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  • Reception

    Mastery

    Scheme of Work

    Enjoying mathematics Creating mathematicians Breaking down barriers

    www.glowmathshub.org @GLOWmaths

  • MathematicsOverview:ReceptionMasteryofmathematicsintheEarlyYearswillmostlybeevidentwhenthepupilsinitiatetheirmathematicssuccessfully.Theywillusetheirmathsconsistentlyandwithoutovertadultsupportwhentheyaresecurewithaconcept.(EarlyYearsHandbook,December2015).

    Directteachingcouldbewithwholeclassorsmallergroupsandwillbeadultledandsuccessfullearningshouldbeobservedandassessedindependentofthis.ManyoftheseunitslinkwitheachotherandwithotherEarlyLearningGoalssuchasELG01ListeningandAttention,ELG2-UnderstandingandELG3Speaking.

    ThemasteryapproachtomathematicsalsoembracestheCharacteristicsofEffectiveLearningasstatedinDevelopmentMattersdocument.

    CharacteristicsofEffectiveLearning(DevelopmentMatters) PrinciplesofMastery(NCETM2015)PlayingandExploringEngagement

    Findingoutandexploring Playingwithwhattheyknow Beingwillingtohaveago

    Thereasoningbehindthemathematicalprocessesisemphasised.Teacher/pupilinteractionexploresindetailhowanswerswereobtained,whatthemethod/strategyworkedandwhatmightthemostefficientmethod/strategy.Teachingisunderpinnedbyabeliefoftheimportanceofmathsandthatthevastmajorityofchildrencansuceedinthelearningofmathematicsinlinewithnationalexpectationsfortheendofkeystage.

    ActivelearningMotivation Beinginvolvedandconcentrating Keepingtrying Enjoyingachievingwhattheysetouttodo

    Lessonsareshortbutintense.Teacherleddiscussionisinterspersedwithshorttasksand/orpupiltopupilorpupiltoteacherdiscussion.

    CreatingandThinkingCriticallyThinking Havingtheirownideas Makinglinks Choosingwaystodothings

    Learningisbrokendownintosmall,connectedstepsbuildingonwhatthepupilsalreadyknow.Thereisregularinterchangebetweenconcrete/contextualideasandtheirabstractorsymbolicrepresentation.

    Childrenshouldapplytheirmathematicsintoavarietyofcontextsandplaysituationstomakeconnections.Pupilsshoulduseanappropriateandrelevantvocabularyandshouldbeactivelyencouragedtodiscusstheirmathsandreasonmathematically.Childrenshouldusewell-chosenconcrete,pictorialandiconicrepresentations.Theyshouldrecogniseandbeencouragedtouseabstractsymbolsalongsidelessformaljottingsandrecordings.

    SuggesteddirectteachingNumbersandthenumbersystem Introducedinterm1(continuous)Calculating (Introducedinterm1&thenrevised

    throughthetopicsinthefollowingterms)ExploringLength Term2Describingposition Term2ExploringWeight Term2ExploringCapacity Term2UnderstandingTime Term3UsingMoney Term3DescribingPatterns Continuousinnumber,shape,etc.DescribingShapes Term3

    MasteryIndicators(EarlyLearningGoals)Numbers:childrencountreliablywithnumbersfrom1to20,placetheminorderandsaywhichnumberisonemoreoronelessthanagivennumber.Usingquantitiesandobjects,theyaddandsubtracttwosingle-digitnumbersandcountonorbacktofindtheanswer.Theysolveproblems,includingdoubling,halvingandsharing.Shape,spaceandmeasures:childrenuseeverydaylanguagetotalkaboutsize,weight,capacity,position,distance,timeandmoneytocomparequantitiesandobjectsandtosolveproblems.Theyrecognise,createanddescribepatterns.Theyexplorecharacteristicsofeverydayobjectsandshapesandusemathematicallanguagetodescribethem.

