MathematicsCurriculumMap–Years7-11KS3 National Curriculum Purpose of Study: The purposes of this qualification are to: ● provide evidence of students’ achievements against demanding and fulfilling content, to give students the confidence that the mathematical skills, knowledge and understanding that they will have acquired during the course of their study are as good as that of the highest performing jurisdictions in the world ● provide a strong foundation for further academic and vocational study and for employment, to give students the appropriate mathematical skills, knowledge and understanding to help them progress to a full range of courses in further and higher education. This includes Level 3 mathematics courses as well as Level 3 and undergraduate courses in other disciplines such as biology, geography and psychology, where the understanding and application of mathematics is crucial Aims: We aim to build fluency and nurture confidence in Maths by focusing on problem-solving and reasoning throughout. The aims are to enable students to: ● develop fluent knowledge, skills and understanding of mathematical methods and concepts ● acquire, select and apply mathematical techniques to solve problems ● reason mathematically, make deductions and inferences, and draw conclusions ● comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

Y7 Y8 Y9 Y10 Y11 GCSEExamSpecification(Edexcel)AUTUMN

Consolidatetherapidrecallofnumberfacts,includingpositiveintegercomplementsto100andmultiplicationfactsto10´10,andquicklyderiveassociateddivisionfacts.Usestandardcolumnprocedurestoaddandsubtractwholenumbersanddecimalswithuptotwoplaces.Understandandusedecimalnotationandplacevalue;multiplyanddivideintegersand

AUTUMN"Add,subtract,multiplyanddivideintegers.Understandtheinfintenatureofthesetsofintegers,realandrationalnumbers."Recogniseandusemultiples,factors(divisors),commonfactor,highestcommonfactor,lowestcommonmultipleandprimes;findtheprimefactordecompositionofanumber(e.g.8000=26x53).

FOUNDATION1aBasicUseofNumbersUnderstandandorderintegers WritenumbersinwordsandwritingnumbersfromwordsAddandsubtractintegersRecallallmultiplicationfactsto10×10,andusethemtoderivequicklythecorrespondingdivisionfactsMultiplyordivideanynumberbypowersof10Multiplyanddivideintegers

FOUNDATIONPatterns&SequencesGeneratesimplesequencesofoddorevennumbers Findthemissingnumbersinanumberpatternorsequence Findthenthtermofanumbersequence Usethenthnumberofanarithmeticsequence

FOUNDATION

RatioBy the end of the modulethe student should be ableto:Understand what is meantbyratio Write a ratio in its simplestform;andfindanequivalentratio Solve a ratio problem incontext,egrecipes

Examinedonthefollowingareas:1 Number 2 Algebra 3 Ratio, proportion and rates of change 4 Geometry and measures 5 Probability 6 StatisticsTwo tiers are available: Foundation and Higher (content is defined for each tier). ● Each student is permitted to take assessments in either the Foundation tier or Higher tier. ● The qualification consists of three

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decimalsby10,100,1000,andexplaintheeffect.Compareandorderdecimalsindifferentcontexts;knowthatwhencomparingmeasurementstheymustbeinthesameunits.Understandnegativenumbersaspositionsonanumberline;order,addandsubtractpositiveandnegativeintegersincontext.Makeandjustifyestimatesandapproximationsofcalculations.Enternumbersandinterpretthedisplayindifferentcontexts(decimals,money).Solvewordproblemsandinvestigateinarangeofcontexts:number;compareandevaluatesolutions.Generateanddescribesimpleintegersequences.Generatetermsofasimplesequence,givenarule(e.g.findingatermfromthepreviousterm,findingatermgivenitspositioninthesequence).Generatesequencesfrompracticalcontextsanddescribethegeneral

Usesquares,positiveandnegativesquareroots,cubesandcuberoots,andindexnotationforsmallpositiveintegerpowers.Generateanddescribeintegersequences.Generatetermsofalinearsequenceusingterm-to-termandposition-to-termdefinitionsofthesequence,onpaperandusingaspreadsheetorgraphicalcalculator.Begintouselinearexpressionstodescribethenthtermofanarithmeticsequence,justifyingitsformbyreferringtotheactivityorpracticalcontextfromwhichitwasgenerated.Identifyalternateanglesandcorrespondingangles;understandaproofthat:-thesumoftheanglesofatriangleis180°andofaquadrilateralis360°;theexteriorangleofatriangleisequaltothesumofthetwointerioroppositeangles.Solvegeometricalproblemsusingsideandanglepropertiesofequilateral,isoscelesandright-angledtrianglesandspecialquadrilaterals,explaining

Add,subtract,multiplyanddividenegativenumbers Roundwholenumberstothenearest:10,100,1000,… 1bTypesofNumberRecogniseevenandoddnumbersIdentifyfactors,multiplesandprimenumbers Findtheprimefactordecompositionofpositiveintegers Findthecommonfactorsandcommonmultiplesoftwoorthreenumbers FindtheLowestcommonmultiple(LCM)andHighestcommonfactor(HCF)oftwonumbers Recallintegersquaresupto15×15andthecorrespondingsquarerootsRecallthecubesof2,3,4,5and10 FindsquaresandcubesFindsquarerootsandcuberoots

Findwhetheranumberispartofagivensequence Continueasequencederivedfromdiagrams Useacalculatortoproduceasequenceofnumbers ExtendsimplesequencesinvolvingcubenumbersUseandextendFibonaccitypesequencesUseandextendQuadraticsequencesUseandextendGeometricsequencesPerimeters&AreasMeasureshapestofindperimetersandareas Findtheperimeterofrectanglesandtriangles Findtheperimeterofcompoundshapes Findtheareaofarectangleandtriangle Recallandusetheformulaefortheareaofatriangle,rectangleanda

Share a quantity in a givenratio Understand and useexamples in directproportion Use direct and inverseproportion graphically andalgebraically Scattergraphs&CorrelationBy the end of the modulethe student should be ableto:Drawandproducea scattergraph Lookatdatatofindpatternsandexceptions Distinguish betweenpositive, negative and zerocorrelation using lines ofbestfit Interpret correlation intermsoftheproblem Understand that correlationdoesnotimplycausality Drawlinesofbestfitbyeyeand understand what itrepresents

equally-weighted written examination papers at either Foundation tier or Higher tier. ● All three papers must be at the same tier of entry and must be completed in the same assessment series. ● Paper 1 is a non-calculator assessment and a calculator is allowed for Paper 2 and Paper 3. ● Each paper is 1 hour and 30 minutes long. ● Each paper has 80 marks. ● The content outlined for each tier will be assessed across all three papers. ● Each paper will cover all Assessment Objectives, in the percentages outlined for each tier. (See the section Breakdown of Assessment Objectives for more information.) ● Each paper has a range of question types; some questions will be set in both mathematical and non-mathematical contexts. ● See Appendix 3 for a list of formulae that can be provided in the examination (as part of the relevant question). ● Two assessment series available per year: May/June and November*. ● First assessment series: May/June 2017. ● The qualification will be graded and certificated on a nine-grade scale from 9 to 1 using the total mark across all three papers where 9 is the highest grade. Individual papers are not graded. ● Foundation tier: grades 1 to 5. ● Higher tier: grades 4 to 9 (grade 3

terminsimplecases.Suggestextensionstoproblemsbyasking‘Whatif…?’;begintogeneraliseandtounderstandthesignificanceofacounter-example.Expresssimplefunctionsinwords,thenusingsymbols;representtheminmappings.Uselettersymbolstorepresentunknownnumbersorvariables.Use2-Drepresentationstovisualise3-Dshapesanddeducesomeoftheirproperties.Usenamesandabbreviationsofunitsofmeasurementtomeasure,estimate,calculateandsolveproblemsineverydaycontextsinvolvinglength,area.Knowandusetheformulafortheareaofarectangle;calculatetheperimeterandareaofshapesmadefromrectangles.Knowandusetheformulafortheareaofarectangle;calculatetheperimeterandareaofshapesmadefromrectangles.Solvewordproblemsandinvestigateinarangeofcontexts:

reasoningwithdiagramsandtext;classifyquadrilateralsbytheirgeometricproperties.Applyanglefacts,trianglecongruence,similarityandpropertiesofnamedquadrilateralstoderiveresultsaboutanglesandsides,usingtransformational,axiomaticandproperty-basedreasoning.Usestraightedgeandcompassestoconstruct:-themid-pointandperpendicularbisectorofalinesegment;-thebisectorofanangle;-theperpendicularfromapointtoaline;-theperpendicularfromapointonaline.Usethevocabularyofprobabilitywheninterpretingtheresultsofanexperiment;appreciatethatrandomprocessesareunpredictable.Knowthatiftheprobabilityofaneventoccurringisp,thentheprobabilityofitnotoccurringis1–p;findandrecordallpossiblemutuallyexclusiveoutcomesforsingleeventsandtwosuccessiveeventsinasystematicway,usingdiagramsandtables.

