mathematics department – curriculum outline year 7 … · mathematics department – curriculum...

MathematicsDepartment–CurriculumOutline

Year7

2016-17 Unit WhatwillIdo? HowwillIbeassessed?Term1 Number

PlaceValue

Understandanduseplacevaluefordecimals,measuresandintegersofanysize.Orderpositiveandnegativeintegers,usethenumberlineasamodelfororderingoftherealnumbers;usethesymbols=,≠,<,>,≤,≥Roundnumbersandmeasurestoanappropriatedegreeofaccuracy[forexample,toanumberofdecimalplacesorsignificantfigures]Useapproximationthroughroundingtoestimateanswersandcalculatepossibleresultingerrorsexpressedusinginequalitynotationa<x≤b

NumberAdditionandSubtraction

Useformalwrittenmethodsforadditionandsubtractionofintegersanddecimals.Recogniseanduserelationshipsbetweenadditionandsubtractionincludinginverseoperations.Calculateandsolveproblemsinvolvingperimeter.

Weekbeg.17thOctober2016Halfterm1FCATAssessment1hour

NumberMultiplicationandDivision

Multiplyanddivideby10,100and1000Useformalwrittenmethodsformultiplicationanddivisionofintegersanddecimals.Recogniseanduserelationshipsbetweenoperationsincludinginverseoperations.Understandtheorderofoperations.Usetheconceptsandvocabularyofprimenumbers,factors(or

divisors),commonfactorsandhighestcommonfactor(HCF).Useintegerpowersandassociatedrealroots(square,cubeandhigher),recognisepowersof2,3,4,5anddistinguishbetweenexactrepresentationsofrootsandtheirdecimalapproximations.Calculateandsolveproblemsinvolvingareaofrectangles,trianglesandparallelograms.Calculatethemeanofasetofdiscretedata.

Weekbeg.12thDecember2016MasteryTerm1Assessment1hour

Term2 NumberFractions1

Identifyanduseequivalentfractions.Compareandorderfractions;usethesymbols=,≠,<,>,≤,≥Convertbetweenmixednumbersandimproperfractions.Simplifyfractions.Usetheconceptsandvocabularyofmultiplesandlowestcommonmultiple(LCM).Addandsubtractanyfraction

• Fractionswiththesamedenominator.

• Fractionswithadenominatorthatisamultipleoftheother.

• Fractionswithdifferentdenominators

Convertbetweenfractionsanddecimals

• Tenths,hundredths,thousandths

• Associatingafractionwithdivisiontoconvertanyfractiontoadecimal.

Findafractionofanamount.

Statistics1 Understandthedatahandlingcycle.

Collect,organiseandinterpretdata.

• Tallycharts• Median,modeandrange

Drawandinterpretbarcharts,pictogramsandlinegraphs.

NumberNegativenumbers

Usethefouroperationswithnegativenumbers.

Mid-yearexamWeekbeg.13th&20thMarch2017MasteryTerm2Assessment1hour

Term3 Algebra1 IntroductiontoalgebraUnderstandthataletterrepresentsavariable.Understandthedifferencebetweenanexpression,equation,formula,term,functionandidentity.Pupilsshouldbetaughtto:useandinterpretalgebraicnotation,including:abinplaceofa×b3yinplaceofy+y+yand3×ya²inplaceofa×aa³inplaceofa×a×aa²binplaceofa×a×b!"inplaceofa÷bcoefficientswrittenasfractionsratherthanasdecimalsbracketsSubstitutenumericalvaluesintoformulaeandexpressions,includingscientificformulae.Simplifyandmanipulatealgebraicexpressionstomaintainequivalencebycollectingliketerms.Usealgebraicmethodstosolvesimplelinearequationsinonevariablewheretheunknown

Weekbeg.5thJune2017HalftermFCATAssessment1hour

appearsononesideoftheequation.

GeometryLinesandAngles

Describe,sketchanddrawusingconventionaltermsandnotations:points,lines,parallellines,perpendicularlines,rightangles,regularpolygons,andotherpolygonsthatarereflectivelyandrotationallysymmetric.Deriveandillustratepropertiesoftriangles,quadrilaterals,circles,andotherplanefigures[forexample,equallengthsandangles]usingappropriatelanguageandtechnologiesUseaprotractortomeasureanddrawangles.Applythepropertiesofanglesatapoint,anglesatapointonastraightline,verticallyoppositeangles.Deriveandusethesumofanglesinatriangleandaquadrilateral.Drawandinterpretpiecharts.

Weekbeg.10thJuly2017MasteryTerm3Assessment1hour


Year8

2016-17 Unit WhatwillIdo? HowwillIbeassessed?Term1 Unit1

CalculationApplythefouroperations,includingformalwrittenmethods,tointegers,decimalsandsimplefractions,andmixednumbers(includingnegatives)Useconventionalnotationforpriorityofoperations,includingbrackets,powers,rootsandreciprocalsCalculateexactlywithfractionsRoundnumbersandmeasurestoanappropriatedegreeofaccuracy(e.g.toaspecifiednumberofdecimalplacesorsignificantfigures)Useterminatingdecimalsandtheircorrespondingfractions

Unit2Geometry

UnderstandandusealternateandcorrespondinganglesonparallellinesDeriveandusethesumofanglesinatriangle(e.g.todeduceandusetheanglesuminanypolygon,andtoderivepropertiesofregularpolygons)Interpretplansandelevationsof3DshapesCalculateperimetersof2Dshapes,includingcirclesCalculateareasofcirclesandcompositeshapesKnowandapplyformulaetocalculatevolumeofrightprisms(includingcylinders)

Weekbeg.17thOctoberCycle1Assessment1hour

Unit3Proportion

IdentifyandworkwithfractionsinratioproblemsExpressthedivisionofaquantityintotwopartsasaratio;applyratiotorealcontextsandproblems

ExpressamultiplicativerelationshipbetweentwoquantitiesasaratioorafractionUnderstandanduseproportionasequalityofratiosRelateratiostofractionsandtolinearfunctionsComparelengths,areasandvolumesusingrationotation

Unit4Probability

ApplythepropertythattheprobabilitiesofanexhaustivesetofmutuallyexclusiveeventssumtooneEnumeratesetsandcombinationsofsetssystematically,usingtables,gridsandVenndiagramsConstructtheoreticalpossibilityspacesforcombinedexperimentswithequallylikelyoutcomesandusethesetocalculatetheoreticalprobabilities

Term2 Unit5Algebra

Useandinterpretalgebraicnotation,including:a²binplaceofa×a×b,coefficientswrittenasfractionsratherthanasdecimalsSubstitutenumericalvaluesintoscientificformulaeSimplifyandmanipulatealgebraicexpressionsbyfactorisingandsimplifyingexpressionsinvolvingsums,productsandpowers,includingthelawsofindices

Weekbeg.16thJanCycle2Assessment1hour

Unit6Graphs

Plotgraphsofequationsthatcorrespondtostraight-linegraphsIdentifyandinterpretgradientsandinterceptsoflinearfunctionsgraphicallyandalgebraicallyRecognise,sketchandinterpretgraphsoflinearfunctionsandquadraticfunctionsPlotandinterpretgraphsandgraphsofnon-standardfunctionsinrealcontexts,tofind

approximatesolutionstoproblemssuchassimplekinematicproblemsinvolvingdistance,speedandacceleration

Unit7Geometry

Usescalefactors,scalediagramsandmapsMeasurelinesegmentsandanglesingeometricfigures,includinginterpretingmapsandscaledrawingsanduseofbearingsIdentify,describeandconstructsimilarshapes,includingoncoordinateaxes,byconsideringenlargement

Unit8Statistics

ApplystatisticstodescribeapopulationUseandinterpretscattergraphsRecognisecorrelationInterpret,analyseandcomparethedistributionsofdatasetsinvolvingdiscrete,continuousandgroupeddataInterpretandcomparethedistributionsofdatasetsusingmedian,mean,modeandmodalclass,andspread(range,includingunderstandingoutliers)

Weeksbeg.13/3/17and20/3/17Mid-YearExams

Term3 Unit9Algebra

SolvelinearequationswiththeunknownonbothsidesoftheequationFindapproximatesolutionstolinearequationsusingagraphRearrangeformulaetochangethesubject

Unit10Proportion

Changefreelybetweencompoundunits(e.g.speed,ratesofpay,prices)innumericalcontextsUsecompoundunitssuchasspeed,ratesofpay,unitpricing)Workwithpercentagesgreaterthan100%

Solveproblemsinvolvingpercentagechange,includingoriginalvalueproblems,andsimpleinterestincludinginfinancialmathematicsSolveproblemsinvolvingdirectandinverseproportion,includinggraphicalandalgebraicrepresentationsInterpretfractionsandpercentagesasoperators

Unit11Calculation

UnderstandandusetheconceptsandvocabularyofinequalitiesandfactorsUsetheconceptsandvocabularyofprimenumbers,highestcommonfactor,lowestcommonmultiple,primefactorisation(usingindexnotation)CalculatewithandinterpretstandardformAx10n,where1≤A<10andnisanintegerApplysystematiclistingstrategies

Weekbeg.5/6/17Cycle4Assessment1hour

Unit12Algebra

Generatetermsofasequencefromeitheraterm-to-termoraposition-to-termruleFindthenthtermoflinearsequences.


Year9FOUNDATION

2016-17 Unit WhatwillIdo? HowwillIbeassessed?Term1 Unit1a

IntegersandPlaceValue

Use and order positive and negativenumbers(integers).Order integers, decimals, use thesymbols <, > and understand the ≠symbol.Add and subtract positive andnegativenumbers(integers).Recall allmultiplication facts to 10 ×10,andusethemtoderivequicklythecorrespondingdivisionfacts.Multiply or divide any number bypowersof10.Multiply and divide positive andnegativenumbers(integers).Use brackets and the hierarchy ofoperations(notincludingpowers).Round numbers to a given power of10.Checkanswersbyroundingandusinginverseoperations.

