National Curriculum for Mathematics (England)

• Represent NumbersCount objects, actions and sounds to 10 and beyond
• Represent NumbersSubitise (recognise quantities without counting) up to 5
• AdditionUnderstand 'one more' and 'one less' within 10
• AdditionAutomatically recall number bonds for numbers 0–5
• Skip CountingCount beyond ten (skip count by 2s to 20)
• Tens & OnesCompare quantities up to 10, in different contexts
• Recognising 2D ShapesRecognise and name 2D shapes (circle, square, triangle, rectangle)
• Coordinates (First Quadrant)Describe position using 'in, on, under, next to'
• Compare MeasurementsCompare sizes and weights using everyday language
• TimeRecognise daily routines and sequence events

• Skip CountingCount to and across 100; identify one more/less
• Represent NumbersRead and write numbers to 20 in numerals and words
• Tens & OnesIdentify one more and one less
• AdditionAdd and subtract one-digit and two-digit numbers to 20
• AdditionNumber bonds within 20
• Equality & InequalityRead, write and interpret +, − and = signs
• MultiplicationSolve problems involving multiplication and division using materials
• Skip CountingCount in multiples of 2, 5 and 10
• Introduction to FractionsRecognise and find halves and quarters
• Compare MeasurementsCompare and describe lengths, mass, capacity
• TimeTell time to o'clock and half past
• Decimal ArithmeticRecognise and know value of coins and notes
• Recognising 2D ShapesRecognise and name common 2D and 3D shapes
• Coordinates (First Quadrant)Describe position, direction and movement

SATs

• Tens & OnesPlace value in two-digit numbers
• Tens & OnesCompare and order numbers to 100
• AdditionAdd and subtract with two-digit numbers
• AdditionSolve two-step addition/subtraction problems
• MultiplicationRecall and use 2, 5, 10 times tables
• Introduction to FractionsRecognise fractions ½, ¼, ⅓, ¾ of shapes and quantities
• Basic UnitsChoose and use appropriate units (cm, m, g, kg, mL, L)
• TimeTell time to 5 minutes
• Decimal ArithmeticFind combinations of coins; make amounts; give change
• Representing DataInterpret and construct pictograms, tally charts, tables
• Shape PropertiesIdentify and describe properties of 2D and 3D shapes
• SymmetryIdentify lines of symmetry in 2D shapes

• Tens & OnesRecognise place value of each digit in 3-digit number
• AdditionAdd and subtract using formal column method
• MultiplicationRecall and use 3, 4, 8 times tables
• MultiplicationWrite and calculate using multiplication/division
• Introduction to FractionsCount up and down in tenths
• Fraction RepresentationsRecognise simple equivalent fractions
• Adding FractionsAdd/subtract fractions with same denominator within one whole
• Introduction to FractionsSolve problems involving fractions of amounts
• Basic ConversionsMeasure, compare, add/subtract: mm, cm, m, g, kg, mL, L
• TimeTell and write time to nearest minute; vocabulary
• Decimal ArithmeticAdd and subtract amounts of money; give change
• Representing DataInterpret and present data using bar charts and pictograms
• AnglesRecognise right angles; identify horizontal/vertical/parallel/perpendicular
• Recognising 2D ShapesDraw 2D shapes

MTC (Multiplication Tables Check)

• Tens & OnesRecognise place value in 4-digit numbers
• Rounding & EstimationRound to nearest 10, 100, 1,000
• Tens & OnesRead Roman numerals to 100
• MultiplicationRecall multiplication and division facts to 12×12
• MultiplicationMultiply 2-digit and 3-digit by 1-digit using formal written method
• Fraction RepresentationsRecognise and show families of equivalent fractions
• Introduction to FractionsRecognise and write hundredths
• Decimal ArithmeticRecognise and write tenths and hundredths as decimals
• Decimal ArithmeticCompare numbers with up to two decimal places
• Basic ConversionsConvert between metric units
• TimeRead, write and convert 12/24-hour time
• Area & PerimeterFind area of rectilinear shapes by counting squares
• Classify Triangles & QuadrilateralsClassify triangles and quadrilaterals
• AnglesIdentify acute and obtuse angles; compare/order angles
• Coordinates (First Quadrant)Describe positions on a 2D grid as coordinates in first quadrant
• SymmetryDescribe movements as translations
• Representing DataInterpret and present discrete and continuous data