Angles,LinesandTriangles Measureanddrawlines,tothenearestmmMeasureanddrawangles,tothenearestdegree Estimatesizesofangles Recallandusepropertiesofangles: atapointanglesatapointonastraightline,includingrightanglesverticallyoppositeanglesFindthesizeofmissinganglesatapointoratapointonastraightlineDistinguishbetweenacute,obtuse,reflexandrightanglesNameanglesGivereasonsforcalculationsUsegeometriclanguageappropriately Identifypoints,lines

parallelogram Calculateareasofcompoundshapesmadefromtrianglesandrectangles Findtheareaofatrapeziumbyusingtheformula SolvearangeofproblemsinvolvingareasincludingcostofcarpettypequestionsStraightLineGraphsBytheendofthemodulethestudentshouldbeableto:Useaxesandcoordinatestospecifypointsinallfourquadrantsin2-D Identifypointswithgivencoordinates Identifycoordinatesofgivenpoints(NB:Pointsmaybeinthefirstquadrantorallfourquadrants) Findthecoordinatesofpointsidentifiedbygeometricalinformationin2-D

Use a line of best fit topredict values of onevariable given values of theothervariable Draw: Pictograms CompositebarchartsComparative and dual barchartsFrequencypolygons,HistogramswithequalclassintervalsFrequencydiagramsforgroupeddiscretedataLinegraphsInterpret: compositebarcharts comparativeanddualbarchartsstemandleafdiagramsscattergraphsfrequencypolygons

allowed).

length,perimeterandarea.Begintoidentifyanduseangle,sideandsymmetrypropertiesoftrianglesandquadrilaterals.Usecorrectlythevocabulary,notationandlabellingconventionsforlines,anglesandshapes.Usefractionnotationtodescribepartsofshapesandtoexpressasmallerwholenumberasafractionofalargerone;simplifyfractionsbycancellingallcommonfactorsandidentifyequivalentfractions;convertterminatingdecimalstofractionse.g.0.23=23/100;useadiagramtocomparetwoormoresimplefractions.Begintoaddandsubtractsimplefractionsandthosewithcommondenominators;calculatesimplefractionsofquantitiesandmeasurements(whole-numberanswers);multiplyafractionbyaninteger.Understandpercentageasthe‘numberofpartsper100’;recognisetheequivalenceofpercentages,fractions

Estimateprobabilitiesfromexperimentaldata;understandthat:-ifanexperimentisrepeatedtheremaybe,andusuallywillbe,differentoutcomes;increasingthenumberoftimesanexperimentisrepeatedgenerallyleadstobetterestimatesofprobability.Useunitsofmeasurementtoestimate,calculateandsolveproblemsineverydaycontextsinvolvinglength,area,volume,capacity,mass,timeandangle;knowroughmetricequivalentsofimperialmeasuresindailyuse(feet,miles,pounds,pints,gallons).Deduceanduseformulaefortheareaofatriangle,parallelogramandtrapezium;calculateareasofcompoundshapesmadefromrectanglesandtriangles."Usecompoundunitssuchasspeed,unitpricinganddensitytosolveproblems.Solvekinematicproblemsinvolvingconstantspeed."Knowthatarecurringdecimalisafraction;usedivisiontoconvertafractiontoadecimal;

andanglesUsetwoletternotationforalineandthreeletternotationforanangle Distinguishbetweenscalene,equilateral,isoscelesandright-angledtrianglesUnderstandandusetheanglepropertiesoftrianglesFindamissingangleinatriangle,usingtheanglesumofatriangleis180º Usetheside/anglepropertiesofisoscelesandequilateraltrianglesUnderstandandusetheanglesumoftrianglesCollectingDataBytheendofthemodulethestudentshouldbeableto:Specifytheproblemandplan Decidewhatdatatocollectandwhatstatisticalanalysisisneeded

Findthecoordinatesofthemidpointofalinesegment,AB,giventhecoordinatesofAandB Draw,labelandputsuitablescalesonaxes Recognisethatequationsoftheformy=mx+ccorrespondtostraight-linegraphsinthecoordinateplane Plotanddrawgraphsoffunctions Plotanddrawgraphsofstraightlinesoftheformy=mx+c Findthegradientofastraightlinefromagraph Findtheequationofalinethrough2points. Findtheequationofalinethroughonepointgiventhegradient. Averages&RangeBytheendofthemodulethestudentshouldbeableto:Calculatethemean,mode,medianandrangefor

Recognisesimplepatternsandcharacteristicrelationshipsinbarcharts,linegraphsandfrequencypolygons Knowthatcorrelationdoesnotimplycausation.ProbabilityBy the end of the modulethe student should be ableto:Distinguishbetweeneventswhichare:impossible,unlikely,evenchance,likely,andcertaintooccurMarkeventsand/orprobabilitiesonaprobabilityscaleof0to1 Writeprobabilitiesinwords,fractions,decimalsandpercentages Findtheprobabilityofaneventhappeningusingtheoreticalprobability Findtheprobabilityofaneventhappeningusingrelativefrequency Estimatethenumberof

anddecimals;calculatesimplepercentages.Consolidateandextendmentalmethodsofcalculationtoincludedecimals,fractionsandpercentages,accompaniedwhereappropriatebysuitablejottings;solvesimplewordproblemsmentally.Checkaresultbyconsideringwhetheritisoftherightorderofmagnitudeandbyworkingtheproblembackwards.Breakacomplexcalculationintosimplersteps,choosingandusingappropriateandefficientoperations,methodsandresources,includingICT.Presentandinterpretsolutionsinthecontextoftheoriginalproblem;explainandjustifymethodsandconclusions,orallyandinwriting.Uselettersymbolstorepresentunknownnumbersorvariables;knowthemeaningsofthewordsterm,expressionandequation.Understandthatalgebraicoperationsfollowthesameconventionsandorder

orderfractionsbywritingthemwithacommondenominatororbyconvertingthemtodecimals.Addandsubtractfractionsbywritingthemwithacommondenominator;calculatefractionsofquantities(fractionanswers);multiplyanddivideanintegerbyafraction.Interpretpercentageastheoperator‘somanyhundredthsof’andexpressonegivennumberasapercentageofanother;usetheequivalenceoffractions,decimalsandpercentagestocompareproportions;calculatepercentagesandfindtheoutcomeofagivenpercentageincreaseordecrease.Understandadditionandsubtractionoffractions;usethelawsofarithmeticandinverseoperations.Recallknownfacts,includingfractiontodecimalconversions;useknownfactstoderiveunknownfacts,includingproductssuchas0.7and6,and0.03and8.Consolidateandextendmentalmethodsofcalculation,workingwith

Collectdatafromavarietyofsuitableprimaryandsecondarysources Usesuitabledatacollectiontechniques Processandrepresentthedata Interpretanddiscussthedata UnderstandhowsourcesofdatamaybebiasedIdentifywhichprimarydatatheyneedtocollectandinwhatformat,includinggroupeddataConsiderfairnessUnderstandsampleandpopulationsDesignaquestionforaquestionnaire Criticisequestionsforaquestionnaire Designandusedata-collectionsheetsforgrouped,discreteandcontinuousdata

discretedata Calculatethemean,mode,medianandrangefromanorderedstemandleafdiagram Produceanorderedstemandleafdiagram Calculatethemodalclassandintervalcontainingthemedianforcontinuousdata Calculatethemean,medianandmodefromafrequencytable Estimatethemeanofgroupeddatausingthemid-intervalvalueComparethemeanandrangeoftwodistributions RecognisetheadvantagesanddisadvantagesbetweenmeasuresofaverageCalculatethemeanofasmalldataset,usingtheappropriatekeyonascientificcalculator Draw: Pictograms CompositebarchartsComparativeanddualbarchartsFrequencypolygons,HistogramswithequalclassintervalsFrequencydiagramsforgroupeddiscretedataLinegraphsInterpret: compositebarcharts comparativeanddualbarchartsstemandleafdiagramsscattergraphs

timesaneventwilloccur,giventheprobabilityandthenumberoftrials Usetheoreticalmodelstoincludeoutcomesusingdice,spinners,coins Listalloutcomesforsingleeventssystematically Listalloutcomesfortwosuccessiveeventssystematically Useanddrawsamplespacediagrams Addsimpleprobabilities Identifydifferentmutuallyexclusiveoutcomesandknowthatthesumoftheprobabilitiesofalltheseoutcomesis1 Use1−pastheprobabilityofaneventnotoccurringwherepistheprobabilityoftheeventoccurring Findamissingprobabilityfromalistortable Compareexperimentaldataandtheoreticalprobabilities

asarithmeticoperations.Simplifylinearalgebraicexpressionsbycollectingliketerms;begintomultiplyasingletermoverabracket(integercoefficients).Usesimpleformulaefrommathematicsandothersubjects,substitutepositiveintegersintosimplelinearexpressionsandformulaeand,insimplecases,deriveaformula.Identifythenecessaryinformationtosolveaproblem;representproblemsmathematically,makingcorrectuseofsymbols,words,diagramsandtables.Identifyparallelandperpendicularlines;knowthesumofanglesatapoint,onastraightlineandinatriangleandrecogniseverticallyoppositeangles.Useconventionsandnotationfor2-Dcoordinatesinallfourquadrants;findcoordinatesofpointsdeterminedbygeometricinformation.Calculatestatisticsforsmallsetsofdiscretedata:-findthemode,

decimals,fractionsandpercentages;solvewordproblemsmentally.Begintodistinguishthedifferentrolesplayedbylettersymbolsinequations,formulaeandfunctions;knowthemeaningsofthewordsformulaandfunction.Knowthatalgebraicoperationsfollowthesameconventionsandorderasarithmeticoperations;useindexnotationforsmallpositiveintegerpowers.Simplifyortransformlinearexpressionsbycollectingliketerms;multiplyasingletermoverabracket.Useformulaefrommathematicsandothersubjects;substituteintegersintosimpleformulae,andpositiveintegersintoexpressionsinvolvingsmallpowers(e.g.3x2+4or2x3);derivesimpleformulae.Knowandusetheformulaforthevolumeofacuboid;calculatevolumesandsurfaceareasofcuboidsandshapesmadefromcuboids.Investigateinarangeofcontexts:measures.Estimateprobabilitiesfromexperimentaldata;

