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Variation Theory

Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

  • Please read!
    • Introduction
    • Activity type 1: Practice
    • Activity type 2: Rule
    • Activity type 3: Pattern
    • Activity type 4: Demonstration
    • Top Tips for using these sequences in the classroom
    • Further reading
    • My book
  • Topics
    • Number
      • Arithmetic
      • Decimals
      • Factors, multiples, primes
      • Fraction decimal percentage equivalence
      • Fractions
      • Modulo arithmetic
      • Negative numbers
      • Order of operations (BIDMAS)
      • Percentages
      • Place value
      • Powers and Indices
      • Proportion
      • Ratio
      • Rounding and estimating
      • Standard form
      • Surds
    • Algebra
      • Algebraic fractions
      • Brackets – expand
      • Brackets – factorise
      • Coordinates
      • Formula
      • Function Machines
      • Functions
      • Inequalities
      • Introducing algebra
      • Quadratic graphs
      • Proof
      • Sequences
      • Simplifying expressions
      • Simultaneous equations
      • Solving linear Equations
      • Solving other equations
      • Solving quadratic equations
      • Straight line graphs
    • Geometry and Measures
      • 3D
      • Angles
      • Circle theorems
      • Circles
      • Compound measures
      • Perimeter and area
      • Pythagoras’ theorem
      • Shape properties
      • Similarity
      • Surface area
      • Transformations
      • Trigonometry
      • Units of measurement
      • Volume
    • Statistics and Probability
      • Averages and range
      • Probability
      • Representing data
      • Sampling
      • Sorting data
    • A Level
      • Binomial expansion
      • Differentiation
      • Functions
      • Logarithms
      • Polynomial division
      • Statistics
  • Get involved!
  • Websites
  • Books
  • Podcast
  • Newsletters
  • CPD
  • Support
May 22, 2018July 30, 2018 Craig BartonGeometry and Measures, Trigonometry

Finding missing angles

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May 22, 2018March 26, 2019 Craig BartonAlgebra, Simultaneous equestions

The final step

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May 14, 2018July 30, 2018 Craig BartonAlgebra, Coordinates

Plotting coordinates to form a square

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May 9, 2018July 30, 2018 Craig BartonAlgebra, Algebraic fractions

Simplifying algebraic fractions (basic)

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May 9, 2018July 30, 2018 Craig BartonFractions, Number

Reverse fractions of an amount

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May 9, 2018July 30, 2018 Craig BartonAlgebra, Solving linear Equations

Solving linear equations by cross multiplication

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May 9, 2018July 30, 2018 Craig BartonGeometry and Measures, Time

Converting decimals to hours and minutes

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May 7, 2018July 30, 2018 Craig BartonAlgebra, Straight line graphs

Effect of varying y co-ordinates on gradient

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May 2, 2018July 30, 2018 Craig BartonAlgebra, Algebraic fractions

Adding and subtracting algebraic fractions

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May 2, 2018July 30, 2018 Craig BartonAlgebra, Algebraic fractions

Multiplying and dividing algebraic fractions

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May 1, 2018July 30, 2018 Craig BartonRepresenting data, Statistics and Probability

Scatter diagrams – correlation strength

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April 27, 2018September 7, 2021 Craig BartonGeometry and Measures, Pythagoras' theorem

Missing lengths with Pythagoras’ theorem

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April 26, 2018July 30, 2018 Craig BartonAlgebra, Algebraic fractions

Simplifying algebraic fractions

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April 24, 2018July 30, 2018 Craig BartonAlgebra, Solving linear Equations

Eliminating variables

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April 23, 2018July 30, 2018 Craig BartonFraction decimal percentage equivalence, Number

Converting decimals to percentages

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April 23, 2018July 30, 2018 Craig BartonFraction decimal percentage equivalence, Number

Converting percentages to decimals

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April 23, 2018July 30, 2018 Craig BartonDecimals, Number

Ordering decimals

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April 23, 2018July 30, 2018 Craig BartonAlgebra, Coordinates

Midpoint of two coordinates

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April 18, 2018July 30, 2018 Craig BartonAlgebra, Formula

Writing formula

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April 18, 2018July 25, 2018 Craig BartonNumber, Proportion

Direct proportion (rulers)