Unit1bDecimals

Usedecimalnotationandplacevalue;Identifythevalueofdigitsinadecimalorwholenumber.Compareandorderdecimalnumbersusingthesymbols<,>Understandthe≠symbol(notequal);Write decimal numbers of millions,e.g.2300000=2.3millionAdd, subtract, multiply and dividedecimals, including calculationsinvolvingmoney.Multiply or divide by any numberbetween0and1Roundtothenearestinteger.Round to a given number of decimalplaces.Round to any given number ofsignificantfigures.Estimate answers to calculations byrounding numbers to 1 significantfigure.

Useonecalculationtofindtheanswertoanother.

Unit1cIndices,PowersandRoots

Findsquaresandcubes.Recall integer squares up to 10 x 10andthecorrespondingsquareroots.Understand the difference betweenpositiveandnegativesquareroots.Recallthecubesof1,2,3,4,5and10Use index notation for squares andcubesRecognisepowersof2,3,4,5Evaluate expressions involvingsquares,cubesandroots.Add, subtract, multiply and dividenumbersinindexform.Canceltosimplifyacalculation.Use indexnotation forpowersof10,includingnegativepowers.Usethelawsofindicestomultiplyanddivide numbers written in indexnotation.Usethesquare,cubeandpowerkeysonacalculator.Use brackets and the hierarchy ofoperations with powers inside thebrackets, or raising brackets topowers.

Use calculators for all calculations:positive and negative numbers,brackets, powers and roots, fouroperations.

Unit1dFactors,MultiplesandPrimes

Listallthree-digitnumbersthatcanbemadefromthreegivenintegers.Recogniseoddandevennumbers;Identify factors, multiples and primenumbers.Recognisetwo-digitprimenumbers;List all factors of a number and listmultiplessystematically.Find the prime factor decompositionof positive integers and write as aproductusingindexnotation.

Weekbeg.17/10/16Cycle1Assessment

Find common factors and commonmultiplesoftwonumbers.FindtheLCMandHCFoftwonumbers,by listing, Venn diagrams and usingprimefactors:includefindingLCMandHCF given the prime factorisation oftwonumbers.Understand that the prime factordecompositionofapositiveintegerisunique – whichever factor pair youstartwith–andthateverynumbercanbewrittenasaproductoftwofactors.SolvesimpleproblemsusingHCF,LCMandprimenumbers.

Unit2aAlgebra–thebasics

Usenotationandsymbolscorrectly.Writeanexpression.Selectanexpression/equation/formula/identityfromalist.Manipulateandsimplifyalgebraicexpressionsbycollecting‘like’terms.Multiplytogethertwosimplealgebraicexpressions,e.g.2a×3bSimplifyexpressionsbycancelling,

e.g. 42x =2x

Useindexnotationwhenmultiplyingordividingalgebraicterms.Useindexlawsinalgebra.Useindexnotationinalgebra.Understandthe≠symbolandintroducetheidentity≡sign.

Unit2bExpandingandfactorisingsinglebrackets

Multiplyasinglenumbertermoverabracket.Writeandsimplifyexpressionsusingsquaresandcubes.Simplifyexpressionsinvolvingbrackets,i.e.expandthebrackets,thenadd/subtract.Arguemathematicallytoshowalgebraicexpressionsareequivalent.Recognisefactorsofalgebraictermsinvolvingsinglebrackets.

Factorisealgebraicexpressionsbytakingoutcommonfactors.

Unit2cExpressionsandsubstitutionintoformulae

Write expressions to solve problemsrepresentingasituation.Substitute numbers in simplealgebraicexpressions.Substitute numbers into expressionsinvolvingbracketsandpowers.Substitute positive and negativenumbersintoexpressions.Derive a simple formula, includingthosewithsquares,cubesandroots.Substitute numbers into a wordformula.Substitutenumbersintoaformula.

Term2 Unit3aTables

Usesuitabledatacollectiontechniques(datatobeintegeranddecimalvalues).Designandusedata-collectionsheetsforgrouped,discreteandcontinuousdata,useinequalitiesforgroupeddata,andintroduce≤and≥signs.Interpretanddiscussthedata;Sort,classifyandtabulatedata,bothdiscreteandcontinuousquantitativedata,andqualitativedata.Constructtablesfortime–seriesdata;Extractdatafromlistsandtables.Usecorrectnotationfortime,12-and24-hourclock.Workouttimetakenforajourneyfromatimetable.Designandusetwo-waytablesfordiscreteandgroupeddata.Useinformationprovidedtocompleteatwo-waytable.Calculatethetotalfrequencyfromafrequencytable.Readofffrequencyvaluesfromatable.Findgreatestandleastvaluesfromafrequencytable.


Identifythemodefromafrequencytable.Identifythemodalclassfromagroupedfrequencytable.

Unit3bChartsandgraphs

Plotting coordinates in first quadrantandreadgraphscalesinmultiples.ProduceandinterpretdataforPictograms,compositebarcharts,dual/comparative bar charts forcategorical and ungrouped discretedata, bar-line charts, vertical linecharts, line graphs, line graphs fortime-series data, histograms withequalclassintervals.stem and leaf (including back-to-back).Calculate totalpopulation fromabarchartortable.Findgreatestand leastvalues fromabarchartortable.Find themode from a stem and leafdiagram;Identifythemodefromabarchart.Recognise simple patterns,characteristics, relationships in barchartsandlinegraphs.

Unit3cPieCharts

Drawcirclesandarcstoagivenradius.KnowtheanglefactsrelatedtocirclesMeasure and draw angles, to thenearestdegree.Interpret tables; represent data intablesandcharts.Knowwhichchartstousefordifferenttypesofdatasets.Construct pie charts for categoricaldata and discrete/continuousnumericaldata.Findthemodeandthetotalfrequencyfromapiechart.

Unit3dScatterGraphs

Drawscattergraphs.Interpretpointsonascattergraph.

Identify outliers and ignore them onscattergraphs.Draw the lineofbest fit ona scatterdiagrambyeye,andunderstandwhatitrepresents.Distinguishbetweenpositive,negativeandnocorrelationusing linesofbestfit.Usealineofbestfittopredictvaluesofavariablegivenvaluesoftheothervariable.Interpret scatter graphs in terms ofthe relationship between twovariables.Interpret correlation in terms of theproblem.

Unit4aFractions

Use diagrams to find equivalentfractionsorcomparefractions.Expressagivennumberasafractionofanother, using very simple numbers,some cancelling, and where thefractionisboth<1and>1Write a fraction in its simplest formandfindequivalentfractions.Order fractions, by using a commondenominator.Compare fractions, use inequalitysigns,compareunitfractions.Convertbetweenmixednumbersandimproperfractions.Addandsubtractfractions.Multiplyanddividefractions.

Unit4bFractions,decimalsandpercentages

Recall the fraction-to-decimalconversion.Convert between fractions anddecimals.Convert a fraction to a decimal tomakeacalculationeasier.Recognise recurring decimals and

convert fractions such as 37, 13 and

23intorecurringdecimals.

Compare and order fractions,decimalsandintegers,usinginequalitysigns.Express a given number as apercentageofanothernumber.Convert between fractions, decimalsandpercentages.Order fractions, decimals andpercentages, including use ofinequalitysigns.

Unit4cPercentages

Express a given number as apercentageofanothernumber.Find a percentage of a quantitywithout a calculator: 50%, 25% andmultiplesof10%and5%.Find a percentage of a quantity ormeasurement.Calculate amount of percentageincreaseordecrease.Use percentages to solve problems,including comparisons of twoquantitiesusingpercentages.Percentagesover100%;Usepercentagesinreal-lifesituations:PriceafterVAT(notpricebeforeVAT).Valueofprofitorloss.Simpleinterest.Incometaxcalculations.Find a percentage of a quantity,includingusingamultiplier.Use a multiplier to increase ordecrease by a percentage in anyscenariowherepercentagesareused.Understand themultiplicative natureofpercentagesasoperators.


Term3 Unit5aEquations

Select an expression, equation,formulaoridentityfromalist.Write expressions and set up simpleequations.Usefunctionmachines.Solvesimpleequations.Solve linear equations, with integercoefficients, in which the unknown

appearsoneithersideoronbothsidesoftheequation.Solve linear equations which containbrackets, including those that havenegative signs occurring anywhere inthe equation, and those with anegativesolution.Solve linear equations in oneunknown, with integer or fractionalcoefficients.Rearrangesimpleequations.Substitute into a formula, and solvetheresultingequation.Find an approximate solution to alinearequationusingagraph.Solve angle or perimeter problemsusingalgebra.Write an equation to solve a wordproblem.

Unit5bInequalities

Showinequalitiesonnumberlines.Writedownwholenumbervaluesthatsatisfyaninequality.Solveaninequalitysuchas–3<2x+1<7andshowthesolutionsetonanumberline.Solve two inequalities in x, find thesolutionsetsandcomparethemtoseewhichvalueofxsatisfiesboth.Use the correct notation to showinclusiveandexclusiveinequalities.Construct inequalities to represent asetshownonanumberline.Solvesimplelinearinequalitiesinonevariable, and represent the solutionsetonanumberline.Round answers to a given degree ofaccuracyUse inequality notation to specifysimple error intervals due totruncationorrounding.

Unit5cSequences

Recognisesequencesofoddandevennumbers, and other sequencesincludingFibonaccisequences.

Usefunctionmachinestofindtermsofasequence.Writetheterm-to-termdefinitionofasequenceinwords.Find a specific term in the sequenceusing position-to-term or term-to-termrules.Generate arithmetic sequences ofnumbers, triangular number, squareand cube integers and sequencesderivedfromdiagrams.Recognise such sequences fromdiagramsanddrawthenextterminapatternsequence.Find the next term in a sequence,includingnegativevalues.Findthenthtermofalinearsequence.Find the nth term of an arithmeticsequence.Use the nth term of an arithmeticsequencetogenerateterms.Use the nth term of an arithmeticsequencetodecideifagivennumberisaterminthesequence,orfindthefirsttermoveracertainnumber.Continueageometricprogressionandfind the term-to-term rule, includingnegatives,fractionanddecimalterms.Continue a quadratic sequence andusethenthtermtogenerateterms.Distinguish between arithmetic andgeometricsequences.

