Common Core State Standards for Mathematics
Common Core State Standards for Mathematics (CCSSM) definerer hva elever skal forstå på hvert trinn. Bla gjennom alle standarder nedenfor med lenker til gratis trening og gjennomgåtte eksempler.
Kindergarten
0–20 (counting to 100)▶
Kindergarten
0–20 (counting to 100)- TellemønsterCount to 100 by ones and by tens
- Representere tallWrite numbers 0–20; represent quantities
- Sammenlign og sorter tallCount to determine how many; compare groups
- AddisjonRepresent addition/subtraction with objects and equations
- AddisjonFluently add and subtract within 5
- AddisjonDecompose numbers ≤10 into pairs
- Tiere og enereCompose and decompose 11–19 as ten and ones
- Sammenlign målDescribe and compare measurable attributes
- Representere dataClassify objects into categories; count each
- Gjenkjenne 2D-figurerIdentify and describe 2D and 3D shapes; positions
Grade 1
0–120▶
Grade 1
0–120- AddisjonAdd and subtract within 20; word problems
- AddisjonAdd three whole numbers whose sum ≤ 20
- AddisjonsegenskaperApply commutative and associative properties
- SubtraksjonSubtraction as unknown-addend
- AddisjonFluently add/subtract within 10
- Likhet og ulikhetMeaning of equals sign; true/false equations
- Finn det manglende talletFind unknown in equation
- TellemønsterCount to 120; read and write numerals
- Tiere og enereTwo-digit numbers as tens and ones
- Tiere og enereCompare two two-digit numbers using >, =, <
- AddisjonAdd within 100
- Sammenlign målOrder objects by length; measure using non-standard units
- TidTell time to hour and half-hour
- Gjenkjenne 2D-figurerDistinguish between defining/non-defining attributes
- Introduksjon til brøkPartition circles and rectangles into halves/fourths
Grade 2
0–1000▶
Grade 2
0–1000- AddisjonFluently add/subtract within 100
- AddisjonSolve two-step word problems
- Partall og oddetallDetermine even/odd; write equations for even numbers
- Tiere og enereThree-digit place value
- TellemønsterSkip count by 5s, 10s, 100s
- Tiere og enereCompare three-digit numbers
- AddisjonAdd/subtract within 1,000
- Grunnleggende enheterMeasure in inches, feet, cm, meters
- TidTell time to 5 minutes
- DesimalregningSolve word problems involving money
- Representere dataGenerate measurement data; line plots
- Gjenkjenne 2D-figurerRecognise and draw shapes; identify faces
- Introduksjon til brøkPartition shapes into halves, thirds, fourths
Grade 3
0–10,000; fractions introduced▶
Grade 3
0–10,000; fractions introduced- MultiplikasjonInterpret products of whole numbers
- Lang divisjonDivision as unknown factor
- MultiplikasjonSolve multiplication/division word problems
- MultiplikasjonFluently multiply/divide within 100
- MultiplikasjonsegenskaperApply commutative, associative, distributive properties
- Algebraiske mønstreIdentify arithmetic patterns
- Avrunding og estimeringRound whole numbers to nearest 10 or 100
- AddisjonFluently add/subtract within 1,000 using strategies
- BrøkrepresentasjonerUnderstand fractions as numbers
- BrøkrepresentasjonerRepresent fractions on number line
- BrøkrepresentasjonerExplain equivalent fractions; compare fractions
- TidTell time to nearest minute; elapsed time
- Grunnleggende enheterMeasure mass and capacity (g, kg, L)
- Areal og omkretsUnderstand area; measure by counting unit squares
- Areal og omkretsSolve perimeter problems
- Klassifiser trekanter og firkanterUnderstand 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- MultiplikasjonMultiply up to 4-digit by 1-digit
- Lang divisjonDivide with remainders (1-digit divisor)
- Faktorer, SFF og MFMFind factor pairs; identify prime/composite
- Algebraiske mønstreGenerate and analyse number patterns
- Tiere og enereRead/write multi-digit whole numbers
- Tiere og enereCompare multi-digit numbers
- Avrunding og estimeringRound to any place
- AddisjonFluently add/subtract using standard algorithm
- BrøkrepresentasjonerExplain and generate equivalent fractions
