National Curriculum for Mathematics (England)

• Counting — RepresentCount objects, actions and sounds to 10 and beyond
• Counting — Read WriteSubitise (recognise quantities without counting) up to 5
• AddSub — Within 20Understand 'one more' and 'one less' within 10
• AddSub — DecomposeAutomatically recall number bonds for numbers 0–5
• Counting — Skip CountCount beyond ten (skip count by 2s to 20)
• PlaceValue — CompareCompare quantities up to 10, in different contexts
• Geometry2d — Shapes BasicRecognise and name 2D shapes (circle, square, triangle, rectangle)
• Geometry2d — PositionDescribe position using 'in, on, under, next to'
• Measurement — CompareCompare sizes and weights using everyday language
• Measurement — Time BasicRecognise daily routines and sequence events

• Counting — To 100Count to and across 100; identify one more/less
• Counting — Read WriteRead and write numbers to 20 in numerals and words
• PlaceValue — One More LessIdentify one more and one less
• AddSub — Within 20Add and subtract one-digit and two-digit numbers to 20
• AddSub — DecomposeNumber bonds within 20
• AddSub — SymbolsRead, write and interpret +, − and = signs
• MulDiv — ConceptSolve problems involving multiplication and division using materials
• Counting — Skip CountCount in multiples of 2, 5 and 10
• Fractions — Halves QuartersRecognise and find halves and quarters
• Measurement — CompareCompare and describe lengths, mass, capacity
• Measurement — Time BasicTell time to o'clock and half past
• Measurement — MoneyRecognise and know value of coins and notes
• Geometry2d — Shapes BasicRecognise and name common 2D and 3D shapes
• Geometry2d — PositionDescribe position, direction and movement

SATs

• PlaceValue — Tens OnesPlace value in two-digit numbers
• PlaceValue — CompareCompare and order numbers to 100
• AddSub — Within 100Add and subtract with two-digit numbers
• AddSub — Two StepSolve two-step addition/subtraction problems
• MulDiv — Tables 2 5 10Recall and use 2, 5, 10 times tables
• Fractions — IntroRecognise fractions ½, ¼, ⅓, ¾ of shapes and quantities
• Measurement — Units BasicChoose and use appropriate units (cm, m, g, kg, mL, L)
• Measurement — Time 5minTell time to 5 minutes
• Measurement — MoneyFind combinations of coins; make amounts; give change
• Statistics — BasicInterpret and construct pictograms, tally charts, tables
• Geometry2d — PropertiesIdentify and describe properties of 2D and 3D shapes
• Geometry2d — SymmetryIdentify lines of symmetry in 2D shapes

• PlaceValue — HundredsRecognise place value of each digit in 3-digit number
• AddSub — ColumnarAdd and subtract using formal column method
• MulDiv — Tables 3 4 8Recall and use 3, 4, 8 times tables
• MulDiv — Written IntroWrite and calculate using multiplication/division
• Fractions — TenthsCount up and down in tenths
• Fractions — Equivalent BasicRecognise simple equivalent fractions
• Fractions — Add Sub LikeAdd/subtract fractions with same denominator within one whole
• Fractions — Of SetSolve problems involving fractions of amounts
• Measurement — Metric ConversionsMeasure, compare, add/subtract: mm, cm, m, g, kg, mL, L
• Measurement — TimeTell and write time to nearest minute; vocabulary
• Measurement — MoneyAdd and subtract amounts of money; give change
• Statistics — Bar ChartsInterpret and present data using bar charts and pictograms
• Geometry2d — Angles IntroRecognise right angles; identify horizontal/vertical/parallel/perpendicular
• Geometry2d — DrawDraw 2D shapes

MTC (Multiplication Tables Check)