CollectdatausingvariousmethodsSort,classifyandtabulatedataanddiscreteorcontinuousquantitativedataGroupdiscreteandcontinuousdataintoclassintervalsofequalwidth Extractdatafromlistsandtables Designandusetwo-waytablesfordiscreteandgroupeddata Useinformationprovidedtocompleteatwowaytable Inferpropertiesofapopulationfromasamplewhilstknowingthelimitationofthesample.Limitationofasample.IntroductiontoAlgebraBytheendofthemodulethestudentshouldbeableto:Usenotationandsymbolscorrectly Writeanexpression

frequencypolygonsConsideroutlierswhencalculatingrange.CirclesBytheendofthemodulethestudentshouldbeableto:FindcircumferencesofcirclesandareasenclosedbycirclesRecallandusetheformulaeforthecircumferenceofacircleandtheareaenclosedbyacircle Useπ≈3.142orusetheπbuttononacalculator Findtheperimetersandareasofsemicirclesandquartercircles Calculatewithmultiplesofπ.Findareasandperimetersofcompoundshapesinvolvingcirclesandcalculatearclengthsandareasofsectors.CirclesBytheendofthemodulethestudentshouldbeableto:

Findcircumferencesofcirclesandareasenclosed

Comparerelativefrequenciesfromsamplesofdifferentsizes Usetreediagramstosolveprobabilityproblems. UseVenndiagrams Pythagoras’TheoremUnderstand and recallPythagoras’Theorem UsePythagoras’ theoremtofindthehypotenuse UsePythagoras’ theoremtofindaside UsePythagoras’ theoremtofind the length of a linesegment from a coordinategrid ApplyPythagoras’theoremtopracticalsituations FormulaeDeriveasimpleformula,includingthosewithsquares,cubesandroots Useformulaefrommathematicsandothersubjectsexpressedinitiallyinwordsandthenusinglettersandsymbols

medianandrange,andthemodalclassforgroupeddata;calculatethemean,includingfromasimplefrequencytable,usingacalculatorforalargernumberofitems.Interpretdiagramsandgraphs(includingpiecharts),anddrawconclusionsbasedontheshapeofgraphsandsimplestatisticsforasingledistribution.Usevocabularyandideasofprobability,drawingonexperience.Understandandusetheprobabilityscalefrom0to1;findandjustifyprobabilitiesbasedonequallylikelyoutcomesinsimplecontexts;identifyallthepossiblemutuallyexclusiveoutcomesofasingleevent.Collectdatafromasimpleexperimentandrecordinafrequencytable;estimateprobabilitiesbasedonthisdata.SPRINGRoundpositivewholenumberstothenearest10,100or1000anddecimalstothenearestwholenumberorone

understandthat:-ifanexperimentisrepeatedtheestimatebecomesmorereliableandclosertothetheoreticalprobability.AUTUMNReadandwritepositiveintegerpowersof10;multiplyanddivideintegersanddecimalsby0.1,0.01.Orderdecimals.Roundpositivenumberstoanygivenpowerof10;rounddecimalstothenearestwholenumberortooneortwodecimalplaces.Consolidateandextendmentalmethodsofcalculation,workingwithdecimals,squaresandsquareroots,cubesandcuberoots;solvewordproblemsmentally.Makeandjustifyestimatesandapproximationsofcalculations.Consolidatestandardcolumnproceduresforadditionandsubtractionofintegersanddecimalswithuptotwoplaces.Discussaproblemthatcanbeaddressedbystatisticalmethodsandidentifyrelatedquestionstoexplore.

Simplifyalgebraicexpressionsinoneormoreliketerms,byaddingandsubtractingUnderstandthedifferencebetweentheword‘equation’,‘formula’,and‘expression’Multiplyanddividewithvariablesandnumbers Multiplyasinglealgebraictermoverabracket Writeexpressionsusingsquaresandcubes Factorisealgebraicexpressionsbytakingoutcommonfactors DecimalsUnderstandplacevalue,identifyingthevaluesofthedigits Writedecimalsinascendingorderofsize Approximatedecimalstoagivennumberofdecimalplacesorto

bycircles Recallandusetheformulaeforthecircumferenceofacircleandtheareaenclosedbyacircle Useπ≈3.142orusetheπbuttononacalculator Findtheperimetersandareasofsemicirclesandquartercircles Calculatewithmultiplesofπ.Findareasandperimetersofcompoundshapesinvolvingcirclesandcalculatearclengthsandareasofsectors.Constructions,Loci&CongruenceBytheendofthemodulethestudentshouldbeableto:Usestraightedgeandapairofcompassestodostandardconstructionssuchas ConstructatriangleConstructanequilateraltriangleUnderstand,fromtheexperienceofconstructing

Substitutenumbersintoaformula Substitutepositiveandnegativenumbersintoexpressionssuchas3x²+4and2x³ Changethesubjectofaformula Findthesolutiontoaproblembywritinganequationandsolvingit SimultaneousEquations&QuadraticsBy the end of the modulethe student should be ableto:Multiply 2 brackets andfactorise.Expanddoublebrackets.SolveQuadraticsbyfactorising.Generatepointsandplotgraphsofsimplequadraticfunctions,thenmoregeneralquadraticfunctions Findapproximatesolutionsofaquadraticequationfromthegraphofthecorrespondingquadraticfunction

decimalplace.Understandaddition,subtraction,multiplicationanddivisionastheyapplytowholenumbersanddecimals;knowhowtousethelawsofarithmeticandinverseoperations.Knowandusetheorderofoperations,includingbrackets.Consolidateandextendmentalmethodsofcalculationtoincludedecimals,fractionsandpercentages,accompaniedwhereappropriatebysuitablejottings;solvesimplewordproblemsmentally.Makeandjustifyestimatesandapproximationsofcalculations.Multiplyanddividethree-digitbytwo-digitwholenumbers;extendtomultiplyinganddividingdecimalswithoneortwoplacesbysingle-digitwholenumbers.Checkaresultbyconsideringwhetheritisoftherightorderofmagnitudeandbyworkingtheproblembackwards.Carryoutcalculationswithmorethanonestep

Decidewhichdatatocollecttoansweraquestion,andthedegreeofaccuracyneeded;identifypossiblesources.Planhowtocollectthedata,includingsamplesize;designandusetwo-waytablesfordiscretedata.Collectdatausingasuitablemethod,suchasobservation,controlledexperimentusingICT,orquestionnaire.Calculatestatistics,includingwithacalculator;recognisewhenitisappropriatetousetherange,mean,medianandmode;constructandusestem-and-leafdiagrams.Construct,onpaperandusingICT:piechartsforcategoricaldata;barchartsandfrequencydiagramsfordiscretedata;simplescattergraphs;identifywhicharemostusefulinthecontextoftheproblem.Interprettables,graphsanddiagramsfordiscretedataanddrawinferencesthatrelatetotheproblembeingdiscussed;relatesummariseddatatothequestionsbeingexplored.Communicateorallyand

onesignificantfigureAddandsubtractdecimalsMultiplyanddividedecimalnumbersbyintegersanddecimalnumbers Recallintegersquaresupto15×15andthecorrespondingsquareroots Recallthecubesof2,3,4,5and10 Findsquaresandcubes Findsquarerootsandcuberoots Knowthat,eg13.5÷0.5=135÷5 Checktheiranswersbyrounding,andknowthateg29´31»30´30 Useinverseoperations(useonecalculationtofindtheanswertoanother) Checkcalculationsbyrounding,eg29´31»30´30

them,thattrianglessatisfyingSSS,SAS,ASAandRHSareunique,butSSAtrianglesarenotConstructtheperpendicularbisectorofagivenlineConstructtheperpendicularfromapointtoalineConstructthebisectorofagivenangleConstructanglesof60º,90º,30º,45ºDrawparallellinesConstructdiagramsofeveryday2-Dsituationsinvolvingrectangles,triangles,perpendicularandparallellinesDrawandconstructdiagramsfromgiveninstructions AregionboundedbyacircleandanintersectinglineAgivendistancefromapointandagivendistancefromalineEqualdistancesfrom2pointsor2linesegmentsRegionswhichmaybe

Sketchandrecognisecubicandreciprocalgraphs.NewAdditionalContentforExams–StandardForm&SimultaneousEquationsCalculate using standardformwithoutacalculator.Solve simultaneousequations (algebraically andgraphically).Derivesimultaneousfromreallifesituations

HIGHERSimultaneous&QuadraticEquationsFindtheexactsolutionsoftwosimultaneousequationsintwounknowns Useeliminationorsubstitutiontosolvesimultaneousequations Interpretapairofsimultaneousequationsasapairofstraightlinesandtheirsolutionasthepointofintersection.Considerthereallifeapplications,egmobilephonebills Setupandsolveapairofsimultaneousequationsintwovariables

usingbracketsandthememory;usethesquarerootandsignchangekeys.Usenamesandabbreviationsofunitsofmeasurementtomeasure,estimate,calculateandsolveproblemsineverydaycontextsinvolvinglength,area,mass,capacityandtime;convertonemetricunittoanother(e.g.gramstokilograms);readandinterpretscalesonarangeofmeasuringinstruments.Begintoidentifyanduseangle,sideandsymmetrypropertiesoftrianglesandquadrilaterals;solvegeometricalproblemsinvolvingtheseproperties,usingstep-by-stepdeductionandexplainingreasoningwithdiagramsandtext.Use2-Drepresentationstovisualise3-Dshapesanddeducesomeoftheirproperties.Recogniseandusemultiples,factors(divisors),common

onpapertheresultsofastatisticalenquiryandthemethodsused,usingICTasappropriate;justifythechoiceofwhatispresented.Expresssimplefunctionsinsymbols;representmappingsexpressedalgebraically."Generatepointsinallfourquadrantsandplotthegraphsoflinearfunctions,whereyisgivenexplicitlyintermsofx,onpaperandusingICT;recognisethatequationsoftheformy=mx+ccorrespondtostraight-linegraphs.RefertotheCartesianPlaneorCartesianAxesasthemathematicalwaytonamethesegraphs."Constructlinearfunctionsarisingfromreal-lifeproblemsandplottheircorrespondinggraphs;discussandinterpretgraphsarisingfromrealsituations.Usestandardcolumnproceduresformultiplicationanddivisionofintegersanddecimals,includingbydecimalssuchas0.6or0.06;understandwheretopositionthedecimalpointbyconsideringequivalentcalculations.

