graph points in first quadrant
- Classify Triangles & QuadrilateralsClassify 2D shapes in a hierarchy
Grade 6
rational numbers; ratios; expressions▶
Grade 6
rational numbers; ratios; expressions- Ratios & ProportionsUnderstand ratio concepts; use ratio reasoning
- Ratios & ProportionsUnit rates; solve problems
- PercentagesFind percent of a quantity
- Long DivisionFluently divide multi-digit numbers
- Dividing FractionsDivide fractions by fractions
- Negative NumbersUnderstand positive and negative numbers
- Negative NumbersOrder and absolute value of rational numbers
- Simplify ExpressionsWrite and evaluate expressions
- Simplify ExpressionsApply properties to generate equivalent expressions
- Introduction to EquationsSolve one-variable equations and inequalities
- FormulasRepresent relationships between quantities
- Area & PerimeterArea of triangles, quadrilaterals, polygons
- 3D Formulas (Volume & Surface Area)Surface area from nets
- VolumeVolume with fractional edges
- Comparing Data SetsStatistical questions; centre and variability
- Mean, Median & ModeMean, median, MAD, IQR
Grade 7
rational numbers; proportional relationships▶
Grade 7
rational numbers; proportional relationships- Ratios & ProportionsAnalyse proportional relationships
- Ratios & ProportionsCompute unit rates with fractions
- PercentagesMulti-step percent problems
- Negative NumbersAdd, subtract, multiply, divide rational numbers
- Manipulate ExpressionsUse properties to rewrite expressions
- Two-Step EquationsSolve multi-step real-life problems
- InequalitiesSolve inequalities of the form px + q > r
- Recognising 2D ShapesDraw geometric shapes with given conditions
- Area & PerimeterArea and circumference of circles; angle relationships
- VolumeVolume and surface area of prisms
- Shape PropertiesDescribe cross-sections of 3D shapes
- Statistical InvestigationUnderstand sampling; draw inferences
- Comparing Data SetsCompare two populations
- Introduction to ProbabilityDevelop probability models
- Systematic ListingCompound events; tree diagrams
Grade 8
real numbers; linear equations; functions▶
Grade 8
real numbers; linear equations; functions- Exponents & PowersKnow and apply properties of integer exponents
- Exponents & PowersSquare root and cube root symbols
- Scientific NotationScientific notation; operations
- Introduction to Linear RelationshipsGraph proportional relationships; interpret slope
- Systems of EquationsSolve systems of two linear equations
- FunctionsDefine, evaluate, compare functions
- Introduction to Linear RelationshipsUse functions to model linear relationships
- FunctionsDistinguish linear from nonlinear
- SymmetryUnderstand congruence via transformations
- Similarity & Scale FactorsUnderstand congruence and similarity
- Pythagorean TheoremExplain and apply Pythagorean theorem
- Pythagorean TheoremApply Pythagorean theorem to find distance
- VolumeVolume of cylinders, cones, spheres
- Comparing Data SetsConstruct and interpret scatter plots
- Comparing Data SetsUse line of best fit; interpret slope/intercept
Algebra I
real numbers; polynomials; quadratics▶
Algebra I
real numbers; polynomials; quadratics- Simplify ExpressionsInterpret the structure of expressions
- Manipulate ExpressionsRewrite expressions in equivalent forms
- Quadratic EquationsFactor quadratic expressions
- Advanced EquationsCreate equations in one variable
- Systems of EquationsCreate equations in two variables
- Introduction to EquationsSolve linear equations and inequalities
- Systems of EquationsSolve systems of equations
- Quadratic EquationsSolve quadratic equations
- FunctionsUnderstand function notation
- FunctionsInterpret key features of graphs
- FunctionsWrite function from relationships
- FunctionsDistinguish linear and exponential
- Compound InterestApply compound-interest models to savings and investment
- Comparing Data SetsSummarise and interpret bivariate data
Geometry
geometric reasoning; proofs▶
Geometry
geometric reasoning; proofs- SymmetryRepresent transformations in the plane
- Similarity & Scale FactorsProve geometric theorems
- Similarity & Scale FactorsUnderstand similarity via transformations
- Trigonometry (SOH CAH TOA)Define trig ratios; solve problems
- CirclesUnderstand and apply circle theorems
- CirclesDerive circle equation; complete the square
- Coordinates (Four Quadrants)Use coordinates to prove theorems
- 3D ShapesIdentify cross-sections of 3D objects
- VolumeUse volume formulas
- Polygon PropertiesApply geometric concepts in modelling
- Formal Probability RulesUnderstand conditional probability
- Formal Probability RulesCounting principles; permutations; combinations
Algebra II
complex numbers; polynomials; exponentials; logarithms▶
Algebra II
complex numbers; polynomials; exponentials; logarithms- Number SetsPerform operations with complex numbers
- PolynomialsAdd, subtract, multiply polynomials
- PolynomialsPolynomial long division; remainder theorem
- PolynomialsIdentify zeros; construct rough graph
- Manipulate ExpressionsSolve simple rational and radical equations
- FunctionsCompare properties of functions
- LogarithmsLogarithmic functions
- FormulasFunction composition and inverses
- FunctionsConstruct exponential models
- Unit Circle — Exact ValuesExtend trig to unit circle
- Trigonometric GraphsModel periodic phenomena
- Advanced StatisticsUnderstand statistical inference
- Formal Probability RulesCalculate expected values; use in decisions
Pre-Calculus / AP
limits; advanced functions; series▶
Pre-Calculus / AP
limits; advanced functions; series- LimitsLimits and continuity
- DifferentiationDifferentiation rules and applications
- IntegrationIntegration and applications
- SequencesArithmetic and geometric series
- Quadratic EquationsConic sections
- Trigonometric IdentitiesProve and use trig identities
- Trigonometric EquationsSolve trig equations
- FunctionsAnalyse polynomial, rational, exponential, log functions
- Linear ModellingCompare linear, quadratic, exponential models
- Vectors — Introduction (2D)Vectors: magnitude, direction, addition, scalar multiplication
- Vectors — Advanced (3D)Vectors: dot product, cross product, 3D operations
- Advanced StatisticsHypothesis testing and significance
- Formal Probability RulesNormal distribution and z-scores
- Formal Probability RulesBinomial probability distributions
- Formal Probability RulesPermutations, combinations, and counting principles