National Curriculum for Mathematics (England)

• Representere tallCount objects, actions and sounds to 10 and beyond
• Representere tallSubitise (recognise quantities without counting) up to 5
• AddisjonUnderstand 'one more' and 'one less' within 10
• AddisjonAutomatically recall number bonds for numbers 0–5
• TellemønsterCount beyond ten (skip count by 2s to 20)
• Tiere og enereCompare quantities up to 10, in different contexts
• Gjenkjenne 2D-figurerRecognise and name 2D shapes (circle, square, triangle, rectangle)
• Koordinater (første kvadrant)Describe position using 'in, on, under, next to'
• Sammenlign målCompare sizes and weights using everyday language
• TidRecognise daily routines and sequence events

• TellemønsterCount to and across 100; identify one more/less
• Representere tallRead and write numbers to 20 in numerals and words
• Tiere og enereIdentify one more and one less
• AddisjonAdd and subtract one-digit and two-digit numbers to 20
• AddisjonNumber bonds within 20
• Likhet og ulikhetRead, write and interpret +, − and = signs
• MultiplikasjonSolve problems involving multiplication and division using materials
• TellemønsterCount in multiples of 2, 5 and 10
• Introduksjon til brøkRecognise and find halves and quarters
• Sammenlign målCompare and describe lengths, mass, capacity
• TidTell time to o'clock and half past
• DesimalregningRecognise and know value of coins and notes
• Gjenkjenne 2D-figurerRecognise and name common 2D and 3D shapes
• Koordinater (første kvadrant)Describe position, direction and movement

SATs

• Tiere og enerePlace value in two-digit numbers
• Tiere og enereCompare and order numbers to 100
• AddisjonAdd and subtract with two-digit numbers
• AddisjonSolve two-step addition/subtraction problems
• MultiplikasjonRecall and use 2, 5, 10 times tables
• Introduksjon til brøkRecognise fractions ½, ¼, ⅓, ¾ of shapes and quantities
• Grunnleggende enheterChoose and use appropriate units (cm, m, g, kg, mL, L)
• TidTell time to 5 minutes
• DesimalregningFind combinations of coins; make amounts; give change
• Representere dataInterpret and construct pictograms, tally charts, tables
• Egenskaper til figurerIdentify and describe properties of 2D and 3D shapes
• SymmetriIdentify lines of symmetry in 2D shapes

• Tiere og enereRecognise place value of each digit in 3-digit number
• AddisjonAdd and subtract using formal column method
• MultiplikasjonRecall and use 3, 4, 8 times tables
• MultiplikasjonWrite and calculate using multiplication/division
• Introduksjon til brøkCount up and down in tenths
• BrøkrepresentasjonerRecognise simple equivalent fractions
• Addere brøkerAdd/subtract fractions with same denominator within one whole
• Introduksjon til brøkSolve problems involving fractions of amounts
• Grunnleggende omregningerMeasure, compare, add/subtract: mm, cm, m, g, kg, mL, L
• TidTell and write time to nearest minute; vocabulary
• DesimalregningAdd and subtract amounts of money; give change
• Representere dataInterpret and present data using bar charts and pictograms
• VinklerRecognise right angles; identify horizontal/vertical/parallel/perpendicular
• Gjenkjenne 2D-figurerDraw 2D shapes

MTC (Multiplication Tables Check)

• Tiere og enereRecognise place value in 4-digit numbers
• Avrunding og estimeringRound to nearest 10, 100, 1,000
• Tiere og enereRead Roman numerals to 100
• MultiplikasjonRecall multiplication and division facts to 12×12
• MultiplikasjonMultiply 2-digit and 3-digit by 1-digit using formal written method
• BrøkrepresentasjonerRecognise and show families of equivalent fractions
• Introduksjon til brøkRecognise and write hundredths
• DesimalregningRecognise and write tenths and hundredths as decimals
• DesimalregningCompare numbers with up to two decimal places
• Grunnleggende omregningerConvert between metric units
• TidRead, write and convert 12/24-hour time
• Areal og omkretsFind area of rectilinear shapes by counting squares
• Klassifiser trekanter og firkanterClassify triangles and quadrilaterals
• VinklerIdentify acute and obtuse angles; compare/order angles
• Koordinater (første kvadrant)Describe positions on a 2D grid as coordinates in first quadrant
• SymmetriDescribe movements as translations
• Representere dataInterpret and present discrete and continuous data

• Tiere og enereRead, write, order, compare numbers to 1,000,000
• Negative tallInterpret negative numbers in context
• Avrunding og estimeringRound any number up to 1,000,000
• MultiplikasjonMultiply up to 4-digit by 2-digit using long multiplication
• Lang divisjonDivide up to 4-digit by 1-digit using short division
• Faktorer, SFF og MFMIdentify multiples, factors, prime numbers, squares, cubes
• BrøkrepresentasjonerCompare and order fractions
• Addere brøkerAdd/subtract fractions with related denominators
• Multiplisere brøkerMultiply proper fractions and mixed numbers by whole numbers
• DesimalregningRead, write, order, compare decimals to 3dp
• ProsentRecognise the per cent symbol; equivalences
• Avanserte omregningerConvert between metric and imperial units
• Areal og omkretsCalculate area of rectangles and composite shapes
• VinklerMeasure angles with protractor; know angle facts
• SymmetriIdentify, describe and represent reflection and translation
• Representere dataSolve comparison, sum and difference problems using line graphs