Checkanswersbyreversecalculation,egif9´23=207then207÷9=23 Useinverseoperations(useonecalculationtofindtheanswertoanother)Checkcalculationsbyrounding,eg29´31»30´30 Checkanswersbyreversecalculation,egif9´23=207then207÷9=23Roundtobothdecimalplacesandsignificantfigures.Specifyerrorduetorounding.Similarity,SymmetryandCongruenceBytheendofthemodulethestudentshouldbeableto:Recognisereflectionsymmetryof2-Dshapes Identifyanddrawlinesofsymmetryonashape

definedby‘nearerto’or‘greaterthan’FindanddescriberegionssatisfyingacombinationoflociConstructforexamplearegularhexagoninsideacircle UsecongruencecriteriafortrianglesFractions,Decimals&PercentagesUnderstandthatapercentageisafractioninhundredths Convertbetweenfractionsdecimalsandpercentages Writeonenumberasapercentageofanothernumber Calculatethepercentageofagivenamount Usepercentagestosolveproblems Convertbetweenfractions,decimalsandpercentagestofindpercentagechange Findapercentageofaquantityinorderto

Solvesimplequadraticequationsbyfactorisationandcompletingthesquare SolvequadraticinequalitiesSolvesimplequadraticequationsbyusingthequadraticformula LearnthequadraticequationformulaSelectandapplyalgebraicandgraphicaltechniquestosolvesimultaneousequationswhereoneislinearandonequadratic Solveequationsinvolvingalgebraicfractionswhichleadtoquadraticequations Solvequadraticequationsbycompletingthesquare Plotandrecognisecubic,reciprocal,exponentialandcircularfunctionsy=sinxandy=cosx,withintherange-360ºto+360º(seeabove) Usethegraphsofthesefunctionstofindapproximatesolutionstoequations,eggivenxfindy(andviceversa) Matchequationswiththeirgraphs

factorandprimes(lessthan100);usesimpletestsofdivisibility.Recognisethefirstfewtriangularnumbers,squaresofnumberstoatleast12´12,andthecorrespondingroots.Usethesquarerootkey.Generatetermsofasimplesequence,givenarule(e.g.findingatermfromthepreviousterm,findingatermgivenitspositioninthesequence).Generatesequencesfrompracticalcontextsanddescribethegeneralterminsimplecases.Expresssimplefunctionsinwords,thenusingsymbols;representtheminmappings.Generatecoordinatepairsthatsatisfyasimplelinearrule;plotthegraphsofsimplelinearfunctions,whereyisgivenexplicitlyintermsofx,onpaperandusingICT;recognisestraight-linegraphsparalleltothex-axisory-axis.Breakacomplexcalculationintosimplersteps,choosingandusingappropriateandefficientoperations,methodsandresources,

CheckaresultbyconsideringwhetheritisoftherightorderofmagnitudeandbyworkingtheproblembackwardsCarryoutmoredifficultcalculationseffectivelyandefficientlyusingthefunctionkeysofacalculatorforsignchange,powers,rootsandfractions;usebracketsandthememory.Enternumbersandinterpretthedisplayofacalculatorindifferentcontexts(negativenumbers,fractions,decimals,percentages,money,metricmeasures,time).Knowthatiftwo2-Dshapesarecongruent,correspondingsidesandanglesareequal.Transform2-Dshapesbysimplecombinationsofrotations,reflectionsandtranslations,onpaperandusingICT;identifyallthesymmetriesof2-Dshapes.Transform2-Dshapesbysimplecombinationsofrotations,reflectionsandtranslations,onpaperandusingICT;identifyallthesymmetriesof2-Dshapes.Understandandusethe

Recogniserotationsymmetryof2-Dshapes Identifytheorderofrotationalsymmetryofa2-Dshape Draworcompletediagramswithagivennumberoflinesofsymmetry Draworcompletediagramswithagivenorderofrotationalsymmetry Understandcongruence Identifyshapeswhicharecongruent Understandsimilarity Identifyshapeswhicharesimilar,includingallcirclesorallregularpolygonswithequalnumberofsides

increaseordecrease Usepercentagesinreal-lifesituationsValueofprofitorlossSimpleinterestIncometaxcalculationsSolveproblemsinvolvingpercentagechangeandreversepercentages.

Calculatecompoundinterest. Usegrowthanddecaytosolveproblems.LinearEquations&InequalitiesBy the end of themodulethestudentshouldbeableto:Setupsimpleequations Rearrangesimpleequations Solvesimpleequations Solvelinearequations,withintegercoefficients,inwhichtheunknownappearsoneithersideoronbothsidesoftheequation

Recognisethecharacteristicshapesofallthesefunctions Constructthegraphsofsimplelociincludingthecirclex²+y²=r²foracircleofradiusrcentredattheoriginofthecoordinateplane Findtheintersectionpointsofagivenstraightlinewiththiscirclegraphically Selectandapplyconstructiontechniquesandunderstandingoflocitodrawgraphsbasedoncirclesandperpendicularsoflines Derivethequadraticequationbycompletingthesquare Locateturningpointsbycompletingthesquare.(Itdoesnotspecifyturningpointsinthetextbooks.)Applyconceptsofrateschangesbylookingatthegradientsoftangentsandchordstoacurve.Recogniseandusetheequationofacirclecentredattheorigin.Findtheequationofatangenttoacircleatagivenpoint,usingthefactitisperpendiculartotheradius.

includingICT.Recognisetheequivalenceofpercentages,fractionsanddecimals;calculatesimplepercentagesandusepercentagestocomparesimpleproportions.Understandtherelationshipbetweenratioandproportion;usedirectproportioninsimplecontexts;userationotation,reducearatiotoitssimplestformanddivideaquantityintotwopartsinagivenratio;solvesimpleproblemsaboutratioandproportionusinginformalstrategies.Checkaresultbyconsideringwhetheritisoftherightorderofmagnitudeandbyworkingtheproblembackwards.Givenaproblemthatcanbeaddressedbystatisticalmethods,suggestpossibleanswers.Decidewhichdatawouldberelevanttoanenquiryandpossiblesources.Planhowtocollectandorganisesmallsetsofdata;designadatacollectionsheetor

languageandnotationassociatedwithenlargement;enlarge2-Dshapes,givenacentreofenlargementandapositivewhole-numberscalefactor;exploreenlargementusingICT.Begintodistinguishthedifferentrolesplayedbylettersymbolsinequations,formulaeandfunctions;knowthemeaningsofthewordsformulaandfunction.Constructandsolvelinearequationswithintegercoefficients(unknownoneitherorbothsides,withoutandwithbrackets)usingappropriatemethods(e.g.inverseoperations,transformingbothsidesinthesameway).Useformulaefrommathematicsandothersubjects;substituteintegersintosimpleformulae,includingexamplesthatleadtoanequationtosolve;derivesimpleformulae.SUMMERUnderstandadditionandsubtractionoffractionsandintegers,andmultiplicationanddivisionofintegers;usethelawsofarithmetic

Recallthepropertiesanddefinitionsofspecialtypesofquadrilaterals,includingsymmetryproperties Listthepropertiesofeach,oridentify(name)agivenshape Drawsketchesofshapes Nameallquadrilateralsthathaveaspecificproperty Identifyquadrilateralsfromeverydayusage Classifyquadrilateralsbytheirgeometricproperties Distinguishbetweenscalene,equilateral,isoscelesandright-angledtriangles Understandanduse

Solvelinearequationswhichincludebrackets,thosethathavenegativesignsoccurringanywhereintheequation,andthosewithanegativesolution Solvelinearequationsinoneunknown,withintegerorfractionalcoefficients Uselinearequationstosolvewordproblems Solvesimplelinearinequalitiesinonevariable,andrepresentthesolutionsetonanumberline Usethecorrectnotationtoshowinclusiveandexclusiveinequalities Solvealgebraicequationsinvolvingsquaresandcubesegx³+3x=40 Solve‘reallife’problemsonareasandvolumes,egthelengthofarectangularroomis2mlongerthanthewidth.Iftheareais30m²,findthewidth.

SurfaceArea&VolumeFindthesurfaceareaofsimpleshapes(prisms)usingtheformulaefortrianglesandrectangles,andothershapes RecallandusetheformulaeforthecircumferenceofacircleandtheareaenclosedbyacircleGiveanexactanswertoaquestioninvolvingtheareaofacircle Calculatethelengthsofarcsandtheareasofsectorsofcircles Answersintermsofπmayberequired Findthesurfaceareaofacylinder FindtheareaofasegmentofacirclegiventheradiusandlengthofthechordConvertbetweenunitsofarea Useaxesandcoordinatestospecifypointsinallfourquadrantsin2-Dand3-D

questionnairetouseinasimplesurvey;constructfrequencytablesfordiscretedata,groupedwhereappropriateinequalclassintervals.Collectsmallsetsofdatafromsurveysandexperiments,asplanned."Construct,onpaperandusingICT,graphsanddiagramstorepresentdata,including:bar-linegraphs;frequencydiagramsforgroupeddiscretedata;useICTtogeneratepiecharts."Interpretdiagramsandgraphs(includingpiecharts),anddrawsimpleconclusionsbasedontheshapeofgraphs.Solvewordproblemsandinvestigateinarangeofcontexts:handlingdata.Solvewordproblemsandinvestigateinarangeofcontexts:numberandalgebra.Identifythenecessaryinformationtosolveaproblem;representproblemsmathematically,makingcorrectuseofsymbols,words,diagrams,tablesandgraphs.Uselettersymbolstorepresentunknown

andinverseoperations."Usetheorderofoperations,includingbrackets,withmorecomplexcalculations.Makeandjustifyestimatesandapproximationsofcalculations."Consolidateandextendmentalmethodsofcalculation,workingwithdecimals,fractionsandpercentages,squaresandsquareroots,cubesandcuberoots;solvewordproblemsmentally.Consolidatestandardcolumnproceduresforadditionandsubtractionofintegersanddecimalswithuptotwoplaces.Usestandardcolumnproceduresformultiplicationanddivisionofintegersanddecimals,includingbydecimalssuchas0.6or0.06;understandwheretopositionthedecimalpointbyconsideringequivalentcalculations.Simplifyortransformlinearexpressionsbycollectingliketerms;multiplyasingletermoverabracket.Constructandsolvelinearequationswithintegercoefficients(unknownoneitherorbothsides,withoutand

theanglepropertiesoftriangles Makeaccuratedrawingoftrianglesandother2-Dshapesusingarulerandaprotractor Recallthedefinitionofacircleandidentifyanddrawpartsofacircle Drawacirclegivenitsradiusordiameter AnglesandShapesCalculateandusethesumsoftheinterioranglesofpolygons Usegeometricallanguageappropriatelyandrecogniseandnamepentagons,hexagons,heptagons,octagonsanddecagons Know,orworkout,therelationshipbetweenthenumberofsidesofapolygonandthesumofitsinteriorangles