Unit6aPropertiesofshapes,parallellinesandanglefacts

Estimatesizesofangles.Measureangles.UseanglenotationcorrectlyKnowthatthereare360°inafullturn,180°inahalfturnand90°inaquarterturn.Identifyalineperpendiculartoagivenline.Identifyparallellines.Recallthepropertiesanddefinitionsofspecial types of quadrilaterals,includingsymmetryproperties.


Givensomeinformationaboutashapeon coordinate axes, complete theshape.Classify quadrilaterals by theirgeometricproperties.Use the fact that angle sum of aquadrilateralis360°.Use geometrical languageappropriately and give reasons foranglecalculations.Recallandusepropertiesofanglesatapoint,anglesatapointonastraightline, right angles, and verticallyoppositeangles.Distinguish between scalene,equilateral,isoscelesandright-angledtriangles.Deriveandusethesumofanglesinatriangle.Findamissingangleinatriangle,usingtheanglesumofatriangleis180°.Understand and use the angleproperties of triangles, use thesymmetry property of isoscelestriangletoshowthatbaseanglesareequal.Show step-by-step deduction whensolvingproblems.Understand and use the anglepropertiesofintersectinglines.Understand a proof that the exteriorangleofatriangleisequaltothesumoftheinterioranglesattheothertwovertices.Findmissinganglesusingpropertiesofcorrespondingandalternateangles.Understand and use the anglepropertiesofparallellines.

Unit6bInteriorandexterioranglesofpolygons

Recognise and name pentagons,hexagons, heptagons, octagons anddecagons.Understand‘regular’and‘irregular’asappliedtopolygons.

Use the sum of angles of irregularpolygons.Calculate and use the sums of theinterioranglesofpolygons.Calculateandusetheanglesofregularpolygons.Use thesumof the interioranglesofann-sidedpolygon.Usethesumoftheexterioranglesofanypolygonis360°.Usethesumoftheinteriorangleandtheexteriorangleis180°.Identify shapes which are congruent(byeye).Explain why some polygons fittogetherandothersdonot.


Year9HIGHER

2016-17 Unit WhatwillIdo? HowwillIbeassessed?Term1 Unit1a

Calculations,checkingandrounding

Add, subtract, multiply and dividedecimalsandwholenumbers.Multiply or divide by any numberbetween0and1;Put digits in the correct place in adecimal calculation and use onecalculation to find the answer toanother;Usetheproductruleforcounting(i.e.iftherearemwaysofdoingonetaskandforeachofthese,therearenwaysof doing another task, then the totalnumberofwaysthetwotaskscanbedoneism×nways);Round numbers to the nearest 10,100,1000;Round to the nearest integer, to agivennumberofdecimalplacesandtoagivennumberofsignificantfigures;Estimateanswerstoone-ortwo-stepcalculations,includinguseofroundingnumbers and formal estimation to 1significant figure: mainly wholenumbersandthendecimals.

Unit1bIndices,roots,reciprocalsandhierarchyofoperations

Useindexnotationforintegerpowersof10,includingnegativepowers;Recognisepowersof2,3,4,5;Usethesquare,cubeandpowerkeyson a calculator and estimate powersand roots of any given positivenumber, by considering the values itmustliebetween,e.g.thesquarerootof42mustbebetween6and7;Find the value of calculations usingindices including positive, fractionalandnegativeindices;

Recall that n0 = 1 and n–1 =1n for

positiveintegersnaswellas,12n =√n

and13n =3√nforanypositivenumber

n;Understandthattheinverseoperationof raising a positive number to apower n is raising the result of this

operationtothepower1n ;

Use index laws to simplify andcalculate the value of numericalexpressions involving multiplicationand division of integer powers,fractional and negative powers, andpowersofapower;Solveproblemsusingindexlaws;Usebracketsandthehierarchyofoperationsuptoandincludingwithpowersandrootsinsidethebrackets,orraisingbracketstopowersortakingrootsofbrackets;Useanextendedrangeofcalculatorfunctions,including+,–,×,÷,x²,√x,

memory,xy,1yx ,brackets;

Usecalculatorsforallcalculations:positiveandnegativenumbers,brackets,powersandroots,fouroperations.

Unit1cFactors,multiplesandprimes.

Identify factors, multiples and primenumbers;Find the prime factor decompositionof positive integers – write as aproductusingindexnotation;Find common factors and commonmultiplesoftwonumbers;FindtheLCMandHCFoftwonumbers,by listing, Venn diagrams and usingprime factors – include finding LCMandHCFgiventheprimefactorisationoftwonumbers;Solve problems using HCF and LCM,andprimenumbers;Understand that the prime factordecompositionofapositiveintegeris

unique, whichever factor pair youstartwith,andthateverynumbercanbe written as a product of primefactors.

Unit1dStandardformandsurds

Convertlargeandsmallnumbersintostandardformandviceversa;Addandsubtractnumbersinstandardform;Multiply and divide numbers instandardform;Interpret a calculator display usingstandardformandknowhowtoenternumbersinstandardform;UnderstandsurdnotationSimplify surd expressions involvingsquares(e.g.√12=√(4×3)=√4×√3=2√3).


Unit2aAlgebra–thebasics

Use algebraic notation and symbolscorrectly;Writeanexpression;Knowthedifferencebetweenaterm,expression,equation, formulaandanidentity;Manipulate an expression bycollectingliketerms;Substitute positive and negativenumbersintoexpressionssuchas3x+4 and 2x3 and then into expressionsinvolvingbracketsandpowers;Substitute numbers into formulaefrommathematics and other subjectusingsimplelinearformulae,e.g.l×w,v=u+at;Simplifyexpressionsbycancelling,e.g.42x =2x

Use instances of index laws forpositiveintegerpowers;Use index notation (positive powers)whenmultiplyingordividingalgebraicterms;

Useinstancesofindexlaws,includinguse of zero, fractional and negativepowers;Multiplyasingletermoverabracket;Recognise factors of algebraic termsinvolving single brackets and simplifyexpressions by factorising, includingsubsequentlycollectingliketerms;Expand the product of two linearexpressions, i.e. double bracketsworking up to negatives in bothbrackets and also similar to (2x +3y)(3x–y);Knowthatsquaringalinearexpressionis the same as expanding doublebrackets;Factorisequadraticexpressionsoftheformax2+bx+c;Factorise quadratic expressions usingthedifferenceoftwosquares.

Unit2bSettingup,solvingandrearrangingequations

Set up simple equations from wordproblemsandderivesimpleformulae;Understandthe≠symbol(notequal),e.g. 6x + 4 ≠ 3(x + 2), and introduceidentity≡sign;Solve linear equations, with integercoefficients, in which the unknownappearsoneithersideoronbothsidesoftheequation;Solve linear equations which containbrackets, including those that havenegative signs occurring anywhere inthe equation, and those with anegativesolution;Solve linear equations in oneunknown, with integer or fractionalcoefficients;Set up and solve linear equations tosolvetosolveaproblem;Derive a formula and set up simpleequations fromword problems, thensolve these equations, interpretingthe solution in the context of theproblem;

Substitute positive and negativenumbers into a formula, solve theresultingequation includingbrackets,powersorstandardform;Use and substitute formulae frommathematics and other subjects,includingthekinematicsformulaev=

u+at,v2–u2=2as,ands=ut+ 12at2;

Change the subject of a simpleformula,i.e.linearone-step,suchasx=4y;Change the subject of a formula,includingcaseswherethesubjectisonboth sidesof theoriginal formula,orinvolving fractions and small powersofthesubject;Simple proofs and use of ≡ in “showthat” style questions; know thedifference between an equation andanidentity;Use iteration to find approximatesolutions to equations, for simpleequations in the first instance, thenquadraticandcubicequations.

Unit2cSequences

Recognisesimplesequencesincludingat the most basic level odd, even,triangular, square and cube numbersand Fibonacci-type sequences(includingthose involvingnumbers instandardformorindexform);Generate sequences of numbers,squared integers and sequencesderivedfromdiagrams;Describe in words a term-to-termsequence and identify which termscannotbeinasequence;Generatespecifictermsinasequenceusing the position-to-term rule andterm-to-termrule;Findanduse (togenerate terms) thenthtermofanarithmeticsequence;Use the nth term of an arithmeticsequencetodecideifagivennumberisaterminthesequence,orfindthe

first term above or below a givennumber;Identify which terms cannot be in asequencebyfindingthenthterm;Continue a quadratic sequence andusethenthtermtogenerateterms;Find the nth term of quadraticsequences;Distinguish between arithmetic andgeometricsequences;Use finite/infinite andascending/descending to describesequences;Recognise and use simple geometricprogressions(rnwherenisaninteger,and r is a rational number > 0 or asurd);Continue geometric progression andfind term to term rule, includingnegative,fractionanddecimalterms;Solve problems involving sequencesfromreallifesituations.

Term2 Unit3aAveragesandrange

Design and use two-way tables fordiscreteandgroupeddata;Useinformationprovidedtocompleteatwo-waytable;Sort, classify and tabulate data anddiscrete or continuous quantitativedata;Calculate mean and range, findmedianandmodefromsmalldataset;Usea spreadsheet to calculatemeanandrange,andfindmedianandmode;Recognise the advantages anddisadvantages between measures ofaverage;Constructandinterpretstemandleafdiagrams (including back-to-backdiagrams):

• findthemode,median,range,as well as the greatest andleast values from stem andleaf diagrams, and comparetwo distributions from stem


and leaf diagrams (mode,median,range);

Calculate the mean, mode, medianand range from a frequency table(discretedata);Construct and interpret groupedfrequencytablesforcontinuousdata:

• for grouped data, find theinterval which contains themedianandthemodalclass;

• estimate the mean withgroupeddata;

Understand that the expression‘estimate’ will be used whereappropriate,whenfindingthemeanofgrouped data using mid-intervalvalues.