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April 18, 2018July 30, 2018 Craig BartonFractions, Number

Fractions of fractions

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Posts navigation

Older posts
Newer posts

Most recent sequences

  • Integer Solutions to Inequalities
  • Transformation of functions (2 activities)
  • Using samples
  • General Binomial Expansion: Range of Validity
  • Arithmetic Sequences: Finding a and d

Most popular sequences

  • Expanding Single Brackets (4 exercises)
  • Sharing in a ratio: Fill in the gaps
  • Multiplying Fractions: Cross Cancelling
  • Adding Fractions
  • Changing the subject of a formula (6 exercises)

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Categories

  • A Level
    • Binomial expansion
    • Complex numbers
    • Differentiation
    • Functions
    • Integration
    • Logarithms
    • Polynomial division
    • Statistics
  • Algebra
    • Algebraic fractions
    • Brackets – expand
    • Brackets – factorise
    • Coordinates
    • Formula
    • Function Machines
    • Functions
    • Inequalities
    • Introducing algebra
    • Proof
    • Quadratic graphs
    • Sequences
    • Simplifying expressions
    • Simultaneous equestions
    • Solving linear Equations
    • Solving other equations
    • Solving quadratic equations
    • Straight line graphs
    • Writing expressions
  • Geometry and Measures
    • 3D
    • Angles
    • Circle theorems
    • Circles
    • Compound measures
    • Constructions
    • Perimeter and area
    • Pythagoras' theorem
    • Shape properties
    • Similarity
    • Surface area
    • Time
    • Transformations
    • Trigonometry
    • Units of measurement
    • Vectors
    • Volume
  • Number
    • Arithmetic
    • Decimals
    • Factors, multiples, primes
    • Fraction decimal percentage equivalence
    • Fractions
    • Modulo arithmetic
    • Negative numbers
    • Order of operations (BIDMAS)
    • Percentages
    • Place value
    • Powers and Indices
    • Proportion
    • Ratio
    • Rounding and estimating
    • Standard form
    • Surds
  • Statistics and Probability
    • Averages and range
    • Probability
    • Representing data
    • Sampling
    • Sorting data