(

3DShapesandVolumeBy the end of themodulethestudentshouldbeableto:Identifyandnamecommonsolids:cube,cuboid,cylinder,prism,pyramid,sphereandcone Knowthetermsface,edgeandvertex Use2-Drepresentationsof3-Dshapes Useisometricgrids Drawnetsandshowhowtheyfoldtomakea3-Dsolid Understandanddrawfrontandsideelevationsandplansofshapesmadefromsimplesolids Giventhefrontandsideelevationsandtheplanofasolid,drawasketchofthe3-Dsolid Findvolumesofshapesbycountingcubes Recallanduseformulaeforthevolumeofcubesandcuboids

Findthecoordinatesofpointsidentifiedbygeometricalinformationin2-Dand3-D Knowanduseformulaetocalculatethesurfaceareasandvolumesofcuboidsandright-prismsSolvearangeofproblemsinvolvingsurfaceareaandvolume,eggiventhevolumeandlengthofacylinderfindtheradius Findthevolumeofacylinderandsurfaceareaofacylinder Convertbetweenvolumemeasures,includingcubiccentimetresandcubicmetres Solveproblemsinvolvingmorecomplexshapesandsolids,includingsegmentsofcirclesandfrustumsofcones Findthesurfaceareaandvolumesofcompoundsolidsconstructedfrom;cubes,cuboids,cones,pyramids,spheres,hemispheres,cylinder,egsolidsineverydayuse IndexNotation&Surds

numbersorvariables;knowthemeaningsofthewordsterm,expressionandequation.Understandthatalgebraicoperationsfollowthesameconventionsandorderasarithmeticoperations.Simplifylinearalgebraicexpressionsbycollectingliketerms;begintomultiplyasingletermoverabracket(integercoefficients).Constructandsolvesimplelinearequationswithintegercoefficients(unknownononesideonly)usinganappropriatemethod(e.g.inverseoperations)."Usearulerandprotractorto:measureanddrawlinestonearestmillimetreandangles,includingreflexangles,tothenearestdegree;constructatrianglegiventwosidesandtheincludedangle(SAS)ortwoanglesandtheincludedside(ASA);exploretheseconstructionsusingICT."SUMMERRecogniseandusemultiples,factors

withbrackets)usingappropriatemethods(e.g.inverseoperations,transformingbothsidesinthesameway).Begintousegraphsandsetupequationstosolvesimpleproblemsinvolvingdirectproportion.Discussaproblemthatcanbeaddressedbystatisticalmethodsandidentifyrelatedquestionstoexplore.Decidewhichdatatocollecttoansweraquestion,andthedegreeofaccuracyneeded;identifypossiblesources.Planhowtocollectthedata,includingsamplesize;constructfrequencytableswithgivenequalclassintervalsforsetsofcontinuousdata.GiventhecoordinatesofpointsAandB,findthemid-pointofthelinesegmentAB.Usestraightedgeandcompassestoconstruct:atriangle,giventhreesides(SSS);useICTtoexplorethisconstruction.(Findsimpleloci,bothbyreasoningandbyusingICT,toproduceshapesandpaths,e.g.anequilateraltriangle.)-Lociandbearingsareno

7.2)

Knowthatthesumoftheexterioranglesofanypolygonis360° Calculatethesizeofeachexterior/interiorangleofaregularpolygon Understandtessellationsofregularandirregularpolygons Tessellatecombinationsofpolygons Explainwhysomeshapestessellateandwhyothershapesdonot Understandandusetheanglepropertiesofparallellines Markparallel&perpendicularlinesonadiagram

Calculatethevolumesofrightprismsandshapesmadefromcubesandcuboids Convertbetweenunitsofvolume Convertbetweenunitsofarea Findthesurfaceareaandvolumeofacylinder RealLife&QuadraticGraphsBy the end of themodulethestudentshouldbeableto:

Drawgraphsrepresenting‘real’exampleslikefillingabath/containers

Interpretanddrawlineargraphs,includingconversiongraphs,fuelbillsetc Solveproblemsrelatingtomobilephonebillswithfixedchargeandpriceperunit Interpretnon-lineargraphslikethenumberofcansinavendingmachineattimesthroughoutthe

Findthevalueofcalculationsusingindices

Useindexlawstosimplifyandcalculatenumericalexpressionsinvolvingpowers,eg(23´25)÷24,40,8–2/3

Useindexnotationforintegerpowersof10 Usestandardform,expressedinconventionalnotation Beabletowriteverylargeandverysmallnumberspresentedinacontextinstandardform Convertbetweenordinaryandstandardformrepresentations Interpretacalculatordisplayusingstandardform Calculatewithstandardform Useindexlawstosimplifyandcalculatethevalueofnumericalexpressionsinvolvingmultiplicationanddivisionofintegerpowers,andpowersofapower

(divisors),commonfactor,highestcommonfactorandlowestcommonmultipleinsimplecases,andprimes(lessthan100);usesimpletestsofdivisibility.Consolidatetherapidrecallofnumberfacts,includingpositiveintegercomplementsto100andmultiplicationfactsto10´10,andquicklyderiveassociateddivisionfacts.Consolidateandextendmentalmethodstoincludedecimals,fractionsandpercentages,accompaniedwhereappropriatebysuitablejottings;solvesimplewordproblemsmentally.Makeandjustifyestimatesandapproximationsofcalculations.Constructandsolvesimplelinearequationswithintegercoefficients(unknownononesideonly)usinganappropriatemethod(e.g.inverseoperations).Generatesequencesfrompracticalcontextsanddescribethegeneralterminsimplecases.Expresssimplefunctions(inwords,then)usingsymbols;representthem

longerinKS3-sothissectiondoesn'tneedcovering.SATLevel4-6Usestandardcolumnproceduresformultiplicationanddivisionofintegersanddecimals,includingbydecimalssuchas0.6or0.06;understandwheretopositionthedecimalpointbyconsideringequivalentcalculations.Checkaresultbyconsideringwhetheritisoftherightorderofmagnitudeandbyworkingtheproblembackwards.Consolidateunderstandingoftherelationshipbetweenratioandproportion;reducearatiotoitssimplestform,includingaratioexpressedindifferentunits,recognisinglinkswithfractionnotation.Calculatemissingquantitiesandtotalsusinggivenratios,includingreductiontosimplestform.Useunitsofmeasurementtoestimate,calculateandsolveproblemsineverydaycontexts.Plotthegraphsoflinearfunctions,whereyis

Findmissinganglesusingpropertiesofcorrespondingandalternateangles Understandandusetheanglepropertiesofquadrilaterals Usethefactthatanglesumofaquadrilateralis360º Givereasonsforanglecalculations Usethreefigure-bearingstospecifydirection MarkonadiagramthepositionofpointBgivenitsbearingfromthepointA Giveabearingbetweenthepointsonamaporscaledplan GiventhebearingofpointAfrompointB,workoutthebearingofBfromA Recallandusepropertiesof

day(

22.1–22.3)

Substitutevaluesofx intoa quadratic function tofind the correspondingvaluesofy Draw graphs of quadraticfunctions Use quadratic graphs tosolve approximatesolution of a quadraticequation from the graphof the correspondingquadraticfunction Interpretgradientsfromreallifegraphsegforheightofbathwatervstime,thegradientistherateoffilling Solveproblemsinvolvingmoneyconversions,eg£’stoEurosetc