• PlaceValue — ThousandsRecognise place value in 4-digit numbers
• PlaceValue — RoundingRound to nearest 10, 100, 1,000
• PlaceValue — Roman NumeralsRead Roman numerals to 100
• MulDiv — TablesRecall multiplication and division facts to 12×12
• MulDiv — Short MultiplicationMultiply 2-digit and 3-digit by 1-digit using formal written method
• Fractions — EquivalentRecognise and show families of equivalent fractions
• Fractions — HundredthsRecognise and write hundredths
• Decimals — IntroRecognise and write tenths and hundredths as decimals
• Decimals — CompareCompare numbers with up to two decimal places
• Measurement — Convert BasicConvert between metric units
• Measurement — Time 24hrRead, write and convert 12/24-hour time
• Geometry2d — Area IntroFind area of rectilinear shapes by counting squares
• Geometry2d — ClassifyClassify triangles and quadrilaterals
• Geometry2d — AnglesIdentify acute and obtuse angles; compare/order angles
• Geometry2d — Coordinates BasicDescribe positions on a 2D grid as coordinates in first quadrant
• Geometry2d — TranslationsDescribe movements as translations
• Statistics — Bar ChartsInterpret and present discrete and continuous data

• PlaceValue — MillionsRead, write, order, compare numbers to 1,000,000
• NegNumbers — IntroInterpret negative numbers in context
• PlaceValue — RoundingRound any number up to 1,000,000
• MulDiv — Long MultiplicationMultiply up to 4-digit by 2-digit using long multiplication
• MulDiv — Short DivisionDivide up to 4-digit by 1-digit using short division
• Expressions — Factors PrimesIdentify multiples, factors, prime numbers, squares, cubes
• Fractions — CompareCompare and order fractions
• Fractions — Add Sub RelatedAdd/subtract fractions with related denominators
• Fractions — Multiply WholeMultiply proper fractions and mixed numbers by whole numbers
• Decimals — ThousandthsRead, write, order, compare decimals to 3dp
• Decimals — PercentRecognise the per cent symbol; equivalences
• Measurement — Convert AdvancedConvert between metric and imperial units
• Geometry2d — Area PerimeterCalculate area of rectangles and composite shapes
• Geometry2d — AnglesMeasure angles with protractor; know angle facts
• Geometry2d — Transformations BasicIdentify, describe and represent reflection and translation
• Statistics — Line GraphsSolve comparison, sum and difference problems using line graphs

SATs

• PlaceValue — MillionsRead, write, order, compare numbers to 10,000,000
• NegNumbers — IntervalsUse negative numbers in context; calculate intervals
• MulDiv — Long DivisionDivide by two-digit long divisor using written methods
• Expressions — Order Of OpsUse order of operations (BIDMAS)
• Fractions — Simplify ConvertUse common factors to simplify; common denominators to compare
• Fractions — Add Sub UnlikeAdd and subtract fractions with different denominators
• Fractions — MultiplyMultiply simple fractions; write answer in simplest form
• Fractions — Divide IntroDivide fractions by whole numbers
• Fractions — Equiv Decimal PercentRecall and use equivalences between fractions, decimals, percentages
• Decimals — Percent OfSolve problems involving percentages of amounts
• RatiosProp — IntroSolve problems involving ratio and proportion
• Expressions — NotationUse simple formulae; generate and describe linear number sequences
• Expressions — Missing NumberExpress missing number problems algebraically; enumerate possibilities
• Geometry2d — Area AdvancedCalculate area of parallelograms and triangles
• Geometry3d — Rectangular PrismCalculate volume of cuboids
• Geometry2d — Angle RulesFind unknown angles (at point, on line, vertically opposite)
• Geometry2d — Coordinates 4qDescribe positions on full coordinate grid (4 quadrants)
• Statistics — Pie ChartsInterpret and construct pie charts; calculate mean