Unit3bRepresentingandinterpretingdata

Knowwhichchartstousefordifferenttypesofdatasets;Produceand interpret compositebarcharts;Produce and interpret comparativeanddualbarcharts;Produceandinterpretpiecharts:

• find the mode and thefrequency represented byeachsector;

• comparedatafrompiechartsthat represent different-sizedsamples;

Produce and interpret frequencypolygonsforgroupeddata:

• from frequency polygons,read off frequency values,compare distributions,calculate total population,mean, estimate greatest andleast possible values (andrange);

Produce frequency diagrams forgroupeddiscretedata:

• read off frequency values,calculate total population,findgreatestandleastvalues;

Produce histograms with equal classintervals:

• estimate the median from ahistogram with equal classwidth or any otherinformation, such as thenumber of people in a giveninterval;

Producelinegraphs:• read off frequency values,

calculate total population,findgreatestandleastvalues;

Construct and interpret time–seriesgraphs,commentontrends;Comparethemeanandrangeoftwodistributions, or median or mode asappropriate;Recognise simple patterns,characteristics relationships in barcharts, line graphs and frequencypolygons.

Unit3cScattergraphs

Drawandinterpretscattergraphs;Interpret scatter graphs in terms ofthe relationship between twovariables;Draw lines of best fit by eye,understandingwhattheserepresent;Identify outliers and ignore them onscattergraphs;Usealineofbestfit,orotherwise,topredict values of a variable givenvaluesoftheothervariable;Distinguishbetweenpositive,negativeandzerocorrelationusinglinesofbestfit,and interpretcorrelation in termsoftheproblem;Understandthatcorrelationdoesnotimply causality, and appreciate thatcorrelation is a measure of thestrength of the association betweentwovariablesandthatzerocorrelationdoes not necessarily imply ‘norelationship’ but merely ‘no linearcorrelation’;

Explainan isolatedpointonascattergraph;Use the line of best fit makepredictions; interpolate andextrapolate apparent trends whilstknowingthedangersofsodoing.

Unit4aFractions

Expressagivennumberasafractionofanother;Findequivalentfractionsandcomparethesizeoffractions;Write a fraction in its simplest form,including using it to simplify acalculation,

e.g.50÷20= 5020

= 52=2.5;

Find a fraction of a quantity ormeasurement, including within acontext;Convert a fraction to a decimal tomakeacalculationeasier;Convertbetweenmixednumbersandimproperfractions;Add, subtract, multiply and dividefractions;Multiply and divide fractions,including mixed numbers and wholenumbersandviceversa;Add and subtract fractions, includingmixednumbers;Understand anduseunit fractions asmultiplicativeinverses;Bywritingthedenominatorintermsofits prime factors, decide whetherfractions can be converted torecurringorterminatingdecimals;Convert a fraction to a recurringdecimal;Convert a recurring decimal to afraction;Find the reciprocal of an integer,decimalorfraction.

Unit4bPercentages

Convert between fractions, decimalsandpercentages;

Express a given number as apercentageofanothernumber;Expressonequantityasapercentageof another where the percentage isgreaterthan100%Findapercentageofaquantity;Find the new amount after apercentageincreaseordecrease;Work out a percentage increase ordecrease, including: simple interest,incometaxcalculations,valueofprofitorloss,percentageprofitorloss;Compare two quantities usingpercentages, including a range ofcalculations and contexts such asthoseinvolvingtimeormoney;Findapercentageofaquantityusingamultiplier;Use a multiplier to increase ordecrease by a percentage in anyscenariowherepercentagesareused;Find the original amount given thefinal amount after a percentageincrease or decrease (reversepercentages),includingVAT;Usecalculatorsforreversepercentagecalculations by doing an appropriatedivision;Usepercentagesinreal-lifesituations,including percentages greater than100%;Describe percentage increase ordecrease with fractions, e.g. 150%

increasemeans 122timesasbig;

Understand that fractions are moreaccurateincalculationsthanroundedpercentage or decimal equivalents,and choose fractions, decimals orpercentages appropriately forcalculations.

Unit4cRatioandproportion

Expressthedivisionofaquantityintoanumberpartsasaratio;


Writeratiosinform1:morm:1andtodescribeasituation;Write ratios in their simplest form,includingthree-partratios;Divide a given quantity into two ormorepartsinagivenpart:partorpart:wholeratio;Usearatiotofindonequantitywhentheotherisknown;Writearatioasafraction;Writearatioasalinearfunction;Identifydirectproportionfromatableof values, by comparing ratios ofvalues;Usearatiotocompareascalemodeltoreal-lifeobject;Use a ratio to convert betweenmeasuresandcurrencies,e.g.£1.00=€1.36;Scaleuprecipes;Convertbetweencurrencies.

Term3 Unit5aPolygons,anglesandparallellines

Classify quadrilaterals by theirgeometric properties and distinguishbetween scalene, isosceles andequilateraltriangles;Understand‘regular’and‘irregular’asappliedtopolygons;Understand the proof that the anglesum of a triangle is 180°, and deriveandusethesumofanglesinatriangle;Usesymmetrypropertyofanisoscelestriangletoshowthatbaseanglesareequal;Findmissinganglesinatriangleusingthe angle sum in a triangle AND thepropertiesofanisoscelestriangle;Understand a proof of, and use thefact that, the exterior angle of atriangle is equal to the sum of theinterior angles at the other twovertices;Explain why the angle sum of aquadrilateralis360°;

Understand and use the angleproperties of quadrilaterals and thefact that the angle sum of aquadrilateralis360°;Understand and use the angleproperties of parallel lines and findmissinganglesusingthepropertiesofcorresponding and alternate angles,givingreasons;Use the angle sums of irregularpolygons;Calculate and use the sums of theinterior angles of polygons; use thesumofanglesinatriangleandusetheanglesuminanypolygontoderivethepropertiesofregularpolygons;Usethesumoftheexterioranglesofanypolygonis360°;Use thesumof the interioranglesofann-sidedpolygon;Usethesumoftheinteriorangleandtheexteriorangleis180°;Findthesizeofeachinteriorangle,orthesizeofeachexteriorangle,orthenumberofsidesofaregularpolygon,andusethesumofanglesofirregularpolygons;Calculate the angles of regularpolygons and use these to solveproblems;Use the side/angle properties ofcompound shapes made up oftriangles, lines and quadrilaterals,includingsolvingangleandsymmetryproblems for shapes in the firstquadrant, more complex problemsandusingalgebra;Use angle facts to demonstrate howshapeswould‘fittogether’,andworkout interior angles of shapes in apattern.

Unit5b Understand, recall and usePythagoras’Theoremin2D;

Pythagoras’TheoremandTrigonometry

Giventhreesidesofatriangle,justifyifitisright-angledornot;Calculatethelengthofthehypotenusein a right-angled triangle (includingdecimallengthsandarangeofunits);Find the lengthofa shorter side inaright-angledtriangle;CalculatethelengthofalinesegmentABgivenpairsofpoints;Give an answer to the use ofPythagoras’Theoreminsurdform;Understand, use and recall thetrigonometric ratios sine, cosine andtan,andapplythemtofindanglesandlengths in general triangles in 2Dfigures;Use the trigonometric ratios to solve2Dproblems;Find angles of elevation anddepression;Knowtheexactvaluesofsinθandcosθforθ=0°,30°,45°,60°and90°;knowtheexactvalueoftanθforθ=0°,30°,45°and60°.

Unit6aGraphs:thebasicsandreal-lifegraphs

Identify and plot points in all fourquadrants;Draw and interpret straight-linegraphs for real-life situations,including ready reckoner graphs,conversion graphs, fuel bills, fixedchargeandcostperitem;Drawdistance–timeandvelocity–timegraphs;Use graphs to calculate variousmeasures (of individual sections),including: unit price (gradient),average speed, distance, time,acceleration;includingusingenclosedareas by counting squares or usingareas of trapezia, rectangles andtriangles;Find the coordinatesof themidpointofalinesegmentwithadiagramgivenandcoordinates;

Find the coordinatesof themidpointofalinesegmentfromcoordinates;Calculatethelengthofalinesegmentgiven the coordinates of the endpoints;Find the coordinates of pointsidentifiedbygeometricalinformation.Findtheequationofthe linethroughtwogivenpoints.

Unit6bLineargraphsandcoordinategeometry

Plotanddrawgraphsofy=a,x=a,y=xandy=–x,drawingandrecognisinglinesparalleltoaxes,plusy=xandy=–x;Identifyandinterpretthegradientofalinesegment;Recognisethatequationsoftheformy=mx+ccorrespondtostraight-linegraphsinthecoordinateplane;Identifyandinterpretthegradientandy-interceptofa lineargraphgivenbyequationsoftheformy=mx+c;Find the equation of a straight linefromagraphintheformy=mx+c;Plotanddrawgraphsofstraightlinesoftheformy=mx+cwithandwithoutatableofvalues;Sketch a graph of a linear function,usingthegradientandy-intercept(i.e.withoutatableofvalues);Findtheequationofthe linethroughonepointwithagivengradient;Identify and interpret gradient fromanequationax+by=c;Find the equation of a straight linefromagraphintheformax+by=c;Plotanddrawgraphsofstraightlinesintheformax+by=c;Interpret and analyse informationpresentedinarangeoflineargraphs:

• usegradientstointerprethowone variable changes inrelationtoanother;


• findapproximatesolutions toa linear equation from agraph;

• identify direct proportionfromagraph;

• find theequationof a lineofbest fit (scatter graphs) tomodel the relationshipbetweenquantities;

Explorethegradientsofparallel linesandlinesperpendiculartoeachother;Interpret and analyse a straight-linegraphandgenerateequationsoflinesparallelandperpendiculartothegivenline;Selectandusethefactthatwheny=mx+cistheequationofastraightline,thenthegradientofalineparalleltoitwill have a gradient ofm and a lineperpendicular to this linewill have a

gradientof 1m−

.

Unit6c

Quadratic,cubicandothergraphs

Recognisealinear,quadratic,cubic,reciprocalandcirclegraphfromitsshape;Generatepointsandplotgraphsofsimplequadraticfunctions,thenmoregeneralquadraticfunctions;Findapproximatesolutionsofaquadraticequationfromthegraphofthecorrespondingquadraticfunction;Interpretgraphsofquadraticfunctionsfromreal-lifeproblems;Drawgraphsofsimplecubicfunctionsusingtablesofvalues;Interpretgraphsofsimplecubicfunctions,includingfindingsolutionstocubicequations;Drawgraphsofthereciprocal

function 1y x=withx≠0usingtables

ofvalues;

Drawcircles,centretheorigin,equationx2+y2=r2.