Knowthat,egx3=64Þx=82/3

Rationalisethedenominator,

eg13

1-

=÷÷ø

öççè

æ +213

,and,eg

write(Ö18+10)÷Ö2intheformp+qÖ2

Similarity&CongruenceUnderstandanduseSSS,SAS,ASAandRHSconditionstoprovethecongruenceoftrianglesusingformalarguments,andtoverifystandardrulerandapairofcompassesconstructions Understandsimilarityoftrianglesandofotherplanefigures,andusethistomakegeometricinferences Formalgeometricproofofsimilarityoftwogiventriangles Recognisethatallcorrespondinganglesinsimilarfiguresareequalinsizewhenthelengthsofsidesarenot

inmappings.Calculatestatisticsforsmallsetsofdiscretedata:-findthemode,medianandrange,andthemodalclassforgroupeddata;-calculatethemean,includingfromasimplefrequencytable,usingacalculatorforalargernumberofitems.Understandandusethelanguageandnotationassociatedwithreflections,translationsandrotations.Recogniseandvisualisethetransformationandsymmetryofa2-Dshape:reflectioningivenmirrorlines,andlinesymmetry;rotationaboutagivenpoint,androtationsymmetry;translation;explorethesetransformationsandsymmetriesusingICT.Revise&Prepareforendofyearexam.Set3-SAT-level3-5Set2-SAT-level4-6Multiplyanddividethree-digitbytwo-digitwholenumbers;extendtomultiplyingand

givenexplicitlyintermsofx,onpaperandusingICT.Constructlinearfunctionsarisingfromreal-lifeproblemsandplottheircorrespondinggraphs;discussandinterpretgraphsarisingfromrealsituations.Solvemoredemandingproblemsandinvestigateinarangeofcontexts:algebra.Solvemorecomplexproblemsbybreakingthemintosmallerstepsortasks,choosingandusingefficienttechniquesforalgebraicmanipulation.Knowandusegeometricpropertiesofcuboidsandshapesmadefromcuboids;begintouseplansandelevations.Makesimplescaledrawings.Findsimpleloci,bothbyreasoningandbyusingICT,toproduceshapesandpaths,e.g.anequilateraltriangle."Usebearingstospecifydirection.(ThishasbeenremovedfromKS3)"Knowandusetheformulaforthevolumeofacuboid;calculatevolumesandsurfaceareasofcuboidsand

perpendicularlines Understandtheproofthattheanglesumofatriangleis180° Understandaproofthattheexteriorangleofatriangleisequaltothesumoftheinterioranglesattheothertwovertices Makeanaccuratescaledrawingfromadiagram Identifyshapeswhicharesimilar,includingallcirclesorallregularpolygonswithequalnumberofsides Interpretmap/modelscalesasaratio FractionsBytheendofthemodulethestudentshouldbeableto:Visualiseafractiondiagrammatically

TransformationsDescribeandtransform2-Dshapesusingsinglerotations Understandthatrotationsarespecifiedbyacentreandan(anticlockwise)angle Findthecentreofrotation Rotateashapeabouttheorigin,oranyotherpoint Describeandtransform2-Dshapesusingsinglereflections Understandthatreflectionsarespecifiedbyamirrorline Identifytheequationofamirrorlineofsymmetry Describeandtransform2-Dshapesusingsingletranslations Understandthattranslationsarespecifiedbyadistanceanddirection(usingavector) Translateagivenshapebyavector

Understandtheeffectofenlargementforperimeter,areaandvolumeofshapesandsolids Understandthatenlargementdoesnothavethesameeffectonareaandvolume Usesimpleexamplesoftherelationshipbetweenenlargementandareasandvolumesofsimpleshapesandsolids Usetheeffectofenlargementonareasandvolumesofshapesandsolids Knowtherelationshipsbetweenlinear,areaandvolumescalefactorsofmathematicallysimilarshapesandsolids ProportionCalculateanunknownquantityfromquantitiesthatvaryindirectorinverseproportion Setupanduseequationstosolvewordandotherproblemsinvolvingdirectproportionorinverseproportionandrelatealgebraicsolutionstographicalrepresentationoftheequations

dividingdecimalswithoneortwoplacesbysingle-digitwholenumbers.Interpretthedisplayofacalculatorindifferentcontexts(decimals,percentages).Calculatesimplefractionsofquantitiesandmeasurements(whole-numberanswers);multiplyafractionbyaninteger.Recognisetheequivalenceofpercentages,fractionsanddecimals;calculatesimplepercentagesandusepercentagestocomparesimpleproportions.Breakacomplexcalculationintosimplersteps,choosingandusingappropriateandefficientoperations,methodsandresources,includingICT.Generatecoordinatepairsthatsatisfyasimplelinearrule;plotthegraphsofsimplelinearfunctions,whereyisgivenexplicitlyintermsofx,onpaperandusingICT;recognisestraight-linegraphsparalleltothex-axisory-axis.Begintoplotandinterpretthegraphsof

shapesmadefromcuboids.Collectdatausingasuitablemethod,suchasobservation,controlledexperiment,includingdataloggingusingICT,orquestionnaire.Calculatestatistics,includingwithacalculator;calculateameanusinganassumedmean;knowwhenitisappropriatetousethemodalclassforgroupeddata.Construct,onpaperandusingICT:barchartsandfrequencydiagramsforcontinuousdata;simplelinegraphsfortimeseries;identifywhicharemostusefulinthecontextoftheproblem.Interprettables,graphsanddiagramsforcontinuousdataanddrawinferencesthatrelatetotheproblembeingdiscussed;relatesummariseddatatothequestionsbeingexplored.Comparetwodistributionsusingtherangeandoneormoreofthemode,medianandmean.Communicateorallyandonpapertheresultsofastatisticalenquiryandthemethodsused,using

Understandafractionaspartofawhole Recogniseandwritefractionsineverydaysituations Findfractionsofamounts Writeafractioninitssimplestformandrecogniseequivalentfractions Comparethesizesoffractionsusingacommondenominator Addandsubtractfractionsbyusingacommondenominator Writeanimproperfractionasamixedfraction Convertbetweenfractionsanddecimals

Describeandtransform2-Dshapesusingenlargementsbyapositivescalefactor Understandthatanenlargementisspecifiedbyacentreandascalefactor Scaleashapeonagrid(withoutacentrespecified) Drawanenlargement Enlargeagivenshapeusing(0,0)asthecentreofenlargement Enlargeshapeswithacentreotherthan(0,0) Findthecentreofenlargement Recognisethatenlargementspreserveanglebutnotlength Identifythescalefactorofanenlargementofashapeastheratioofthelengthsoftwocorrespondingsides

Pythagoras’&TrigonometryUnderstand,recallandusePythagoras’theoremin2-D,thenin3-Dproblems Recallandusethetrigonometricratiostosolve2-Dand3-Dproblems Understandthelanguageofplanes,andrecognisethediagonalsofacuboid Calculatethelengthofadiagonalofacuboid Findtheanglebetweenalineandaplane(butnottheanglebetweentwoplanesorbetweentwoskewlines) Plotandrecognisecubic,reciprocal,exponentialandcircularfunctionsy=sinx,y=cosxandy=tanxwithintherange-360ºto+360º(seeabove) Usethegraphsofthesefunctionstofindapproximatesolutionstoequations,eggivenxfindy(andviceversa) Matchequationswiththeirgraphs

simplelinearfunctionsarisingfromreal-lifesituations.Suggestextensionstoproblemsbyasking‘Whatif…?’;begintogeneraliseandtounderstandthesignificanceofacounter-example.Solvewordproblemsandinvestigateinarangeofcontexts:shapeandspace.Suggestextensionstoproblemsbyasking‘Whatif...?’;begintogeneraliseandtounderstandthesignificanceofacounter-example.Begintoidentifyanduseangle,sideandsymmetrypropertiesoftrianglesandquadrilaterals;solvegeometricalproblemsinvolvingtheseproperties,usingstep-by-stepdeductionandexplainingreasoningwithdiagramsandtext.ExploretransformationsandsymmetriesusingICT.Usearulerandprotractorto:constructatrianglegiventwosidesandtheincludedangle(SAS)ortwoanglesandtheincludedside(ASA);explorethese

ICTasappropriate;justifythechoiceofwhatispresented.Compareexperimentalandtheoreticalprobabilitiesindifferentcontexts.MaxBox-Pupilscanproducealinegraphofresults,andpractiserepresentingdatatechniques.

Algebra2Bytheendofthemodulethestudentshouldbeableto:Useindexnotationforsquaresandcubes Useindexnotationforpowersof10 Findthevalueofcalculationsusingindices Useindexlawstosimplifyandcalculatethevalueofnumericalexpressionsinvolvingmultiplicationanddivisionofintegerpowers,andofpowersofapower Multiplyasinglealgebraictermoverabracket Usesimpleinstancesofindexlaws

Describeandtransform2-Dshapesusingcombinedrotations,reflections,translations,orenlargements Understandthatdistancesandanglesarepreservedunderrotations,reflectionsandtranslations,sothatanyshapeiscongruentunderanyofthesetransformations Describeatransformation Recognisethatallcorrespondinganglesinsimilarshapesareequalinsizewhenthecorrespondinglengthsofsidesarenotequalinsize Findcorrespondinglengthsinsimilarshapes.

HIGHERFractions,Decimals&PercentagesBytheendofthemodulethestudentshouldbeable

Recognisethecharacteristicshapesofallthesefunctions Constructthegraphsofsimplelociincludingthecirclex²+y²=r²forFindtheunknownlengths,orangles,innonright-angletrianglesusingthesineandcosinerules Findtheareaoftrianglesgiventwolengthsandanincludedangle Learnsine,cosineandareaoftriangle(usingsine)formulae.Knowexactvaluesforsin,cosandtanatkeyangles(0,30,45,60,90degrees).TransformationsofFunctionsApplytothegraphofy=f(x)thetransformationsy=f(x)+a,y=f(ax),y=f(x+a),y=af(x)forlinear,quadratic,sineandcosinefunctions Selectandapplythetransformationsofreflection,rotation,enlargementandtranslationoffunctionsexpressedalgebraically Interpretandanalyse

constructionsusingICT.Usearulerandprotractortoconstructsimplenetsof3-Dshapes,e.g.cuboid,regulartetrahedron,square-basedpyramid,triangularprism.Interpretdiagramsandgraphs(includingpiecharts),anddrawconclusionsbasedontheshapeofgraphsandsimplestatisticsforasingledistribution.Comparetwosimpledistributionsusingtherangeandoneofthemode,medianormean.Writeashortreportofastatisticalenquiryandillustratewithappropriatediagrams,graphsandcharts,usingICTasappropriate;justifythechoiceofwhatispresented.Understandandusetheprobabilityscalefrom0to1;findandjustifyprobabilitiesbasedonequallylikelyoutcomesinsimplecontexts;identifyallthepossiblemutuallyexclusiveoutcomesofasingleevent.Collectdatafromasimpleexperimentandrecordinafrequencytable;estimateprobabilitiesbasedon