SATs

• Tiere og enereRead, write, order, compare numbers to 10,000,000
• Negative tallUse negative numbers in context; calculate intervals
• Lang divisjonDivide by two-digit long divisor using written methods
• RegnerekkefølgeUse order of operations (BIDMAS)
• Brøk / desimal / prosentUse common factors to simplify; common denominators to compare
• Addere brøkerAdd and subtract fractions with different denominators
• Multiplisere brøkerMultiply simple fractions; write answer in simplest form
• Dividere brøkerDivide fractions by whole numbers
• Brøk / desimal / prosentRecall and use equivalences between fractions, decimals, percentages
• ProsentSolve problems involving percentages of amounts
• Forhold og proporsjonerSolve problems involving ratio and proportion
• Forenkle uttrykkUse simple formulae; generate and describe linear number sequences
• Finn det manglende talletExpress missing number problems algebraically; enumerate possibilities
• Areal og omkretsCalculate area of parallelograms and triangles
• VolumCalculate volume of cuboids
• VinklerFind unknown angles (at point, on line, vertically opposite)
• Koordinater (fire kvadranter)Describe positions on full coordinate grid (4 quadrants)
• Representere dataInterpret and construct pie charts; calculate mean

• Tiere og enereUnderstand and use place value for decimals and large numbers
• Negative tallOrder and perform operations with positive and negative integers
• Faktorer, SFF og MFMUse prime factorisation including for HCF and LCM
• Brøk tekstoppgaverUse four operations with fractions including mixed numbers
• DesimalregningCalculate with decimals using all four operations
• Forhold og proporsjonerUse ratio notation; reduce to simplest form; divide quantity in ratio
• ProsentDefine percentage as 'per hundred'; interpret percentage change
• Forenkle uttrykkUse and interpret algebraic notation; substitute numerical values
• Forenkle uttrykkSimplify expressions by collecting like terms; expand brackets
• Introduksjon til likningerSolve linear equations in one variable
• TallfølgerGenerate terms of a sequence; find nth term of arithmetic sequence
• VinklerUse angle facts: at point, on line, vertically opposite
• Egenskaper til figurerDerive and use properties of triangles, quadrilaterals, other polygons
• Geometriske konstruksjonerUse ruler and compass constructions
• SymmetriDescribe transformations: rotation, reflection, translation, enlargement
• Gjennomsnitt, median og typetallDescribe, interpret and compare data using mean, range and other measures
• Introduksjon til sannsynlighetRecord and describe probability; expected outcomes for single events

• Introduksjon til potenserUse integer powers and associated real roots
• StandardformInterpret and compare standard form (A × 10^n)
• Forhold og proporsjonerUnderstand and use direct proportion
• Forhold og proporsjonerUse compound units: speed, density, pressure
• Omforme uttrykkExpand double brackets; factorise quadratic expressions
• Tostegs-likningerSolve linear equations with unknowns on both sides
• UlikheterSolve linear inequalities; represent on number line
• Introduksjon til lineære sammenhengerRecognise, sketch and produce graphs of linear functions; y = mx + c
• VinklerDerive and apply angle sum of triangles and quadrilaterals
• VinklerApply angle facts for parallel lines (alternate, corresponding, co-interior)
• Pytagoras' setningKnow and apply Pythagoras' theorem
• VolumCalculate surface area and volume of prisms
• Sammenligne datasettDescribe simple mathematical relationships between two variables using scatter graphs
• Systematisk listingEnumerate sets using tables, grids, Venn diagrams, tree diagrams

• Potenser og eksponenterSimplify surd expressions; rationalise denominators
• Avrunding og estimeringApproximate to specified degree of accuracy
• ProsentSolve problems involving reverse percentages
• ProsentSet up and solve growth and decay problems
• Omforme uttrykkRearrange formulae to change the subject
• LikningssettSolve simultaneous equations (one linear, one quadratic)
• AndregradslikningerRecognise, sketch and interpret quadratic and cubic graphs
• Likhet og skaleringsfaktorerApply similarity including trigonometric ratios
• Trigonometri (SOH CAH TOA)Apply trigonometry to find angles and sides in right triangles
• Vektorer — Introduksjon (2D)Describe translations as column vectors; addition of vectors
• Representere dataConstruct and interpret histograms, cumulative frequency, box plots
• Formelle sannsynlighetsreglerCalculate probability of combined events; tree diagrams
• Formelle sannsynlighetsreglerEnumerate sets using Venn diagrams and set notation