Year10FOUNDATION

2016-17 Unit WhatwillIdo? HowwillIbeassessed?

Term1 Unit7aStatisticsandsampling

Specify the problem and plan aninvestigation, decide what data tocollectandwhatstatisticalanalysisisneeded.Recognise types of data: primarysecondary, quantitative andqualitative.Identify which primary data theyneed to collect and in what format,includinggroupeddata.Collectdatafromavarietyofsuitableprimaryandsecondarysources.Understandhowsourcesofdatamaybebiased.Explain why a sample may not berepresentativeofawholepopulation.Understandsampleandpopulation.

Unit7bTheAverages

Calculate the mean, mode, medianandrangefordiscretedata.Interpretandfindarangeofaveragesasfollows:median, mean and range from a(discrete)frequencytable;range, modal class, intervalcontainingthemedian,andestimateof the mean from a grouped datafrequencytable;modeandrangefromabarchart;median,modeand range fromstemandleafdiagrams;meanfromabarchart.Understand that the expression'estimate' will be used whereappropriate,when finding themeanof grouped data using mid-intervalvalues.Compare the mean, median, modeand range (as appropriate) of twodistributions using bar charts, dual

bar charts, pictograms and back-to-backstemandleaf.Recognise the advantages anddisadvantages betweenmeasures ofaverage.

Unit8aPerimeterandArea

Indicate given values on a scale,includingdecimalvalue.Know thatmeasurements using realnumbersdependuponthechoiceofunit.Convert between units of measurewithinonesystem,includingtime.Convertbetweenmetricunits.Measure shapes to find perimetersandareasusingarangeofscales.Find the perimeter of rectangles,triangles, parallelograms andtrapezia. Find the perimeter ofcompoundshapes.Recall and use the formulae for theareaofatriangleandrectangle.Find the area of a trapezium andrecalltheformula.Findtheareaofaparallelogram.Calculate areas and perimeters ofcompound shapes made fromtrianglesandrectangles.Estimate surface areas by roundingmeasurementsto1significantfigure.Findthesurfaceareaofaprism.Find surface area using rectanglesandtriangles.Convert between metric areameasures.

Unit8b3Dformsandvolume

Identify and name common solids:cube, cuboid, cylinder, prism,pyramid,sphereandcone.Sketchnetsofcuboidsandprisms.Recall and use the formula for thevolumeofacuboid.Findthevolumeofaprism,includingatriangularprism,cubeandcuboid.

Weekbeg.17thOct.Cycle1Assessment1hour

Calculatevolumesofrightprismsandshapes made from cubes andcuboids.Estimate volumes by roundingmeasurementsto1significantfigure.Convert between metric volumemeasures.Convertbetweenmetricmeasuresofvolumeandcapacitye.g.1ml=1cm3.

Unit9aReal-lifegraphs

Useinput/outputdiagrams.Use axes and coordinates to specifypoints in all four quadrants in 2D.Identifypointswithgivencoordinatesandcoordinatesofagivenpointinallfourquadrants.Find the coordinates of pointsidentifiedbygeometricalinformationin2D(allfourquadrants).Findthecoordinatesofthemidpointofalinesegment.Draw,labelandscaleaxes.Readvaluesfromstraight-linegraphsforreal-lifesituations.Drawstraightlinegraphsforreal-lifesituations, including ready reckonergraphs, conversion graphs, fuel billsgraphs,fixedchargeandcostperunit.Draw distance–time graphs andvelocity–timegraphs.Work out time intervals for graphscales.Interpret distance–time graphs, andcalculate: the speed of individualsections, total distance and totaltime.Interpret informationpresented inarangeoflinearandnon-lineargraphs.Interpretgraphswithnegativevaluesonaxes.Find the gradient of a straight linefromreal-lifegraphs.Interpret gradient as the rate ofchange indistance–timeandspeed–time graphs, graphs of containers

filling and emptying, and unit pricegraphs.

Unit9bStraightlinegraphs

Use function machines to findcoordinates (i.e. given the input x,findtheoutputy).Plotanddrawgraphsofy=a,x=a,y=xandy=–x;Recognise straight-line graphsparalleltotheaxes.Recognisethatequationsoftheformy=mx+ccorrespondtostraight-linegraphsinthecoordinateplane.Plotanddrawgraphsofstraightlinesoftheformy=mx+cusingatableofvalues.Sketch a graph of a linear function,usingthegradientandy-intercept.Identify and interpret gradient fromanequationy=mx+c.Identify parallel lines from theirequations.Plotanddrawgraphsofstraightlinesintheformax+by=cFind the equation of a straight linefromagraph.Findtheequationofthelinethroughonepointwithagivengradient.Findapproximatesolutionstoalinearequationfromagraph.

Term2 Unit10aTransformations1:translations,rotationsandreflections

Identifycongruentshapesbyeye.Understand clockwise andanticlockwise.Understand that rotations arespecifiedbyacentre,anangleandadirectionofrotation.Findthecentreofrotation,angleanddirection of rotation and describerotations.Describe a rotation fully using theangle,directionofturn,andcentre.Rotate a shape about the origin oranyotherpointonacoordinategrid.

Draw the position of a shape afterrotation about a centre (not on acoordinategrid).Identify correct rotations from achoiceofdiagrams.Understand that translations arespecifiedbyadistanceanddirectionusingavector.Translateagivenshapebyavector.Describe and transform 2D shapesusing single translations on acoordinategrid.Use column vectors to describetranslations.Understandthatdistancesandanglesare preserved under rotations andtranslations, so that any figure iscongruent under either of thesetransformations.

Unit10bTransformations2:enlargementsandcombinations

Understand that reflections arespecifiedbyamirrorline.Identify correct reflections from achoiceofdiagrams.Understand that reflections arespecifiedbyamirrorline.Identify the equation of a line ofsymmetry.Transform 2D shapes using singlereflections (including those not oncoordinate grids) with vertical,horizontalanddiagonalmirrorlines.Describe reflections on a coordinategrid.Scale a shape on a grid (without acentrespecified).Understand that an enlargement isspecified by a centre and a scalefactor.Enlargeagivenshapeusing (0,0)asthe centre of enlargement, andenlarge shapes with a centre otherthan(0,0).Find the centre of enlargement bydrawing.

Weekbeg.6/2/17and13/2/17Mock1

Describe and transform 2D shapesusingenlargementsby:

• apositiveintegerscalefactor;• afractionalscalefactor.

Identify the scale factor of anenlargementofashapeastheratioofthe lengths of two correspondingsides,simpleintegerscalefactors,orsimplefractions.Understandthatdistancesandanglesare preserved under reflections, sothat any figure is congruent underthistransformation.Understand that similar shapes areenlargements of each other andanglesarepreserved–definesimilarinthisunit.

Unit11aRatio

Understandandexpress thedivisionofaquantity intoanumberofpartsasaratio.Writeratiosintheirsimplestform.Write/interpret a ratio todescribeasituation.Share a quantity in a given ratioincludingthree-partratios.Solvearatioproblemincontext.Usearatiotofindonequantitywhentheotherisknown.Usearatiotocompareascalemodeltoareal-lifeobject.Use a ratio to convert betweenmeasuresandcurrencies.Problemsinvolvingmixing,e.g.paintcolours, cement and drawnconclusions.Compareratios.Writeratiosinform1:morm:1Writearatioasafraction.Writearatioasalinearfunction.Write lengths, areasandvolumesoftwoshapesasratiosinsimplestform.Express a multiplicative relationshipbetweentwoquantitiesasaratioorafraction.

Unit11bProportion

Understand and use proportion asequalityofratios.Solvewordproblemsinvolvingdirectandinverseproportion.Workoutwhichproductisthebetterbuy.Scaleuprecipes.Convertbetweencurrencies.Solveproportionproblemsusingtheunitarymethod.Recognisewhen values are in directproportionbyreferencetothegraphform.Understand inverse proportion: as xincreases,ydecreases(inversegraphsdoneinlaterunit).Recognisewhen values are in directproportionbyreferencetothegraphform.Understanddirectproportionandtherelationshipy=kx.

Term3 Unit12Pythagoras’TheoremandTrigonometry

Understand,recallandusePythagoras’Theoremin2D,includingleavinganswersinsurdform.Given3sidesofatriangle,justifyifitisright-angledornot.Calculatethelengthofthehypotenuseinaright-angledtriangle,includingdecimallengthsandarangeofunits.Findthelengthofashortersideinaright-angledtriangle.ApplyPythagoras’Theoremwithatriangledrawnonacoordinategrid.CalculatethelengthofalinesegmentABgivenpairsofpoints.Understand, use and recall thetrigonometric ratiossine,cosineandtan, and apply them to find anglesandlengthsingeneraltrianglesin2Dfigures.Usethetrigonometricratiostosolve2Dproblems.

Find angles of elevation anddepression.Roundanswerstoappropriatedegreeofaccuracy,eithertoagivennumberof significant figures or decimalplaces,ormakeasensibledecisiononroundingincontextofquestion.Knowtheexactvaluesofsinθandcosθ for θ = 0°, 30°, 45°, 60° and 90°;knowtheexactvalueoftanθforθ=0°,30°,45°and60°.

Unit13aProbability1

Distinguishbetweeneventswhichareimpossible, unlikely, even chance,likely,andcertaintooccur.Markeventsand/orprobabilitiesonaprobabilityscaleof0to1.Write probabilities in words orfractions,decimalsandpercentages.Find the probability of an eventhappening using theoreticalprobability.Use theoretical models to includeoutcomes using dice, spinners &coins.List all outcomes for single eventssystematically.Work out probabilities fromfrequencytables.Workoutprobabilitiesfromtwo-waytables.Record outcomes of probabilityexperimentsintables.Addsimpleprobabilities.Identify different mutually exclusiveoutcomesandknowthatthesumoftheprobabilitiesofalloutcomesis1.Using 1 –p as the probability of anevent not occurring where p is theprobabilityoftheeventoccurring.Findamissingprobability froma listortableincludingalgebraicterms.

Weekbeg.8/5/17,15/5/17and22/5/17Mock2

Unit13bProbability2

Find the probability of an eventhappening using relative frequency.