Factorisealgebraicexpressionsbytakingoutcommonfactors Usebracketsandthehierarchyofoperations(BIDMAS) UsingACalculatorBytheendofthemodulethestudentshouldbeableto:Useinverseoperations(useonecalculationtofindtheanswertoanother) Understand‘reciprocal’asmultiplicativeinverse,knowingthatanynon-zeronumbermultipliedbyitsreciprocalis1(andthatzerohasnoreciprocalbecausedivisionbyzeroisundefined) Convertbetweenfractionsanddecimals

to:Understandthatapercentageisafractioninhundredths Convertbetweenfractions,decimalsandpercentages ConvertbetweenrecurringdecimalsandexactfractionsaswellasunderstandingtheproofWriteonenumberasapercentageofanothernumber Calculatethepercentageofagivenamount Findapercentageincrease/decreaseofanamount Findareversepercentage,egfindtheoriginalcostofanitemgiventhecostaftera10%deduction Useamultipliertoincreasebyagivenpercentoveragiventime,eg1.18´64increases64by10%over8years Calculatesimpleandcompoundinterest Userecurringdecimalsasfractions.

transformationsoffunctionsandwritethefunctionsalgebraicallyCircleGeometry/TheoremsRecallthedefinitionofacircleandidentify(name)anddrawthepartsofacircle

Understandrelatedtermsofacircle Drawacirclegiventheradiusordiameter Understandandusethefactthatthetangentatanypointonacircleisperpendiculartotheradiusatthatpoint Understandandusethefactthattangentsfromanexternalpointareequalinlength Findmissinganglesondiagrams Givereasonsforanglecalculationsinvolvingtheuseoftangenttheorems Proveandusethefactsthat: theanglesubtendedbyanarcatthecentreofacircleistwicetheanglesubtendedatanypointonthecircumference

thisdata.Compareexperimentalandtheoreticalprobabilitiesinsimplecontexts.Set3-PenguinInvestigationSet3-CandleboxSet2-PenguininvestigationSet2-Icecreams(howmanycombinations)Funmathematicallesson:e.g.makeahexaflexagon,ordoalessononyourfavouriteaspectofmaths!Havefun.

Recogniseterminating&recurringdecimals Interpretingacalculatordisplay Workingoutpowersandroots Usingacalculatortoworkoutcomplexcalculations Adding,Subtracting,Multiplying&Dividingusingstandardform MeasureInterpretscalesonarangeofmeasuringinstrumentsincmm,cm,m,km,ml,cl,l,mg,g,kg,tonnes,°CIndicategivenvaluesonascale Knowthatmeasurementsusingrealnumbersdependuponthechoiceofunit

Co-ordinates&LinearGraphsBytheendofthemodulethestudentshouldbeableto:Understandthatapercentageisafractioninhundredths Convertbetweenfractions,decimalsandpercentages ConvertbetweenrecurringdecimalsandexactfractionsaswellasunderstandingtheproofWriteonenumberasapercentageofanothernumber Calculatethepercentageofagivenamount Findapercentageincrease/decreaseofanamount Findareversepercentage,egfindtheoriginalcostofanitemgiventhecostaftera10%deduction Useamultipliertoincreasebyagivenpercentoveragiventime,

theangleinasemicircleisarightangleanglesinthesamesegmentareequaloppositeanglesofacyclicquadrilateralsumto180º

alternatesegmenttheorem

theperpendicularfromthecentreofacircletoachordbisectthechordAlgebraSimplifyrationalexpressionsbycancelling,adding,subtracting,andmultiplyingVectorsUnderstandthat2aisparalleltoaandtwiceitslength Understandthataisparallelto-aandintheoppositedirection Useandinterpretvectorsasdisplacementsintheplane(withanassociateddirection) Usestandardvectornotationtocombinevectorsbyaddition,egAB+BC=ACanda+b=c

Recognisethatmeasurementsgiventothenearestwholeunitmaybeinaccuratebyuptoonehalfineitherdirection Convertunitswithinonesystem Convertmetricunitstometricunits(Metricequivalentsshouldbeknown) Convertimperialunitstoimperialunits(NB:Conversionbetweenimperialunitswillbegiven) Convertbetweenmetricandimperialmeasures Knowroughmetricequivalentsofpounds,feet,miles,pintsandgallons,ie MetricImperial1kg=2.2pounds4.5 ints=1litre

eg1.18´64increases64by10%over8years Calculatesimpleandcompoundinterest Userecurringdecimalsasfractions.Ratio&ScaleUseratios Writeratiosintheirsimplestform Divideaquantityinagivenratio Solvearatioprobleminacontext Useandinterpretmapsandscaledrawings Readandconstructscaledrawingsdrawinglinesandshapestoscale Estimatelengthsusingascalediagram Solvewordproblemsaboutratioandproportion Calculateanunknownquantityfromquantitiesthatvaryindirectorinverseproportion

Representvectors,andcombinationsofvectors,intheplane Solvegeometricalproblemsin2-D,egshowthatjoiningthemidpointsofthesidesofanyquadrilateralformsaparallelogram

4.5l=1gallon8km=5miles30m=1footEstimateconversions Convertbetween12–hourand24–hourhourclocktimes Readbusandtraintimetablesandplanjourneys Usetherelationshipbetweendistance,speedandtimetosolveproblems Convertbetweenmetricunitsofspeed,egkm/htom/s Performcalculationswithdensity,massandvolume. Charts&GraphsBytheendofthemodulethestudentshouldbeabletoDraw:

TransformationsUnderstand translation asa combination of ahorizontal and verticalshiftincludingsignsfordirections Translateagivenshapeby

thevector 23

æ öç ÷-è ø

Understand rotation as a(anticlockwise)turnaboutagivenorigin Reflect shapes in a givenmirror line; parallel to thecoordinate axes and theny=xory=–x Enlarge shapes by a givenscale factor from a givenpoint; using positive andnegative scale factorsgreaterandlessthanone Find the centre ofenlargement Understand that shapesproduced by translation,rotationandreflectionarecongruenttotheimageDescribe and transform2-D shapes using singlerotations Understand that rotationsare specified by a centre

PictogramsCompositebarchartsComparativeanddualbarchartsFrequencypolygons,HistogramswithequalclassintervalsFrequencydiagramsforgroupeddiscretedataLinegraphsInterpret: compositebarchartscomparativeanddualbarchartsstemandleafdiagramsscattergraphsfrequencypolygonsFrompictograms,barcharts,linegraphsandhistogramswithequalclassintervals: readofffrequencyvaluescalculatetotalpopulation

and an (anticlockwise)angle Findthecentreofrotation Rotateashapeabouttheorigin,oranyotherpoint Describeandtransform2-Dshapesusingcombinedrotations,reflections,translations,orenlargements

Usecongruencetoshowthattranslations,rotationsandreflectionspreservelengthandangle,sothatanyfigureiscongruenttoitsimageunderanyofthesetransformations Distinguishpropertiesthatarepreservedunderparticulartransformations Recognisethatenlargementspreserveanglebutnotlength,linkingtosimilarity Describeatransformation Formulae&SolutionofLinearEquationsShowthesolutionsetofseveralinequalitiesintwovariablesonagraph

findgreatestandleastvaluesRecognisesimplepatternsandcharacteristicrelationshipsinbarcharts,linegraphsandfrequencypolygons Usedualorcomparativebarchartstocomparedistributions Representdatainapiechart Interpretdatainapiechart Understandthatthefrequencyrepresentedbycorrespondingsectorsintwopiechartsisdependentuponthetotalpopulationsrepresentedbyeachofthepiecharts Frompiecharts findthetotalfrequencyfindthesizeofeach

Deriveaformula Useformulaefrommathematicsandothersubjects Substitutenumbersintoaformula Substitutepositiveandnegativenumbersintoexpressionssuchas3x²+4and2x³ Setuplinearequationsfromwordproblems Solvesimplelinearequations Solvelinearequations,withintegercoefficients,inwhichtheunknownappearsoneithersideoronbothsidesoftheequation Solvelinearequationsthatincludebrackets,thosethathavenegativesignsoccurringanywhereintheequation,andthosewithanegativesolution Solvelinearequationsinoneunknown,withintegerorfractionalcoefficients Solvesimplelinearinequalitiesinonevariable,andrepresent

category

HIGHERNumberIdentifyfactors,multiplesandprimenumbers Findtheprimefactordecompositionofpositiveintegers Findthecommonfactorsandcommonmultiplesoftwonumbers FindtheHighestCommonFactor(HCF)andtheLeastCommonMultiple(LCM)oftwonumbers Recallintegersquaresfrom2×2to15×15andthecorrespondingsquareroots Recallthecubesof2,3,4,5and10 Useindexnotationforsquaresandcubes Usebracketsandthehierarchyofoperations(BIDMAS)

thesolutionsetonanumberlineUsethecorrectnotationtoshowinclusiveandexclusiveinequalities Changethesubjectofaformulaincludingcaseswherethesubjectisonbothsidesoftheoriginalformula,orwhereapowerofthesubjectappearsPythagoras’&TrigonometryUnderstand,recallandusePythagoras’theoremin2-D Calculatethelengthofalinesegmentina2-Dplane GiveananswerintheuseofPythagoras’Theoremas√13 Recallandusethetrigonometricratiostosolve2-Dproblems Findanglesofelevationandanglesofdepression QuadraticFunctions,Equations&GraphsGeneratepointsandplotgraphsofsimplequadraticfunctions,thenmoregeneralquadratic

