Mathematics Curriculum Map – Years...
Transcript of Mathematics Curriculum Map – Years...
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
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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