  • Numbersandthenumbersystem KeyconceptsEarlyLearningGoal11NumberForExpectedachievement

    Childrencountreliablywithnumbersfromonetotwenty Placetheminorder Saywhichisonemoreandonelessthanagivennumber

    Youmaywanttoworkandsecureunderstandingnumbers1-5inthefirstterm,to10inthesecondtermandto20intermthree.

    Themes Possiblekeylearningpoints Cardinality Subitising Conservationofnumber Nominalvaluese.g.thenumber7busisnotnecessarilytheseventhone

    1:1correspondence Conceptofzero

    Recitenumbersto10(thenwhensecure20) Sayandusenumbernamesinrhymesandstories Countupto10moveableobjects Countoutupto10objects(then20)fromalargerquantity Begintomatchnumeralstonumbersofobjectsinaset Countupto10objects(then20)whichcannotbemoved Begintounderstand0 Rehearsecountingbackfrom10(eventually20)includingrhymesandsongs Countactionsorsounds Begintoestimatenumbersofobjectsandcheckbycounting Ordernumbersto10(then20)bothascendinganddescending Understand1morethanagivennumber Understand1lessthanagivennumber Begincountingat10 Partitionnumbersinto10sand1s Noticeandextendnumberpatterns

    MathematicalLanguage PedagogicalNotesNumber,zero,one,two,three..totwenty(andbeyond)teens,eleven,twelve,noneHowmany?counton(toorfrom)countup(to),countback(toorfrom)countinones,twos,fives,tensisthesameas,equals,balances,asmanyasmore,larger,bigger,greater,biggest,mostless,fewer,smaller,smallest,leastodd,even

    Ensurethatthereisadistinctionbetweenfewer(countableobjectse.g.fewertoys,fewerbricks,fewercupsofwater)orless(massorabstracte.g.lesssand,lesswater,lesshonesty).

    Zeroisanimportantwayofexpressingnothing(ortheabsenceofsomethinge.g.3-3=0andhasasymbol/numeraltodenoteit.

    Nurturechildrensnumbersensebydevelopingsubitising(Piaget)whichmeanstobeabletorecognisenumbersinsmallgroupswithouttheneedforcounting(e.g.usingdicepatterns,tensframes,Numiconetc.)

    Moveableobjectsarebestusedinitiallyforcountingtoencourage1:1correspondence

  • patternones,tens,digitscompare,order,sizefirst,second,thirdlast,before,after,next,betweenguess,estimate,nearly,closeto,about,justover,justunder,toomany,toofew,enough,notenough

    andmovingtoensurethatobjectsarenotcountedmorethanonceoromitted.Progressionincountingwillseechildrenabletocountobjectswhichcannot

    bemovedinanirregulararrangement. Childrenneedtounderstandthatthelastnumberspokenisthenumberofobjectsin

    successfulcounting(cardinality). EarlyYearsMathematics:HowtoCreateaNationofMathematicsLoversbyDrSueGifford TheHueysinNonetheNumberbyOliverJeffers

    Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext Howmanyteddiesarethere?IsitstillthesamenumberifIspread

    themout?Howdoyouknow? Useapuppet,toy,classmascot,cheekyelfetc.tomakemistakese.g.

    TommytheTeddycountsobjectsbutmissesoneout/countsonemorethanonce,saysthenextnumberafterthefinalcountetc.

    Herearesomenumberse.g.7,8,10,11whichoneismissing?Howdoyouknow?

    Whatisthesamebetweenthesetwonumbers?Whatisdifferent?(E.g.3and13)

    Closeyoureyes,canyoucountthenumberofpenniesthatIamdroppingintothetin?

    Whatifwehadonemore,howmanywouldtherebe?Whatifwehadoneless,howmanynow?

    Numbertracksingamesandactivities(ensurethereisvariatione.g.horizontal,vertical,diagonal,ascendingvalueanddescendingvalue)

    Numberrhymes(tengreenbottles,fivelittleducks,tenfatsausages,fivelittlealiens,fivespeckledfrogsetc.)