Understandthattheinverseoperationofraisingapositivenumbertoapowernisraisingtheresultofthisoperationtothepower

n1

Useindexlawstosimplifyandcalculatethevalueofnumericalexpressionsinvolvingmultiplicationanddivisionofintegerpowers,andpowersofapower Useindexlawstosimplifyandcalculatenumericalexpressionsinvolvingpowers,eg(23´25)÷24,40,8–2/3Patterns&SequencesUsenotationandsymbolscorrectly Writeanexpression Manipulatealgebraicexpressionsbycollectingliketerms

functions Findapproximatesolutionsofaquadraticequationfromthegraphofthecorrespondingquadraticfunction Findtheintersectionpointsofthegraphsofalinearandquadraticfunction,knowingthatthesearetheapproximatesolutionsofthecorrespondingsimultaneousequationsrepresentingthelinearandquadraticfunctions Plotandrecognisecubic,reciprocal,exponentialandcircularfunctionsy=sinxandy=cosx,withintherange-360ºto+360º(seeabove)Usethegraphsofthesefunctionstofindapproximatesolutionstoequations,

eggivenxfindy(andviceversa)

Usecalculatorstoexploreexponentialgrowthanddecay Solvecubicfunctionsbysuccessivesubstitutionofvaluesofx

Substitutenumbersintoaformula Substitutepositiveandnegativenumbersintoexpressionssuchas3x²+4and2x³ Recognisesequencesofoddandevennumbers Generatesimplesequencesofnumbers,squaredintegersandsequencesderivedfromdiagrams Describetheterm-to-termdefinitionofasequenceinwords Identifywhichtermscannotbeinasequence Generatespecifictermsinasequenceusingtheposition-to-termandterm-to-termrules Findthenthtermofanarithmeticsequence Usethenthtermofan

Usesystematictrialandimprovementtofindapproximatesolutionsofequationswherethereisnosimpleanalyticalmethodofsolvingthem Understandtheconnectionsbetweenchangesofsignandlocationofroots

arithmeticsequence Recognisegeometricsequences(whenthecommonratiomaybeasurd.)FractionsFindequivalentfractionsComparethesizesoffractions Writeafractioninitssimplestform Findfractionsofanamount ConvertbetweenmixednumbersandimproperfractionsAddandsubtractfractions Multiplyanddividefractionsincludingmixednumbers Userecurringdecimalsasfractions.Integers&DecimalsUnderstand and orderintegers and decimals

Findequivalentfractions Writedecimalsinascendingorderofsize Understandandusepositivenumbersandnegativeintegers,bothaspositionsandtranslationsonanumberline Multiplyanddividebyanynumberbetween0and1 Multiplyanddividedecimalnumbersbywholenumbersanddecimalnumbers(upto2d.p.)eg266.22÷0.34 Add,subtract,multiplyanddivideintegers,negativenumbersanddecimals Roundwholenumberstothenearest,10,100,1000,… Rounddecimalstoappropriatenumbersofdecimalplacesorsignificantfigures

Checktheircalculationsbyrounding,eg29´31»30´30 CheckanswerstoadivisionsumusingmultiplicationeguseinverseoperationsMultiplyanddividewholenumbersbyagivenmultipleof10 Putdigitsinthecorrectplaceinadecimalnumber ApproximatedecimalstoagivennumberofdecimalplacesorsignificantfiguresKnowthateg13.5÷0.5=135÷5 Convertbetweenrecurringdecimalsandexactfractionsaswellasunderstandingtheproof Calculatetheupperandlowerboundsofcalculations,particularlywhenworkingwithmeasurements

Findtheupperandlowerboundsofcalculationsinvolvingperimeter,areasandvolumesof2-Dand3-DshapesFindupper&lowerboundsinreallifesituationsusingmeasurementsgiventoappropriatedegreesofaccuracyGivethefinalanswertoanappropriatedegreeofaccuracyfollowingananalysisoftheupperandlowerboundsofacalculation Userecurringdecimalsasfractions.ChangerecurringdecimalsintofractionsShape&AngleRecallandusepropertiesofangles –anglesatapoint –anglesatapointonastraightline –perpendicularlines –verticallyoppositeangles

Understandandusetheanglepropertiesofparallellines Understand,drawandmeasurebearings Calculatebearingsandsolvebearingsproblems Distinguishbetweenscalene,isosceles,equilateral,andright-angledtriangles Understandandusetheanglepropertiesoftriangles Usetheanglesumofatriangleis180º Understandandusetheanglepropertiesofintersectinglines Markparallellinesonadiagram Usethepropertiesofcorrespondingandalternateangles Understandandusetheanglepropertiesofquadrilaterals

Givereasonsforanglecalculations Explainwhytheanglesumofaquadrilateralis360º Understandtheproofthattheanglesumofatriangleis180º UnderstandaproofthattheexteriorangleofatriangleisequaltothesumoftheinterioranglesattheothertwoverticesUsethesize/anglepropertiesofisoscelesandequilateraltriangles Recallandusethesepropertiesofanglesinmorecomplexproblems Calculateandusethesumsoftheinterioranglesofpolygons Usegeometriclanguageappropriatelyandrecogniseandnamepentagons,hexagons,heptagons,octagonsanddecagons

Usetheanglesumsofirregularpolygons Calculateandusetheanglesofregularpolygons Usethesumoftheinterioranglesofannsidedpolygon Usethesumoftheexterioranglesofanypolygonis360º Usethesumoftheinteriorangleandtheexteriorangleis180º FindthesizeofeachinteriorangleorthesizeofeachexteriorangleorthenumberofsidesofaregularpolygonUnderstandtessellationsofregularandirregularpolygonsandcombinationsofpolygonsExplainwhysomeshapestessellatewhenothershapesdonot

CompoundMeasures

Convertbetweenunitsofmeasureinthesamesystem.(NB:Conversionbetweenimperialunitswillbegiven.metricequivalentsshouldbeknown) Knowroughmetricequivalentsofpounds,feet,miles,pintsandgallons:Metric/Imperial1kg=2.2pounds,1litre=1.75pints,4.5litres=1gallon,

30 km=5miles,30 m=1foot

Convertbetweenimperialandmetricmeasures Usetherelationshipbetweendistance,speedandtimetosolveproblems Convertbetweenmetricunitsofspeedegkm/htom/s Knowthatdensityisfoundbymass÷volume

Usetherelationshipbetweendensity,massandvolumetosolveproblems,egfindthemassofanobjectwithagivenvolumeanddensity Convertbetweenmetricunitsofdensityegkg/mtog/cm Calculatespeedwhen,egfractionsofanhourmustbeenteredasfractionsorasdecimals Similarity&CongruenceUnderstandanduseSSS,SAS,ASAandRHSconditionstoprovethecongruenceoftrianglesusingformalarguments,andtoverifystandardrulerandapairofcompassesconstructions Understandsimilarityoftrianglesandofotherplanefigures,andusethistomakegeometricinferences

Formalgeometricproofofsimilarityoftwogiventriangles Recognisethatallcorrespondinganglesinsimilarfiguresareequalinsizewhenthelengthsofsidesarenot AlgebraUsenotationandsymbolscorrectly Writeanexpression Manipulatealgebraicexpressionsbycollectingliketerms Multiplyasingletermoverabracket Factorisealgebraicexpressionsbytakingoutcommonfactors Expandtheproductoftwolinearexpressions Factorisequadraticexpressionsusingthedifferenceoftwosquares Perimeter&Area

Measuresidesofarectangletoworkoutperimeterorarea Calculateperimetersofshapesmadefromtrianglesandrectangles Findtheperimeterofrectanglesandtriangles Calculateareasofshapesmadefromtrianglesandrectangles Recallandusetheformulaefortheareaofatriangle,rectangleandaparallelogram Findtheareaofatrapeziumandaparallelogram Calculateperimeterandareaofcompoundshapesmadefromtriangles,rectanglesandothershapes Findcircumferencesofcirclesandareasenclosedbycircles

Recallandusetheformulaeforthecircumferenceofacircleandtheareaenclosedbyacircle Useπ≈3.142orusetheπbuttononacalculator Findtheperimetersandareasofsemicirclesandquartercircles 2D&3DShapesUse2-Drepresentationsof3-Dshapes Useisometricgrids Drawnetsandshowhowtheyfoldtomakea3-Dsolid Understandanddrawfrontandsideelevationsandplansofshapesmadefromsimplesolids Giventhefrontandsideelevationsandtheplanofasolid,drawasketchofthe3-Dsolid Constructions&Loci

Usestraightedgeandapairofcompassestodostandardconstructions Constructtrianglesincanequilateraltriangle Understand,fromtheexperienceofconstructingthem,thattrianglessatisfyingSSS,SAS,ASAandRHSareunique,butSSAtrianglesarenot Constructtheperpendicularbisectorofagivenline Constructtheperpendicularfromapointtoaline Constructtheperpendicularfromapointonaline Constructthebisectorofagivenangle Constructanglesof60º,90º,30º,45º Drawparallellines

Drawcirclesandarcstoagivenradius Constructaregularhexagoninsideacircle Constructdiagramsofeveryday2-Dsituationsinvolvingrectangles,triangles,perpendicularandparallellines Drawandconstructdiagramsfromgiveninformation Construct:-aregionboundedbyacircleandanintersectingline-agivendistancefromapointandagivendistancefromaline -equaldistancesfrom2pointsor2linesegments-regionswhichmaybedefinedby‘nearerto’or‘greaterthan’ Findanddescriberegionssatisfyingacombinationofloci Useandinterpret

mapsandscaledrawings Readandconstructscaledrawingsdrawinglinesandshapestoscale (12.6)Estimatelengthsusingascalediagram Formulae&SolutionofLinearEquationsSolvesimplelinearequations Selectanexpression/identity/equation/formulafromalist Solvelinearequations,withintegercoefficients,inwhichtheunknownappearsoneithersideoronbothsidesoftheequation Solvelinearequationsthatincludebrackets,thosethathavenegativesignsoccurringanywhereintheequation,andthosewithanegativesolution

Solvelinearequationsinoneunknown,withintegerorfractionalcoefficients Setuplinearequationsfromwordproblems