Estimate the number of times aneventwilloccur,giventheprobabilityand the number of trials – for bothexperimental and theoreticalprobabilities.Listalloutcomesforcombinedeventssystematically.Useanddrawsamplespacediagrams.Work out probabilities from Venndiagrams to represent real-lifesituations and also ‘abstract’ sets ofnumbers/values.Useunionandintersectionnotation.Compare experimental data andtheoreticalprobabilities.Compare relative frequencies fromsamplesofdifferentsizes.Find the probability of successiveevents, such as several throws of asingledice.Use tree diagrams to calculate theprobability of two independentevents.Use tree diagrams to calculate theprobabilityoftwodependentevents.

Unit14Multiplicativereasoning

Understand and use compoundmeasures:density,pressure,speedConvert between metric speedmeasures.Readvaluesinkm/handmphfromaspeedometer.Calculate average speed, distance,time – in miles per hour as well asmetricmeasures.Usekinematicsformulaetocalculatespeed, acceleration (with formulaprovidedandvariablesdefinedinthequestion).Change d/t in m/s to a formula inkm/h.Express a given number as apercentage of another number inmorecomplexsituations.Calculatepercentageprofitorloss.

Makecalculationsinvolvingrepeatedpercentage change, not using theformula.Find the original amount given thefinal amount after a percentageincreaseordecrease.Usecompoundinterest.Useavarietyofmeasuresinratioandproportionproblems:

• currencyconversion;• ratesofpay;• bestvalue;

Set up, solve and interpret theanswers in growth and decayproblems.Understand that X is inverselyproportionaltoYisequivalenttoXis

proportionalto 1Y

Interpret equations that describedirectandinverseproportion.

Unit15aPlansandelevations

Understand clockwise andanticlockwise.Drawcirclesandarcstoagivenradiusorgiventhediameter.Measure and draw lines, to thenearestmm.Measure and draw angles, to thenearestdegree.Knowandusecompassdirections.Drawsketchesof3Dsolids.Know the terms face, edge andvertex.Identify and sketch planes ofsymmetryof3Dsolids.Make accuratedrawingsof trianglesandother2Dshapesusingarulerandaprotractor.Construct diagrams of everyday 2Dsituations involving rectangles,triangles, perpendicular and parallellines.

Understandanddrawfrontandsideelevationsandplansofshapesmadefromsimplesolids.Given the front and side elevationsandtheplanofasolid,drawasketchofthe3Dsolid.

Unit15b

Constructions,lociandbearings

Understand congruence, as twoshapes that are the same size andshape.Visually identify shapes which arecongruent.Use straight edge and a pair ofcompasses to do standardconstructions.Understand, from the experience ofconstructing them, that trianglessatisfyingSSS,SAS,ASAandRHSareunique,butSSAtrianglesarenot.Constructtheperpendicularbisectorofagivenline.Construct the perpendicular from apointtoaline.Construct the bisector of a givenangle.Constructanglesof90°,45°Draw and construct diagrams fromgiven instructions, including thefollowing:

• aregionboundedbyacircleandanintersectingline;

• agivendistancefromapointand a given distance from aline;

• equal distances from twopointsortwolinesegments;

• regions may be defined by‘nearerto’or‘greaterthan’;

Find and describe regionssatisfyingacombinationofloci.

Use constructions to solve lociproblems(2Donly).Use and interpret maps and scaledrawings.

Estimate lengths using a scalediagram.Makeanaccuratescaledrawingfromadiagram.Use three-figure bearings to specifydirection.Mark on a diagram the position ofpointBgivenitsbearingfrompointA;Giveabearingbetweenthepointsonamaporscaledplan.Given thebearingof a pointA frompoint B, work out the bearing of BfromA.Use accurate drawing to solvebearingsproblems.Solve locus problems includingbearings.


Year10HIGHER


Term1 Unit7aPerimeter,areaandcircles

Recall and use the formulae for thearea of a triangle, rectangle,trapeziumandparallelogramusingavarietyofmetricmeasures;Calculate the area of compoundshapes made from triangles,rectangles, trapezia andparallelograms using a variety ofmetricmeasures;Find the perimeter of a rectangle,trapeziumandparallelogramusingavarietyofmetricmeasures;Calculatetheperimeterofcompoundshapes made from triangles andrectangles;Estimate area and perimeter byrounding measurements to 1significant figure to checkreasonablenessofanswers.Recall the definition of a circle andnameanddrawpartsofacircle;Recall and use formulae for thecircumference of a circle and the areaenclosed by a circle (usingcircumference=2πr=πdandareaofacircle = πr2) using a variety of metricmeasures;Useπ≈3.142orusetheπbuttononacalculator;Calculate perimeters and areas ofcomposite shapesmade fromcirclesand parts of circles (includingsemicircles, quarter-circles,combinations of these and alsoincorporatingotherpolygons);Calculate arc lengths, angles andareasofsectorsofcircles;Findradiusordiameter,givenareaorcircumferenceofcirclesinavarietyofmetricmeasures;

Give answers to an appropriatedegreeofaccuracyorintermsofπ;Form equations involving morecomplex shapes and solve theseequations.

Unit7b3Dformsandvolume,cylinders,conesandspheres

Findthesurfaceareaofprismsusingthe formulae for triangles andrectangles,andother(simple)shapeswithandwithoutadiagram;Drawsketchesof3Dsolids;Identify planes of symmetry of 3Dsolids, and sketch planes ofsymmetry;Recall and use the formula for thevolume of a cuboid or prism madefrom composite 3D solids using avarietyofmetricmeasures;Convert between metric volumemeasures;Convertbetweenmetricmeasuresofvolume and capacity, e.g. 1 ml = 1cm3;Usevolumetosolveproblems;Estimating surface area, perimeterand volume by roundingmeasurementsto1significant figuretocheckreasonablenessofanswers.Useπ≈3.142orusetheπbuttononacalculator;Findthevolumeandsurfaceareaofacylinder;Recallandusetheformulaforvolumeofpyramid;Findthesurfaceareaofapyramid;Use the formulae for volume andsurfaceareaofspheresandcones;Solve problems involving morecomplexshapesandsolids, includingsegments of circles and frustums ofcones;Findthesurfaceareaandvolumesofcompound solids constructed fromcubes, cuboids, cones, pyramids,spheres,hemispheres,cylinders;

Weekbeg.17thOct.Cycle1Assessment1hour

Give answers to an appropriatedegreeofaccuracyorintermsofπ;Form equations involving morecomplex shapes and solve theseequations.

Unit7cAccuracyandbounds

Calculate the upper and lowersbounds of numbers given to varyingdegreesofaccuracy;Calculatetheupperandlowerboundsof an expression involving the fouroperations;Find theupper and lower bounds inreal-life situations usingmeasurements given to appropriatedegreesofaccuracy;Find theupperand lowerboundsofcalculations involving perimeters,areas and volumes of 2D and 3Dshapes;Calculatetheupperandlowerboundsof calculations, particularly whenworkingwithmeasurements;Useinequalitynotationtospecifyanerror interval due to truncation orrounding.

Unit8aTransformations

Distinguish properties that arepreserved under particulartransformations;

Recognise and describe rotations –knowthatthattheyarespecifiedbyacentreandanangle;

Rotate2Dshapesusingtheoriginoranyotherpoint(notnecessarilyonacoordinategrid);

Identify the equation of a line ofsymmetry;

Recogniseanddescribereflectionsona coordinate grid – know to includethemirror line as a simple algebraic

equation,x=a,y=a,y=x,y=–xandlinesnotparalleltotheaxes;

Reflect 2D shapes using specifiedmirrorlinesincludinglinesparalleltothe axes and alsoy=xandy=–x;

Recognise and describe singletranslationsusingcolumnvectorsonacoordinategrid;

Translateagivenshapebyavector;

Understand the effect of onetranslation followed by another, intermsofcolumnvectors(tointroducevectorsinaconcreteway);

Enlarge a shape on a gridwithout acentrespecified;

Describe and transform 2D shapesusing enlargements by a positiveinteger, positive fractional, andnegativescalefactor;

Knowthatanenlargementonagridisspecified by a centre and a scalefactor;

Identify the scale factor of anenlargementofashape;

Enlarge a given shape using a givencentre as the centreof enlargementby counting distances from centre,andfindthecentreofenlargementbydrawing;

Find areas after enlargement andcomparewithbeforeenlargement,todeduce multiplicative relationship(areascalefactor);giventheareasoftwo shapes, one an enlargement oftheother,findthescalefactoroftheenlargement (whole number valuesonly);

Use congruence to show thattranslations,rotationsandreflectionspreservelengthandangle,sothatanyfigureiscongruenttoitsimageunderanyofthesetransformations;

Describe and transform 2D shapesusingcombinedrotations,reflections,translations,orenlargements;

Describe thechangesand invarianceachieved by combinations ofrotations, reflections andtranslations.

Unit8bConstructions,lociandbearings

Understandanddrawfrontandsideelevationsandplansofshapesmadefromsimplesolids;Given the front and side elevationsandtheplanofasolid,drawasketchofthe3Dsolid;Use and interpret maps and scaledrawings,usingavarietyofscalesandunits;Read and construct scale drawings,drawinglinesandshapestoscale;Estimate lengths using a scalediagram;Understand, draw and measurebearings;Calculatebearingsandsolvebearingsproblems, including on scaledmaps,andfind/markandmeasurebearingsUse the standard ruler and compassconstructions:

• bisectagivenangle;• construct a perpendicular to

a given line from/at a givenpoint;

• constructanglesof90°,45°;• perpendicular bisector of a

linesegment;Construct:

• a regionboundedbyacircleandanintersectingline;

• agivendistancefromapointand a given distance from aline;

• equal distances from twopointsortwolinesegments;

• regionswhichmaybedefinedby ‘nearer to’ or ‘greaterthan’;

Findanddescriberegionssatisfyingacombinationofloci,includingin3D;Use constructions to solve lociproblemsincludingwithbearings;Knowthattheperpendiculardistancefromapointtoa line istheshortestdistancetotheline.

