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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
September 7, 2021 Craig BartonNumber, Rounding and estimating

Estimating with significant figures

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September 7, 2021 Craig BartonNumber, Rounding and estimating

Identifying significant figures

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September 7, 2021 Craig BartonRepresenting data, Statistics and Probability

Reading Venn Diagrams

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July 5, 2021 Craig BartonAngles, Geometry and Measures

Estimating the size of angles

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June 30, 2021 Craig BartonGeometry and Measures, Number, Pythagoras' theorem, Surds

Finding Hypotenuses With Surds

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June 30, 2021 Craig BartonGeometry and Measures, Pythagoras' theorem

Finding Hypotenuses With Overlapping Triangles

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June 30, 2021 Craig BartonGeometry and Measures, Pythagoras' theorem

The Converse of Pythagoras’ Theorem

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June 30, 2021 Craig BartonNumber, Percentages

Expressing numbers as a percentage (Calculator)

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June 30, 2021 Craig BartonAlgebra, Simplifying expressions

Simplifying Algebraic Expressions: Addition and Multiplication

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June 30, 2021 Craig BartonAlgebra, Solving linear Equations

Solving Two-step Linear Equations with the Four Operations

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June 30, 2021 Craig BartonAlgebra, Solving quadratic equations

Introduction to Solving Quadratic Equations

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June 30, 2021 Craig BartonAlgebra, Brackets - factorise, Quadratic graphs

Sketching Quadratics From Factorised Form

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June 30, 2021 Craig BartonAlgebra, Brackets - factorise, Quadratic graphs

Co-ordinates of Turning Point from Completing the Square

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June 30, 2021 Craig BartonFactors, multiples, primes, Number

Factor, multiple, both, neither?

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June 30, 2021 Craig BartonCircles, Geometry and Measures

Circles – units of answer

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June 15, 2021 Craig BartonNegative numbers, Number, Place value

Ascend, descend, neither?

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May 7, 2021 Craig BartonAlgebra, Formula, Function Machines

Linking Function Machines with Substitution and Solving Equations

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May 7, 2021May 7, 2021 Craig BartonAlgebra, Function Machines

Finding Inputs and Outputs with Function Machines

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May 7, 2021May 7, 2021 Craig BartonAngles, Geometry and Measures

Angles in a triangle

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May 7, 2021 Craig BartonNumber, Percentages

Simple Interest – What is the rate of interest?

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May 7, 2021 Craig BartonNumber, Percentages

Simple interest

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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)
  • Mixed percentage multipliers
  • Missing lengths with Pythagoras' theorem
  • Changing the subject of a formula (6 exercises)
  • Simplifying algebraic fractions

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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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