- BrøkrepresentasjonerCompare fractions with different numerators/denominators
- Addere brøkerAdd fractions with like denominators
- Subtrahere brøkerSubtract fractions with like denominators
- Multiplisere brøkerMultiply fraction by whole number
- DesimalregningDecimal notation for fractions (tenths/hundredths)
- DesimalregningCompare two decimals to hundredths
- Grunnleggende omregningerConvert within measurement system
- Areal og omkretsApply area and perimeter formulas
- VinklerMeasure and classify angles
- SymmetriIdentify line-symmetric figures
- Egenskaper til figurerDraw and identify lines, angles, rays
Grade 5
0–billions; decimals to thousandths▶
Grade 5
0–billions; decimals to thousandths- RegnerekkefølgeEvaluate expressions with parentheses
- Algebraiske mønstreGenerate and compare two numerical patterns
- Tiere og enereUnderstand place value system (powers of 10)
- Tiere og enereMultiply/divide by powers of 10
- MultiplikasjonMultiply multi-digit whole numbers
- Lang divisjonDivide by two-digit divisors
- DesimalregningRead/write/compare decimals to thousandths
- DesimalregningAdd, subtract, multiply, divide decimals
- Addere brøkerAdd fractions with unlike denominators
- Subtrahere brøkerSubtract fractions with unlike denominators
- Multiplisere brøkerMultiply fractions and mixed numbers
- Dividere brøkerDivide with unit fractions
- Avanserte omregningerConvert measurement units within a system
- VolumUnderstand volume; measure by counting cubes
- VolumVolume of rectangular prisms
- Koordinater (første kvadrant)Graph points in first quadrant
- Klassifiser trekanter og firkanterClassify 2D shapes in a hierarchy
Grade 6
rational numbers; ratios; expressions▶
Grade 6
rational numbers; ratios; expressions- Forhold og proporsjonerUnderstand ratio concepts; use ratio reasoning
- Forhold og proporsjonerUnit rates; solve problems
- ProsentFind percent of a quantity
- Lang divisjonFluently divide multi-digit numbers
- Dividere brøkerDivide fractions by fractions
- Negative tallUnderstand positive and negative numbers
- Negative tallOrder and absolute value of rational numbers
- Forenkle uttrykkWrite and evaluate expressions
- Forenkle uttrykkApply properties to generate equivalent expressions
- Introduksjon til likningerSolve one-variable equations and inequalities
- FormlerRepresent relationships between quantities
- Areal og omkretsArea of triangles, quadrilaterals, polygons
- 3D-formler (volum og overflate)Surface area from nets
- VolumVolume with fractional edges
- Sammenligne datasettStatistical questions; centre and variability
- Gjennomsnitt, median og typetallMean, median, MAD, IQR
Grade 7
rational numbers; proportional relationships▶
Grade 7
rational numbers; proportional relationships- Forhold og proporsjonerAnalyse proportional relationships
- Forhold og proporsjonerCompute unit rates with fractions
- ProsentMulti-step percent problems
- Negative tallAdd, subtract, multiply, divide rational numbers
- Omforme uttrykkUse properties to rewrite expressions
- Tostegs-likningerSolve multi-step real-life problems
- UlikheterSolve inequalities of the form px + q > r
- Gjenkjenne 2D-figurerDraw geometric shapes with given conditions
- Areal og omkretsArea and circumference of circles; angle relationships
- VolumVolume and surface area of prisms
- Egenskaper til figurerDescribe cross-sections of 3D shapes
- Statistisk undersøkelseUnderstand sampling; draw inferences
- Sammenligne datasettCompare two populations
- Introduksjon til sannsynlighetDevelop probability models
- Systematisk listingCompound events; tree diagrams
Grade 8
real numbers; linear equations; functions▶
Grade 8
real numbers; linear equations; functions- Potenser og eksponenterKnow and apply properties of integer exponents
- Potenser og eksponenterSquare root and cube root symbols
- StandardformScientific notation; operations
- Introduksjon til lineære sammenhengerGraph proportional relationships; interpret slope
- LikningssettSolve systems of two linear equations