• PlaceValue — Decimal SystemUnderstand and use place value for decimals and large numbers
• NegNumbers — OperationsOrder and perform operations with positive and negative integers
• Expressions — Prime FactorisationUse prime factorisation including for HCF and LCM
• Fractions — All OperationsUse four operations with fractions including mixed numbers
• Decimals — OperationsCalculate with decimals using all four operations
• RatiosProp — Simplify DivideUse ratio notation; reduce to simplest form; divide quantity in ratio
• Decimals — Percent ChangeDefine percentage as 'per hundred'; interpret percentage change
• Expressions — NotationUse and interpret algebraic notation; substitute numerical values
• Expressions — SimplifySimplify expressions by collecting like terms; expand brackets
• Expressions — Equations One StepSolve linear equations in one variable
• Expressions — SequencesGenerate terms of a sequence; find nth term of arithmetic sequence
• Geometry2d — AnglesUse angle facts: at point, on line, vertically opposite
• Geometry2d — PropertiesDerive and use properties of triangles, quadrilaterals, other polygons
• Geometry2d — ConstructionsUse ruler and compass constructions
• Geometry2d — TransformationsDescribe transformations: rotation, reflection, translation, enlargement
• Statistics — MeasuresDescribe, interpret and compare data using mean, range and other measures
• Probability — IntroRecord and describe probability; expected outcomes for single events

• Expressions — Powers IntroUse integer powers and associated real roots
• Expressions — Standard FormInterpret and compare standard form (A × 10^n)
• RatiosProp — DirectUnderstand and use direct proportion
• RatiosProp — Compound UnitsUse compound units: speed, density, pressure
• Expressions — Expand FactoriseExpand double brackets; factorise quadratic expressions
• Expressions — Equations Both SidesSolve linear equations with unknowns on both sides
• Expressions — InequalitiesSolve linear inequalities; represent on number line
• LinearAlg — Slope InterceptRecognise, sketch and produce graphs of linear functions; y = mx + c
• Geometry2d — Angle SumsDerive and apply angle sum of triangles and quadrilaterals
• Geometry2d — Parallel AnglesApply angle facts for parallel lines (alternate, corresponding, co-interior)
• Geometry2d — PythagorasKnow and apply Pythagoras' theorem
• Geometry3d — PrismsCalculate surface area and volume of prisms
• Statistics — Scatter PlotDescribe simple mathematical relationships between two variables using scatter graphs
• Probability — SystematicEnumerate sets using tables, grids, Venn diagrams, tree diagrams

• Expressions — SurdsSimplify surd expressions; rationalise denominators
• Expressions — ApproximateApproximate to specified degree of accuracy
• RatiosProp — Reverse PercentSolve problems involving reverse percentages
• RatiosProp — Growth DecaySet up and solve growth and decay problems
• Expressions — RearrangeRearrange formulae to change the subject
• LinearAlg — Nonlinear SystemSolve simultaneous equations (one linear, one quadratic)
• Quadratics — Graph IntroRecognise, sketch and interpret quadratic and cubic graphs
• Geometry2d — SimilarityApply similarity including trigonometric ratios
• Trigonometry — Right TriangleApply trigonometry to find angles and sides in right triangles
• Geometry2d — Vectors IntroDescribe translations as column vectors; addition of vectors
• Statistics — HistogramsConstruct and interpret histograms, cumulative frequency, box plots
• Probability — Tree DiagramsCalculate probability of combined events; tree diagrams
• Probability — Venn DiagramsEnumerate sets using Venn diagrams and set notation

• Expressions — BoundsUpper and lower bounds; error intervals
  Foundation & Higher
• RatiosProp — AlgebraicSet up and use algebraic direct and inverse proportion
  Foundation & Higher
• Quadratics — All MethodsSolve quadratic equations by factoring, formula, completing square
  Foundation & Higher
• Expressions — Algebraic ProofArgue mathematically; construct algebraic proofs
  Higher
• Expressions — IterationFind approximate solutions using iteration
  Higher
• LinearAlg — Rate Of ChangeInterpret rate of change from graphs (gradient as rate)
  Foundation & Higher
• LinearAlg — Area Under GraphCalculate and interpret area under a graph in real contexts
  Higher
• Geometry2d — Circle TheoremsApply and prove standard circle theorems
  Higher
• Trigonometry — Sine Cosine RuleApply the sine rule and cosine rule for non-right triangles
  Higher
• Geometry2d — VectorsApply addition and subtraction of vectors; parallel vectors
  Higher
• Statistics — Sampling MethodsApply systematic, stratified and random sampling
  Foundation & Higher
• Probability — ConditionalApply conditional probability
  Higher
• PercentagesCalculate percentages of amounts; percentage increase/decrease
  Foundation
• Ratios ProportionsSolve ratio and proportion problems in real-world contexts
  Foundation
• Measurement — Convert BasicConvert between metric units (mm/cm/m/km, g/kg)
  Foundation
• Mean Median ModeCalculate mean, median, mode and range from a data set
  Foundation
• Trigonometry — 3dApply trigonometry to 3D problems (boxes, pyramids, space diagonals)
  Higher