• Tens & OnesRead, write, order, compare numbers to 1,000,000
• Negative NumbersInterpret negative numbers in context
• Rounding & EstimationRound any number up to 1,000,000
• MultiplicationMultiply up to 4-digit by 2-digit using long multiplication
• Long DivisionDivide up to 4-digit by 1-digit using short division
• Factors, GCF & LCMIdentify multiples, factors, prime numbers, squares, cubes
• Fraction RepresentationsCompare and order fractions
• Adding FractionsAdd/subtract fractions with related denominators
• Multiplying FractionsMultiply proper fractions and mixed numbers by whole numbers
• Decimal ArithmeticRead, write, order, compare decimals to 3dp
• PercentagesRecognise the per cent symbol; equivalences
• Advanced ConversionsConvert between metric and imperial units
• Area & PerimeterCalculate area of rectangles and composite shapes
• AnglesMeasure angles with protractor; know angle facts
• SymmetryIdentify, describe and represent reflection and translation
• Representing DataSolve comparison, sum and difference problems using line graphs

SATs

• Tens & OnesRead, write, order, compare numbers to 10,000,000
• Negative NumbersUse negative numbers in context; calculate intervals
• Long DivisionDivide by two-digit long divisor using written methods
• Order of OperationsUse order of operations (BIDMAS)
• Fraction / Decimal / PercentUse common factors to simplify; common denominators to compare
• Adding FractionsAdd and subtract fractions with different denominators
• Multiplying FractionsMultiply simple fractions; write answer in simplest form
• Dividing FractionsDivide fractions by whole numbers
• Fraction / Decimal / PercentRecall and use equivalences between fractions, decimals, percentages
• PercentagesSolve problems involving percentages of amounts
• Ratios & ProportionsSolve problems involving ratio and proportion
• Simplify ExpressionsUse simple formulae; generate and describe linear number sequences
• Missing NumberExpress missing number problems algebraically; enumerate possibilities
• Area & PerimeterCalculate area of parallelograms and triangles
• VolumeCalculate volume of cuboids
• AnglesFind unknown angles (at point, on line, vertically opposite)
• Coordinates (Four Quadrants)Describe positions on full coordinate grid (4 quadrants)
• Representing DataInterpret and construct pie charts; calculate mean

• Tens & OnesUnderstand and use place value for decimals and large numbers
• Negative NumbersOrder and perform operations with positive and negative integers
• Factors, GCF & LCMUse prime factorisation including for HCF and LCM
• Fraction Word ProblemsUse four operations with fractions including mixed numbers
• Decimal ArithmeticCalculate with decimals using all four operations
• Ratios & ProportionsUse ratio notation; reduce to simplest form; divide quantity in ratio
• PercentagesDefine percentage as 'per hundred'; interpret percentage change
• Simplify ExpressionsUse and interpret algebraic notation; substitute numerical values
• Simplify ExpressionsSimplify expressions by collecting like terms; expand brackets
• Introduction to EquationsSolve linear equations in one variable
• SequencesGenerate terms of a sequence; find nth term of arithmetic sequence
• AnglesUse angle facts: at point, on line, vertically opposite
• Shape PropertiesDerive and use properties of triangles, quadrilaterals, other polygons
• Geometric ConstructionsUse ruler and compass constructions
• SymmetryDescribe transformations: rotation, reflection, translation, enlargement
• Mean, Median & ModeDescribe, interpret and compare data using mean, range and other measures
• Introduction to ProbabilityRecord and describe probability; expected outcomes for single events

• Introduction to PowersUse integer powers and associated real roots
• Scientific NotationInterpret and compare standard form (A × 10^n)
• Ratios & ProportionsUnderstand and use direct proportion
• Ratios & ProportionsUse compound units: speed, density, pressure
• Manipulate ExpressionsExpand double brackets; factorise quadratic expressions
• Two-Step EquationsSolve linear equations with unknowns on both sides
• InequalitiesSolve linear inequalities; represent on number line
• Introduction to Linear RelationshipsRecognise, sketch and produce graphs of linear functions; y = mx + c
• AnglesDerive and apply angle sum of triangles and quadrilaterals
• AnglesApply angle facts for parallel lines (alternate, corresponding, co-interior)
• Pythagorean TheoremKnow and apply Pythagoras' theorem
• VolumeCalculate surface area and volume of prisms
• Comparing Data SetsDescribe simple mathematical relationships between two variables using scatter graphs
• Systematic ListingEnumerate sets using tables, grids, Venn diagrams, tree diagrams

• Exponents & PowersSimplify surd expressions; rationalise denominators
• Rounding & EstimationApproximate to specified degree of accuracy
• PercentagesSolve problems involving reverse percentages
• PercentagesSet up and solve growth and decay problems
• Manipulate ExpressionsRearrange formulae to change the subject
• Systems of EquationsSolve simultaneous equations (one linear, one quadratic)
• Quadratic EquationsRecognise, sketch and interpret quadratic and cubic graphs
• Similarity & Scale FactorsApply similarity including trigonometric ratios
• Trigonometry (SOH CAH TOA)Apply trigonometry to find angles and sides in right triangles
• Vectors — Introduction (2D)Describe translations as column vectors; addition of vectors
• Representing DataConstruct and interpret histograms, cumulative frequency, box plots
• Formal Probability RulesCalculate probability of combined events; tree diagrams
• Formal Probability RulesEnumerate sets using Venn diagrams and set notation