    Creatingnumberbookse.g.Mybookof6andtakingphotographs,stampingnumbersandobjectsin.

    NRICH:PlayingInceyWinceySpider NRICH:Goldenbeans TheVeryHungryCaterpillarbyEricCarle,OneisaSnail,TenisaCrabbyAprilPulleySayre,

    MoreorLess?ByStuartJMurphy,EqualScmequalbyVirginiaKroll

    Possiblemisconceptions Eleven,twelve,thirteen(oneteen,twoteen,threeteen) Misconceptionsfromusingactivitieswithdifferentfontse.g.1andI(ordifferentnumeralsfor4or7)orchildrenmayconfuse2and5duetotransposingnumberswhenwritingtheirown

    Countingerrorsencouragechildrentochecktheircountingforsenseanderror.

  • Calculating KeyconceptsEarlyLearningGoal11NumberForExpectedachievement

    Usingobjectsandquantitieschildrenaddandsubtractusingtwosingledigitnumbers

    Theycountonorbacktocalculate Theysolveproblemsusingdoubling,halvingand

    sharing

    ThereisnoexpectationthatchildrenintheEYFSwritesymbolsandcalculationstorecordtheirmathematicalthinkingalthoughtheymaychoosetomaketheirownjottingsandmarkmakingtosupporttheirlearning.

    Themes Possiblekeylearningpoints Composinganddecomposingnumbersusingvisualapparatussuchastensframee.g.7canbea5&2,3&4etc.

    Commutativityi.e.2+3=3+2 Additionascombiningtwoormoregroups Additionasincreasing Subtractionastakeaway Subtractionasdecrease Subtractionasdifferencebetween

    Exploringcomposition(makingnumbers) Exploringdecomposition(breaknumbersdown) Exploringthepart,partwholemodelincontexts. Understandingadditionto10(then20) Understandingsubtractionto10(then20)

    MathematicalLanguage PedagogicalnotesNumber,zero,one,two,three..totwenty(andbeyond)teens,eleven,twelve,noneHowmany?counton(toorfrom)countup(to),countback(toorfrom)countinones,twos,fives,tensisthesameas,equals,balances,asmanyas,makemore,larger,bigger,greater,biggest,mostless,fewer,smaller,smallest,leastodd,evenpatternones,tens,digitsadd,more,and,make,total,sum,altogetherHowmanymoretomake?Howmanymoreis.than.?takeawayHowmanyareleft?Howmanyaregone?Howmanyfeweris.than?differencebetween

    Part, part whole notion is very useful for composing and decomposing numbers andexemplifying number relationships in a variety of orientations and with more than twoparts. Begin with concrete, moveable objects and move to abstract symbols when thechildrenareready.

    Include0inproblemsolvingandrepresentwithanemptysetorgroup Conceptofsharingequally/fairlyisonetoexplorewiththechildrentheyneedtoensurethattheshareawholeobject(i.e.acake/pizza/pieceofpaper)andawholesetofitems(i.e.awholepacketofbiscuitsorcubes)

    Usingpracticalequipmentandcontextstoteachconceptse.g.platesandcupcakesforthepart,partwholemodel,smallworldplaypeopleinbusandmovetotheiconicconcretee.g.unifixcubestorepresentvotesinalinearfashionthusitiseasytoseedifferentbetween(earlybarmodelrepresentations).

    NCETM:ProgressionincalculatingintheEarlyYears

  • sharing,doubling,halvingpartsofawhole,half,quarter

    Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext Showmefiveonthetensframe.Showmeanotherarrangementof

    five.Nowanotherandanother. Useacharacterorpuppettomakedeliberatemistakeswhenadding,

    subtractingorsharing.Askthechildrentocorrectthemistakes. IfIhave5teddiesaltogetherandIneed