Topics

1/2absinC3D shapesAdding algebraic fractionsAdding and subtracting vectorsAdding decimalsAdding fractionsAdding negative numbersAdding surdsAlgebraic fractionsAlgebraic indicesAlgebraic notationAlgebraic proofAlgebraic vocabularyAlternate anglesAlternate segment theoremAngle at the centreAngle bisectorAngle in a semi-circleAnglesAngles at a pointAngles in a polygonAngles in a triangleAngles in isosceles trianglesAngles in the same segmentAngles on a straight lineArc lengthArea of a circleArea of a parallelogramArea of a quadrilateralArea of a rectangleArea of a trapeziumArea of a triangleArea scale factorArithmeticAverages and rangeBar modellingBase 2BearingsBIDMASBinaryBinomial distributionBinomial expansionBounds of errorBox and whisker diagramsBracketsBus-stop methodCapture-RecaptureChain RuleCircle theoremsCircumference of a circleClass widthCo-interior anglesCoefficientsCollecting like termsCombined percentage changeCombining ratioCompleting the squareComplex numbersComposite functionsCompound interestCompound ratioConjugatesConstructionsConversion graphsConverting between 12 hours and 24 hoursConverting decimals to percentagesConverting fractions to decimalsConverting fractions to percentagesConverting percentages to decimalsConverting percentages to fractionsConverting ratio to fractionsConverting to different basesCoordinatesCorrelationCorresponding anglesCosine ruleCube numbersCube rootCumulative probabilitiesCyclic quadrilateralsDefinite integrationde Moivre’s TheoremDenaryDensityDepreciationDifference of two squaresDifferential equationsDifferentiationDirect proportionDistributive lawDividing algebraic fractionsDividing decimalsDividing fractionsDividing negative numbersDividing termsDrawing axesEnlargementEquation of a circleEquation of a straight line graphEquation of a tangentEquations from ratioEquivalent fractionsEquivalent ratioError intervalsEstimating anglesEstimationExact trigonometric valuesExchange ratesExpand double bracketsExpand single bracketsExpand triple bracketsExperimental probabilityExponential functionExterior anglesFactorise into a single bracketFactorise into double bracketsFactorise into triple bracketsFactorsFactors multiples primesFactor theoremFinding one part of a ratioForming expressionsFractional decreaseFractional increaseFractional indicesFraction decimal percentage equivalenceFractionsFractions of an amountFractions on a number lineFrequencyFrequency densityFrequency treeFunction machinesFunction notationGCSE RevisionGeometric sequencesGradientGroup widthHighest common factorHistogramsHorizontal linesHyperbolic functionsHypotenuseImperial unitsImproper fractionsIndicesInequalities on a number lineInequality notationIntegrationInterior anglesInverse functionsInverse operationsInverse proportionIsometric drawingsLaw of indices - divisionLaw of indices - multiplicationLaw of indices - negativesLaw of indices - powersLength of a line segmentLength scale factorLimiting value of sequencesLinear inequalitiesLinear sequencesLine of best fitLociLogarithmsLowest common multipleMeanMean from a frequency tableMean from grouped dataMeasuring anglesMedianMental additionMental multiplicationMental subtractionMidpointMinutes and hoursMixed number fractionsModeMode from a frequency tableMultiplesMultiplication law of indicesMultiplyingMultiplying algebraic expressionsMultiplying algebraic fractionsMultiplying decimalsMultiplying fractionsMultiplying negative numbersMultiplying surdsMultiplying termsMultiplying vectorsMutually exclusive eventsNaming coordinatesNegative numbers - addingNegative numbers - subtractingNormal distributionnth term ruleOperations with surdsOrdering decimalsOrdering fractionsOrdering negative numbersOrder of operationsParallel linesParallel vectorsParts of a circlePercentage changePercentage decreasePercentage increasePercentage of an amountPercentagesPerimeter of a rectanglePerpendicular linesPictogramsPie chart anglesPie chartsPlans and elevationsPolygonsPolynomial divisionPositive integer powersPower of zeroPowersPressurePrime factorsPrime numbersPrismsProbabilityProbability of a single eventProbability of combined eventsProbability on a number lineProduct of factorsProduct of prime factorsProduct ruleProperties of a triangleProperties of quadrilateralsProperties of shapesPythagorasQuadratic inequalitiesQuadratic sequencesQuotient ruleRangeRatio as equationsRatio as fractionsRationalising the denominatorReading scalesRearranging equationsRearranging formulaReciprocalsRecurrence relationsRecurring decimalsReflectionRelated calculationsRepresenting on a number lineReverse percentagesRootsRoots of an equationRotationRounding to 1 decimal placeRounding to 2 decimal placesRounding to 3 decimal placesRounding to nearest 10Rounding to nearest 100Rounding to nearest multipleRounding to nearest wholeRounding to significant figuresSample space diagramScatter diagramsSector areaSector of a circleSet notationSharing in a ratioSignificant figuresSimilar shapesSimplifying algebraic fractionsSimplifying expressionsSimplifying fractionsSimplifying ratioSimplifying surdsSimultaneous equationsSine ruleSketching quadratic graphsSketching straight line graphsSOH CAH TOASolving equations with powersSolving equations with rootsSolving inequalitiesSolving linear equationsSolving quadratic equationsSolving simultaneous equationsSpeed distance timeSquare numbersSquare rootStandard deviationStandard formStem and leaf diagramsStratified samplingSub setsSubstitutionSubtracting algebraic fractionsSubtracting decimalsSubtracting fractionsSubtracting negative numbersSurface area of a cuboidSurface area of a cylinderSurface area of a prismSurface area of a sphereTable of valuesTangent and radiusTangentsTelling the timeTemperatureTerm to term sequencesTimeTransformation of functionsTranslationTree diagramsTrigonometryTurning pointsTwo-way tablesUnitary ratioUnit fractionsUnits of areaUnits of lengthUnits of volumeUsing place valueUsing the quadratic formulaValue of a decimalValue of a digitVector notationVenn diagramsVertical linesVertically opposite anglesVolume of a coneVolume of a cuboidVolume of a cylinderVolume of a frustrumVolume of a prismVolume of a pyramidVolume of a sphereVolume scale factorWriting expressionsWriting formulaWriting ratioWritten additionWritten divisionWritten subtractionx-intercepty-intercept

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