• Avrunding og estimeringUpper and lower bounds; error intervals
  Foundation & Higher
• Forhold og proporsjonerSet up and use algebraic direct and inverse proportion
  Foundation & Higher
• AndregradslikningerSolve quadratic equations by factoring, formula, completing square
  Foundation & Higher
• Omforme uttrykkArgue mathematically; construct algebraic proofs
  Høyere
• Avanserte likningerFind approximate solutions using iteration
  Høyere
• FunksjonerInterpret rate of change from graphs (gradient as rate)
  Foundation & Higher
• FunksjonerCalculate and interpret area under a graph in real contexts
  Høyere
• SirklerApply and prove standard circle theorems
  Høyere
• Sinus- og cosinussetningenApply the sine rule and cosine rule for non-right triangles
  Høyere
• Vektorer — Introduksjon (2D)Apply addition and subtraction of vectors; parallel vectors
  Høyere
• Statistisk undersøkelseApply systematic, stratified and random sampling
  Foundation & Higher
• Formelle sannsynlighetsreglerApply conditional probability
  Høyere
• ProsentCalculate percentages of amounts; percentage increase/decrease
  Grunnleggende
• Forhold og proporsjonerSolve ratio and proportion problems in real-world contexts
  Grunnleggende
• Grunnleggende omregningerConvert between metric units (mm/cm/m/km, g/kg)
  Grunnleggende
• Gjennomsnitt, median og typetallCalculate mean, median, mode and range from a data set
  Grunnleggende
• Renters renteUse compound interest formulae for savings and investment problems
  Foundation & Higher
• Tredimensjonal trigonometriApply trigonometry to 3D problems (boxes, pyramids, space diagonals)
  Høyere

GCSE exam

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

• Avanserte likningerSolve complex equations including with fractions
  Høyere
• AndregradslikningerUse discriminant to determine nature of roots
  Høyere
• FunksjonerApply transformations f(x+a), af(x), f(ax) to graphs
  Høyere
• UlikheterSolve quadratic inequalities
  Høyere
• Potenser og eksponenterSurds: simplify, rationalise denominators
  Høyere
• AndregradslikningerCompleting the square; turning points
  Høyere
• Likhet og skaleringsfaktorerApply congruence criteria (SSS, SAS, ASA, RHS)
  Høyere
• SirklerCircle theorems: angles, tangents, chords
  Høyere
• Vektorer — Introduksjon (2D)Vectors: column notation, magnitude, addition
  Foundation & Higher
• VolumCalculate volume and surface area of composite 3D shapes
  Foundation & Higher
• Representere dataConstruct and interpret frequency tables, histograms, box plots
  Høyere
• Formelle sannsynlighetsreglerCalculate probability of combined events (with/without replacement)
  Høyere
• Introduksjon til sannsynlighetCalculate probability of single events
  Grunnleggende
• FormlerSubstitute values into formulae and expressions
  Grunnleggende
• Lineære likningerSolve linear equations in one variable
  Grunnleggende
• Addere brøkerAdd and subtract fractions with different denominators
  Grunnleggende

• Potenser og eksponenterManipulate surds and rationalise; laws of indices
• AndregradslikningerComplete the square; solve quadratics; discriminant
• Introduksjon til lineære sammenhengerEquations of lines; parallel/perpendicular conditions
• SirklerCircle equations; tangent and normal
• Omforme uttrykkPartial fraction decomposition
• Trigonometriske graferGraphs of sin, cos, tan; transformations
• Trigonometriske identiteterSimple trig identities and equations
• DerivasjonDifferentiation from first principles; power rule; applications
• IntegrasjonDefinite integrals; area under curve
• LogaritmerLaws of logarithms; solving exponential equations
• Statistisk undersøkelseTypes of data; sampling methods
• Representere dataHistograms, frequency polygons, cumulative frequency
• Gjennomsnitt, median og typetallCentral tendency and dispersion: mean, variance, standard deviation
• Formelle sannsynlighetsreglerBinomial distribution

• TallfølgerArithmetic and geometric sequences and series; sigma notation
• Trigonometriske identiteterDouble angle, addition formulae; prove identities
• Invers trigonometriInverse trig functions; solve equations in given intervals
• IntegrasjonIntegration by substitution and by parts
• DerivasjonTangents, normals, stationary points, optimisation
• IntegrasjonSeparable differential equations
• FunksjonerSketch and interpret polynomial, rational, modulus functions
• Vektorer — Videregående (3D)3D vectors; magnitude; scalar product
• Formelle sannsynlighetsreglerNormal distribution; hypothesis testing
• Avansert statistikkHypothesis testing for binomial and normal
• Formelle sannsynlighetsreglerConditional probability; Bayes' theorem
• Vektorer — Videregående (3D)3D vectors: cross product, lines and planes
• Omforme uttrykkPartial fraction decomposition
• LogaritmerNatural logarithms; exponential growth and decay