Unit9aSolvingsimultaneousandquadraticequations

Factorisequadraticexpressionsintheformax2+bx+c;Solve quadratic equations byfactorisation and completing thesquare;Solve quadratic equations that needrearranging;Setupandsolvequadraticequations;Solve quadratic equations by usingthequadraticformula;Find the exact solutions of twosimultaneous equations in twounknowns;Use elimination or substitution tosolvesimultaneousequations;Solve exactly, by elimination of anunknown, two simultaneousequationsintwounknowns:

• linear / linear, includingwhere both needmultiplying;

• linear/quadratic;• linear/x2+y2=r2;

Set up and solve a pair ofsimultaneous equations in twovariables for each of the abovescenarios, including to represent asituation;

Interpret the solution in the contextoftheproblem.

Term2 Unit9bInequalities

Showinequalitiesonnumberlines;Write down whole number valuesthatsatisfyaninequality;Solvesimplelinearinequalitiesinonevariable, and represent the solutionsetonanumberline;Solvetwolinearinequalitiesinx,findthe solution setsandcompare themtoseewhichvalueofxsatisfiesbothsolve linear inequalities in twovariablesalgebraically;Use the correct notation to showinclusiveandexclusiveinequalities.

Unit10Probability

Write probabilities using fractions,percentagesordecimals;Understand and use experimentaland theoretical measures ofprobability, including relativefrequencytoincludeoutcomesusingdice,spinners,coins,etc;Estimate the number of times aneventwilloccur,giventheprobabilityandthenumberoftrials;Find the probability of successiveevents, such as several throws of asingledice;List all outcomes for single events,andcombinedevents,systematically;Drawsamplespacediagramsandusethemforaddingsimpleprobabilities;Know that the sum of theprobabilitiesofalloutcomesis1;Use 1 – p as the probability of anevent not occurring where p is theprobabilityoftheeventoccurring;Work out probabilities from Venndiagrams to represent real-lifesituations and also ‘abstract’ sets ofnumbers/values;Useunionandintersectionnotation;

Weekbeg.6/2/17and13/2/17Mock1

Findamissingprobability froma listortwo-waytable,includingalgebraicterms;Understand conditional probabilitiesand decide if two events areindependent;Draw a probability tree diagrambasedongiven information,andusethis to findprobabilityandexpectednumberofoutcome;Understandselectionwithorwithoutreplacement;Calculate the probability ofindependent and dependentcombinedevents;Use a two-way table to calculateconditionalprobability;Use a tree diagram to calculateconditionalprobability;Use a Venn diagram to calculateconditionalprobability;Compare experimental data andtheoreticalprobabilities;Compare relative frequencies fromsamplesofdifferentsizes.

Unit11Multiplicativereasoning

Express a multiplicative relationshipbetweentwoquantitiesasaratioorafraction,e.g.whenA:Bareintheratio

3:5,Ais 35B.When4a=7b,thena=

74b ora:bis7:4;

Solveproportionproblemsusing theunitarymethod;Work out which product offers bestvalueandconsiderratesofpay;Workoutthemultiplierforrepeatedproportional change as a singledecimalnumber;Represent repeated proportionalchangeusingamultiplier raisedtoapower, use this to solve problemsinvolving compound interest anddepreciation;

Understand and use compoundmeasuresand:

• convert between metricspeedmeasures;

• convert between densitymeasures;

• convert between pressuremeasures;

Use kinematics formulae from theformulae sheet to calculate speed,acceleration, etc (with variablesdefinedinthequestion);Calculateanunknownquantity fromquantities that vary in direct orinverseproportion;Recognisewhen values are in directproportionbyreferencetothegraphform, and use a graph to find thevalueofkiny=kx;Set up and use equations to solveword and other problems involvingdirect proportion (this is covered inmoredetailinunit19);Relatealgebraicsolutionstographicalrepresentationoftheequations;Recognisewhenvaluesareininverseproportionbyreferencetothegraphform;Set up and use equations to solveword and other problems involvinginverse proportion, and relatealgebraic solutions to graphicalrepresentationoftheequations.

Unit12Similarityandcongruencein2Dand3D

Understand and use SSS, SAS, ASAand RHS conditions to prove thecongruenceof trianglesusing formalarguments, and to verify standardruler and pair of compassesconstructions;Solveangleproblemsbyfirstprovingcongruence;Understandsimilarityoftrianglesandofotherplaneshapes,andusethistomakegeometricinferences;

Provethattwoshapesaresimilarbyshowingthatallcorrespondinganglesare equal in size and/or lengths ofsidesareinthesameratio/oneisanenlargementof theother,giving thescalefactor;Use formal geometric proof for thesimilarityoftwogiventriangles;Understandtheeffectofenlargementonangles,perimeter,areaandvolumeofshapesandsolids;Identifythescalefactorofanenlargementofasimilarshapeastheratioofthelengthsoftwocorrespondingsides,usingintegerorfractionscalefactors;Writethelengths,areasandvolumesoftwoshapesasratiosintheirsimplestform;Find missing lengths, areas andvolumesinsimilar3Dsolids;Know the relationships betweenlinear,areaandvolumescalefactorsofmathematicallysimilarshapesandsolids;Use the relationship betweenenlargementandareasandvolumesofsimpleshapesandsolids;Solveproblemsinvolvingfrustumsofconeswhereyouhavetofindmissinglengthsfirstusingsimilartriangles.

Term3 Graphsoftrigonometricfunctions

Recognise, sketch and interpretgraphsofthetrigonometricfunctionsy = sinx,y = cosx andy = tanx foranglesofanysize.Knowtheexactvaluesofsinθandcosθforθ=0°,30°,45°,60°and90°andexactvalueoftanθforθ=0°,30°,45°and60°andfindthemfromgraphs.Apply to the graph of y = f(x) thetransformationsy=–f(x),y=f(–x)forsine,cosineandtanfunctionsf(x).

Apply to the graph of y = f(x) thetransformationsy=f(x)+a,y=f(x+a)forsine,cosineandtanfunctionsf(x).

Unit13bTrigonometryandfurthertrigonometry

KnowandapplyArea= 12absinCto

calculatethearea,sidesoranglesofanytriangle.Know the sineand cosine rules, anduse to solve 2D problems (includinginvolvingbearings).Usethesineandcosinerulestosolve3Dproblems.Understand the language of planes,and recognise the diagonals of acuboid.Solve geometrical problems oncoordinateaxes.Understand, recall and usetrigonometric relationships andPythagoras’ Theorem in right-angledtriangles, and use these to solveproblemsin3Dconfigurations.Calculatethelengthofadiagonalofacuboid.Find theanglebetweena lineandaplane.

Weekbeg.8/5/17,15/5/17and22/5/17Mock2

Unit14aCollectingdata

Specifytheproblemandplan:• decide what data to collect

andwhatanalysisisneeded;• understand primary and

secondarydatasources;• considerfairness;

Understand what is meant by asampleandapopulation;Understand how different samplesizes may affect the reliability ofconclusionsdrawn;Identifypossible sourcesofbias andplantominimiseit;Writequestionstoeliminatebias,andunderstand how the timing and

location of a survey can ensure asampleisrepresentative.

Unit14bCumulativefrequency,boxplotsandhistograms

Use statistics found in allgraphs/chartsinthisunittodescribeapopulation;Know the appropriate uses ofcumulativefrequencydiagrams;Construct and interpret cumulativefrequencytables;Construct and interpret cumulativefrequencygraphs/diagramsandfromthegraph:

• estimate frequencygreater/less than a givenvalue;

• find themedianandquartilevalues and interquartilerange;

Comparethemeanandrangeoftwodistributions, or median andinterquartilerange,asappropriate;Interpret box plots to find median,quartiles, range and interquartilerangeanddrawconclusions;Produceboxplotsfromrawdataandwhen given quartiles, median andidentifyanyoutliers;Know the appropriate uses ofhistograms;Construct and interpret histogramsfrom class intervals with unequalwidth;Use and understand frequencydensity;Fromhistograms:

• complete a groupedfrequencytable;

• understand and definefrequencydensity;

Estimatethemeanfromahistogram;Estimate the median from ahistogramwithunequal classwidthsor any other information from a

histogram, such as the number ofpeopleinagiveninterval.

Unit15Quadratics,expandingmorethantwobrackets,sketchinggraphs,graphsofcircles,cubesandquadratics

Sketch a graph of a quadraticfunction, by factorising or by usingthe formula, identifying roots, y-intercept and turning point bycompletingthesquare;Beable to identify fromagraph if aquadraticequationhasanyrealroots;Find approximate solutions toquadraticequationsusingagraph;Expandtheproductofmorethantwolinearexpressions;Sketchagraphofaquadraticfunctionand a linear function, identifyingintersectionpoints;Sketch graphs of simple cubicfunctions, given as three linearexpressions;Solve simultaneous equationsgraphically:

• findapproximatesolutionstosimultaneous equationsformed from one linearfunction and one quadraticfunction using a graphicalapproach;

• find graphically theintersectionpointsofagivenstraightlinewithacircle;

• solvesimultaneousequationsrepresenting a real-lifesituation graphically, andinterpret the solution in thecontextoftheproblem;

Solve quadratic inequalities in onevariable,byfactorisingandsketchingthegraphtofindcriticalvalues;Represent the solution set forinequalities using set notation, i.e.curlybracketsand ‘isanelementof’notation;

• for problems identifying thesolutions to two differentinequalities, show this as theintersection of the twosolutionsets,i.e.solutionofx²–3x–10<0as{x:–3<x<5};

Solve linear inequalities in twovariablesgraphically;Show the solution set of severalinequalities in two variables on agraph;Use iterationwithsimpleconvergingsequences.

Unit16aCircleTheorems

Recall the definition of a circle andidentify (name) and draw parts of acircle, including sector, tangent,chord,segment;Proveandusethefactsthat:

• the angle subtended by anarcatthecentreofacircleistwicetheanglesubtendedatany point on thecircumference;

• theangle ina semicircle is arightangle;

• the perpendicular from thecentre of a circle to a chordbisectsthechord;

• angles in the same segmentareequal;

• alternatesegmenttheorem;• opposite angles of a cyclic

quadrilateralsumto180°;Understandandusethefactthatthetangent at any point on a circle isperpendicular to the radius at thatpoint;Find and give reasons for missinganglesondiagramsusing:

• circletheorems;• isosceles triangles (radius

properties)incircles;

• the fact that the anglebetweenatangentandradiusis90°;

• thefactthattangentsfromanexternal point are equal inlength.