GCSE exam

Year 11 consolidates and extends Year 10 content for the GCSE exam. Topics overlap.

• Expressions — Equations AdvancedSolve complex equations including with fractions
  Higher
• Quadratics — DiscriminantUse discriminant to determine nature of roots
  Higher
• Expressions — Graph TransformationsApply transformations f(x+a), af(x), f(ax) to graphs
  Higher
• Expressions — Quadratic InequalitiesSolve quadratic inequalities
  Higher
• Expressions — Advanced IndicesSurds: simplify, rationalise denominators
  Higher
• Quadratics — Completing SquareCompleting the square; turning points
  Higher
• Geometry2d — Congruence ProofApply congruence criteria (SSS, SAS, ASA, RHS)
  Higher
• Geometry2d — Circles TheoremsCircle theorems: angles, tangents, chords
  Higher
• Vectors — IntroVectors: column notation, magnitude, addition
  Foundation & Higher
• Geometry3d — CompositeCalculate volume and surface area of composite 3D shapes
  Foundation & Higher
• Statistics — HistogramsConstruct and interpret frequency tables, histograms, box plots
  Higher
• Probability — Combined AdvancedCalculate probability of combined events (with/without replacement)
  Higher
• Probability — IntroCalculate probability of single events
  Foundation
• Expressions — FormulasSubstitute values into formulae and expressions
  Foundation
• Linear EquationSolve linear equations in one variable
  Foundation
• Fractions — Add Sub UnlikeAdd and subtract fractions with different denominators
  Foundation

• Expressions — Advanced IndicesManipulate surds and rationalise; laws of indices
• Quadratics — All MethodsComplete the square; solve quadratics; discriminant
• LinearAlg — LinesEquations of lines; parallel/perpendicular conditions
• Geometry2d — Circles EquationsCircle equations; tangent and normal
• Expressions — Partial FractionsPartial fraction decomposition
• Trigonometry — GraphsGraphs of sin, cos, tan; transformations
• Trigonometry — IdentitiesSimple trig identities and equations
• Calculus — DerivativesDifferentiation from first principles; power rule; applications
• Calculus — IntegralsDefinite integrals; area under curve
• Expressions — LogarithmsLaws of logarithms; solving exponential equations
• Statistics — SamplingTypes of data; sampling methods
• Statistics — HistogramsHistograms, frequency polygons, cumulative frequency
• Statistics — MeasuresCentral tendency and dispersion: mean, variance, standard deviation
• Probability — BinomialBinomial distribution

• Expressions — Sequences AdvancedArithmetic and geometric sequences and series; sigma notation
• Trigonometry — IdentitiesDouble angle, addition formulae; prove identities
• Trigonometry — InverseInverse trig functions; solve equations in given intervals
• Calculus — TechniquesIntegration by substitution and by parts
• Calculus — ApplicationsTangents, normals, stationary points, optimisation
• Calculus — Diff EquationsSeparable differential equations
• Expressions — Advanced GraphsSketch and interpret polynomial, rational, modulus functions
• Geometry2d — Vectors 3d3D vectors; magnitude; scalar product
• Probability — NormalNormal distribution; hypothesis testing
• Statistics — Hypothesis TestingHypothesis testing for binomial and normal
• Probability — ConditionalConditional probability; Bayes' theorem
• Vectors — Advanced3D vectors: cross product, lines and planes
• Expressions — Partial FractionsPartial fraction decomposition
• Expressions — LogarithmsNatural logarithms; exponential growth and decay