- FunksjonerDefine, evaluate, compare functions
- Introduksjon til lineære sammenhengerUse functions to model linear relationships
- FunksjonerDistinguish linear from nonlinear
- SymmetriUnderstand congruence via transformations
- Likhet og skaleringsfaktorerUnderstand congruence and similarity
- Pytagoras' setningExplain and apply Pythagorean theorem
- Pytagoras' setningApply Pythagorean theorem to find distance
- VolumVolume of cylinders, cones, spheres
- Sammenligne datasettConstruct and interpret scatter plots
- Sammenligne datasettUse line of best fit; interpret slope/intercept
Algebra I
real numbers; polynomials; quadratics▶
Algebra I
real numbers; polynomials; quadratics- Forenkle uttrykkInterpret the structure of expressions
- Omforme uttrykkRewrite expressions in equivalent forms
- AndregradslikningerFactor quadratic expressions
- Avanserte likningerCreate equations in one variable
- LikningssettCreate equations in two variables
- Introduksjon til likningerSolve linear equations and inequalities
- LikningssettSolve systems of equations
- AndregradslikningerSolve quadratic equations
- FunksjonerUnderstand function notation
- FunksjonerInterpret key features of graphs
- FunksjonerWrite function from relationships
- FunksjonerDistinguish linear and exponential
- Renters renteApply compound-interest models to savings and investment
- Sammenligne datasettSummarise and interpret bivariate data
Geometry
geometric reasoning; proofs▶
Geometry
geometric reasoning; proofs- SymmetriRepresent transformations in the plane
- Likhet og skaleringsfaktorerProve geometric theorems
- Likhet og skaleringsfaktorerUnderstand similarity via transformations
- Trigonometri (SOH CAH TOA)Define trig ratios; solve problems
- SirklerUnderstand and apply circle theorems
- SirklerDerive circle equation; complete the square
- Koordinater (fire kvadranter)Use coordinates to prove theorems
- 3D-figurerIdentify cross-sections of 3D objects
- VolumUse volume formulas
- MangekantegenskaperApply geometric concepts in modelling
- Formelle sannsynlighetsreglerUnderstand conditional probability
- Formelle sannsynlighetsreglerCounting principles; permutations; combinations
Algebra II
complex numbers; polynomials; exponentials; logarithms▶
Algebra II
complex numbers; polynomials; exponentials; logarithms- TallmengderPerform operations with complex numbers
- PolynomerAdd, subtract, multiply polynomials
- PolynomerPolynomial long division; remainder theorem
- PolynomerIdentify zeros; construct rough graph
- Omforme uttrykkSolve simple rational and radical equations
- FunksjonerCompare properties of functions
- LogaritmerLogarithmic functions
- FormlerFunction composition and inverses
- FunksjonerConstruct exponential models
- Enhetssirkelen — Eksakte verdierExtend trig to unit circle
- Trigonometriske graferModel periodic phenomena
- Avansert statistikkUnderstand statistical inference
- Formelle sannsynlighetsreglerCalculate expected values; use in decisions
Pre-Calculus / AP
limits; advanced functions; series▶
Pre-Calculus / AP
limits; advanced functions; series- GrenseverdierLimits and continuity
- DerivasjonDifferentiation rules and applications
- IntegrasjonIntegration and applications
- TallfølgerArithmetic and geometric series
- AndregradslikningerConic sections
- Trigonometriske identiteterProve and use trig identities
- Trigonometriske likningerSolve trig equations
- FunksjonerAnalyse polynomial, rational, exponential, log functions
- Lineær modelleringCompare linear, quadratic, exponential models
- Vektorer — Introduksjon (2D)Vectors: magnitude, direction, addition, scalar multiplication
- Vektorer — Videregående (3D)Vectors: dot product, cross product, 3D operations
- Avansert statistikkHypothesis testing and significance
- Formelle sannsynlighetsreglerNormal distribution and z-scores
- Formelle sannsynlighetsreglerBinomial probability distributions
- Formelle sannsynlighetsreglerPermutations, combinations, and counting principles