Year11FOUNDATION


Term1 Unit29InterpretingGraphs

Construct and interpret graphs in real-worldcontextsInterpret the gradient of a straight-linegraphasarateofchange

Unit30VectorGeometry

Represent vectors as a diagram or acolumnvectorAddandsubtractvectorsMultiplyvectorsbyascalarRecogniseparallelvectors

Unit31Transformationsinaplane

Carryout,identifyanddescribereflectionsCarry out, identify and describetranslationsusing2DvectorsCarryout,identifyanddescriberotations

Unit32Constructionsandloci

Useruler,protractorandpairofcompassestoaccuratelyconstructanglesandshapesAccuratelycopydiagramsusingarulerandapairofcompassesConstructtheperpendicularbisectorofalineConstructtheperpendicularatagivenpointonalineConstructaperpendicularfromagivenpointtoalineBisectanangleUse constructions to solve loci problemsApply appropriate constructions and lociknowledge to a variety of problemsincludingthosesetincontext

Mock1October2016

Unit33Similarity

Knowwhatismeantbythephrase‘mathematicallysimilar’DeterminewhentwoobjectsaremathematicallysimilarKnowwhatismeantbya‘mathematicalenlargement’EnlargeashapegivenapositiverationalscalefactorKnowwhatthecentreofenlargementisEnlargeashapegivenascalefactorandcentreofenlargement

DetermineagivencentreofenlargementandscalefactorfromadiagramDeterminesimilarpolygons

Unit34Congruence

KnowwhatitmeansfortwoobjectstobecongruentKnowtheconditionsforwhichcongruenceforapairoftriangleisthenimplied:

o SSS–threesidesarethesameinbothtriangles

o ASA–twoanglesandonesidelengtharethesameinbothtriangles

o SAS–twosidesandtheanglebetweenthemarethesameinbothtriangle

RHS–thehypotenuseandanothersideofaright-angledtrianglearethesameinbothtrianglesApplytheconditionsforcongruencytoavarietyofsituations

Unit35Pythagoras’Theorem

DerivePythagoras’theoremanduseittofindthelengthofthehypotenuseinanyright-angledtriangleKnowandusePythagoras’theoremtofindanymissinglengthinaright-angledtriangleUsePythagoras’theoremtoshowwhetheratriangleisright-angledornotApplyPythagoras’theoremto2DproblemsLinkPythagoras’theoremtoreal-lifeskillsforindustry

Unit36Trigonometry

Usethetrigonometricratiosgivenbythesine,cosineandtangentfunctionstofindunknownlengthsandanglesin2Dright-angledtrianglesKnowtheexactratiosgivenbysineandcosineof0,30,45,60and90degreesandtheexactratiosgivenbythetangentfunctionfor0,30,45and60degreesKnowthedifferencebetweenanangleofdepressionandanangleofelevationIdentifywhenthetrigonometricratiosmustbeusedinsteadofPythagoras’theoremtosolve2Dproblemsrelating toright-angledtriangles,includingcontextualproblems

Unit37Graphsofotherfunctionsandequations

Workfluentlywithequationsofstraight-linegraphsIdentifyandplotgraphsofquadraticfunctionsi.e.parabolasFindrootsofquadraticequationsfromthex-interceptoftheparabolaofthequadraticequationthatdefinesthegraphKnowthefeaturesofgraphsofquadraticequationsSketchparabolasWorkfluentlywithcubicpolynomialsandtheirgraphsSketchcubicgraphsWorkfluentlytocalculatereciprocalsofnumbersandplotfunctionsinvolvingreciprocalsIdentifyhyperbolasandmatchthemtotheirequationsPlotandsketchgraphsfromgivenfunctionsRecogniselinear,quadraticandreciprocalgraphs

Unit38Growthanddecay

Calculatewithsimplegrowth,suchassimpleinterestratesCalculatewithcompoundgrowth,suchascompoundinterestratesSolvewordproblemsusingsimpleand/orcompoundgrowthCalculatewithsimpledecayCalculatewithcompounddecay,suchasdepreciationSolvewordproblemsusingsimpleand/orcompounddecay

Mock2January/February2017

Term2 Exampreparationandrevision Term3 Exampreparationandrevision FinalGCSE

examinationsMay/June2017


Year11HIGHER


Term1 Unit33Transformations

Carry out, identify and describereflectionsCarry out, identify and describetranslationsusing2DvectorsCarryout,identifyanddescriberotationsFindthecentreofrotationbyconstructionCarry out, identify and describecombinedtransformations

Unit34Constructionsandloci

Useruler,protractorandpairofcompassestoaccuratelyconstructanglesandshapesAccuratelycopydiagramsusingrulersandapairofcompassesonlyConstructtheperpendicularbisectorofalineConstructtheperpendicularatagivenpointonalineConstructaperpendicularfromagivenpointtoalineBisectanangleUse constructions to solve lociproblemsApply appropriate constructions andloci knowledge to a variety ofproblems including those set incontext

Unit35Similarity

Knowwhatismeantbythephrase‘mathematicallysimilar’DeterminewhentwoobjectsaremathematicallysimilarKnowwhatismeantbya‘mathematicalenlargement’EnlargeashapegivenapositiverationalscalefactorKnowwhatthecentreofenlargementisEnlargeashapegivenascalefactorandcentreofenlargement

DetermineagivencentreofenlargementandscalefactorfromadiagramEnlargeashapegivenanegativerationalscalefactorDeterminesimilarpolygonsDeterminesimilar3DshapesKnowtherelationshipbetweenlengths,areasandvolumesofsimilarshapes

Unit36Congruence

KnowwhatitmeansfortwoobjectstobecongruentKnowtheconditionsforwhichcongruenceforapairoftriangleisthenimplied:

o SSS–threesidesarethesameinbothtriangles

o ASA–twoanglesandonesidelengtharethesameinbothtriangles

o SAS–twosidesandtheanglebetweenthemarethesameinbothtriangle

RHS–thehypotenuseandanothersideofaright-angledtrianglearethesameinbothtrianglesApplytheconditionsforcongruencytoavarietyofsituations

Mock1October2016

Unit37Pythagoras’Theorem

KnowandusePythagoras’theoremtofindanymissinglengthinaright-angledtriangleUsePythagoras’theoremtoshowwhetheratriangleisright-angledornotApplyPythagoras’theoremto2DproblemsApplyPythagoras’theoremto3DproblemsLinkPythagoras’theoremtoreal-lifeskillsforindustry

Unit38Trigonometry

Usethetrigonometricratiosgivenbythesine,cosineandtangentfunctionstofindunknownlengthsandanglesin2Dright-angledtrianglesKnowtheexactratiosgivenbysineandcosineof0,30,45,60and90degreesandtheexactratiosgivenby

thetangentfunctionfor0,30,45and60degreesUsethesine,cosineandarearulestosolveproblemsrelatingtounknownsides,anglesandareasinnon-right-angledtrianglesKnowthedifferencebetweenanangleofdepressionandanangleofelevationIdentifywhenthetrigonometricratiosmustbeusedinsteadofPythagoras’theoremtosolve2Dproblemsrelatingtoright-angledtriangles,includingcontextualproblems

Unit39Graphsofotherfunctionsandequations

Workfluentlywithequationsofstraight-linegraphsIdentifyandplotgraphsofquadraticfunctionsi.e.parabolasFindrootsofquadraticequationsfromthex-interceptoftheparabolaofthequadraticequationthatdefinesthegraphKnowthefeaturesofgraphsofquadraticequationsSketchparabolasWorkfluentlywithcubicpolynomialsandtheirgraphsSketchcubicgraphsWorkfluentlytocalculatereciprocalsofnumbersandplotfunctionsinvolvingreciprocalsIdentifyhyperbolasandmatchthemtotheirequationsPlotandsketchgraphsfromgivenfunctionsRecogniselinear,quadraticandreciprocalgraphsIdentifyandplotexponentialgraphsIdentifyandplottrigonometricgraphsRepresentacirclegivenitscentreontheoriginandradiusrbyafunctionIdentifyequationsofcirclesfromtheirgraphs

Term2 Unit40Growthanddecay

Calculatewithsimplegrowth,suchassimpleinterestratesCalculatewithcompoundgrowth,suchascompoundinterestrates

Solvewordproblemsusingsimpleand/orcompoundgrowthUsetheformulay=a(1+r)nforcompoundgrowthCalculatewithsimpledecayCalculatewithcompounddecay,suchasdepreciationSolvewordproblemsusingsimpleand/orcompounddecayUsetheformulay=a(1−r)nforcompounddecay

Unit41Transformationofcurves

Knowthefeaturesofaquadraticfunction(parabola):axisofsymmetry,rootsandvertex,andidentifythesefeaturesfromthesketchofaquadraticSketchverticaltranslationsofquadraticfunctionsSketchhorizontaltranslationsofquadraticfunctionsSketchquadraticfunctionsthathavebeentranslatedinboththehorizontalandverticaldirectionsKnowtheeffecttranslationshaveontheaxisofsymmetryandvertexofaquadraticUsegraphsketchingtoidentifytheeffectofmultiplyingf(x)by−1Usealgebraicmanipulationskillstoidentifythefeaturesaboveandsketchanyquadraticoftheformy=ax2+bx+cIdentifyreflectionsandtranslationsinthegraphicalrepresentationsoftrigonometricfunctionsSketchatransformedtrigonometriccurveforagivendomainSketchtranslationsandreflectionsofcubic,reciprocalandexponentialfunctionsApplytransformationslearntinthischaptertoavarietyofproblemsincludingidentifyingtheeffectofatransformationonafeatureofagraphandfindingtheequationofafunctiononceatransformationhasbeenapplied

Mock2January/February2017

Exampreparationandrevision

Term3 Exampreparationandrevision FinalGCSEexaminationsMay/June2017

mathematics department – curriculum outline year 7 … · mathematics department – curriculum...

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