• Rounding & EstimationUpper and lower bounds; error intervals
  Foundation & Higher
• Ratios & ProportionsSet up and use algebraic direct and inverse proportion
  Foundation & Higher
• Quadratic EquationsSolve quadratic equations by factoring, formula, completing square
  Foundation & Higher
• Manipulate ExpressionsArgue mathematically; construct algebraic proofs
  Higher
• Advanced EquationsFind approximate solutions using iteration
  Higher
• FunctionsInterpret rate of change from graphs (gradient as rate)
  Foundation & Higher
• FunctionsCalculate and interpret area under a graph in real contexts
  Higher
• CirclesApply and prove standard circle theorems
  Higher
• Sine & Cosine RulesApply the sine rule and cosine rule for non-right triangles
  Higher
• Vectors — Introduction (2D)Apply addition and subtraction of vectors; parallel vectors
  Higher
• Statistical InvestigationApply systematic, stratified and random sampling
  Foundation & Higher
• Formal Probability RulesApply conditional probability
  Higher
• PercentagesCalculate percentages of amounts; percentage increase/decrease
  Foundation
• Ratios & ProportionsSolve ratio and proportion problems in real-world contexts
  Foundation
• Basic ConversionsConvert between metric units (mm/cm/m/km, g/kg)
  Foundation
• Mean, Median & ModeCalculate mean, median, mode and range from a data set
  Foundation
• Compound InterestUse compound interest formulae for savings and investment problems
  Foundation & Higher
• 3D TrigonometryApply 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.

• Advanced EquationsSolve complex equations including with fractions
  Higher
• Quadratic EquationsUse discriminant to determine nature of roots
  Higher
• FunctionsApply transformations f(x+a), af(x), f(ax) to graphs
  Higher
• InequalitiesSolve quadratic inequalities
  Higher
• Exponents & PowersSurds: simplify, rationalise denominators
  Higher
• Quadratic EquationsCompleting the square; turning points
  Higher
• Similarity & Scale FactorsApply congruence criteria (SSS, SAS, ASA, RHS)
  Higher
• CirclesCircle theorems: angles, tangents, chords
  Higher
• Vectors — Introduction (2D)Vectors: column notation, magnitude, addition
  Foundation & Higher
• VolumeCalculate volume and surface area of composite 3D shapes
  Foundation & Higher
• Representing DataConstruct and interpret frequency tables, histograms, box plots
  Higher
• Formal Probability RulesCalculate probability of combined events (with/without replacement)
  Higher
• Introduction to ProbabilityCalculate probability of single events
  Foundation
• FormulasSubstitute values into formulae and expressions
  Foundation
• Linear EquationsSolve linear equations in one variable
  Foundation
• Adding FractionsAdd and subtract fractions with different denominators
  Foundation

• Exponents & PowersManipulate surds and rationalise; laws of indices
• Quadratic EquationsComplete the square; solve quadratics; discriminant
• Introduction to Linear RelationshipsEquations of lines; parallel/perpendicular conditions
• CirclesCircle equations; tangent and normal
• Manipulate ExpressionsPartial fraction decomposition
• Trigonometric GraphsGraphs of sin, cos, tan; transformations
• Trigonometric IdentitiesSimple trig identities and equations
• DifferentiationDifferentiation from first principles; power rule; applications
• IntegrationDefinite integrals; area under curve
• LogarithmsLaws of logarithms; solving exponential equations
• Statistical InvestigationTypes of data; sampling methods
• Representing DataHistograms, frequency polygons, cumulative frequency
• Mean, Median & ModeCentral tendency and dispersion: mean, variance, standard deviation
• Formal Probability RulesBinomial distribution

• SequencesArithmetic and geometric sequences and series; sigma notation
• Trigonometric IdentitiesDouble angle, addition formulae; prove identities
• Inverse TrigonometryInverse trig functions; solve equations in given intervals
• IntegrationIntegration by substitution and by parts
• DifferentiationTangents, normals, stationary points, optimisation
• IntegrationSeparable differential equations
• FunctionsSketch and interpret polynomial, rational, modulus functions
• Vectors — Advanced (3D)3D vectors; magnitude; scalar product
• Formal Probability RulesNormal distribution; hypothesis testing
• Advanced StatisticsHypothesis testing for binomial and normal
• Formal Probability RulesConditional probability; Bayes' theorem
• Vectors — Advanced (3D)3D vectors: cross product, lines and planes
• Manipulate ExpressionsPartial fraction decomposition
• LogarithmsNatural logarithms; exponential growth and decay