Reception

Mastery

Scheme of Work

Enjoying mathematics� Creating mathematicians � Breaking down barriers

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

Directteachingcouldbewithwholeclassorsmallergroupsandwillbeadultledandsuccessfullearningshouldbeobservedandassessedindependentofthis.ManyoftheseunitslinkwitheachotherandwithotherEarlyLearningGoalssuchasELG01–ListeningandAttention,ELG2-UnderstandingandELG3–Speaking.

ThemasteryapproachtomathematicsalsoembracestheCharacteristicsofEffectiveLearningasstatedinDevelopmentMattersdocument.

CharacteristicsofEffectiveLearning(DevelopmentMatters) PrinciplesofMastery(NCETM2015)PlayingandExploring–Engagement

• Findingoutandexploring• Playingwithwhattheyknow• Beingwillingto‘haveago’

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

Activelearning–Motivation• Beinginvolvedandconcentrating• Keepingtrying• Enjoyingachievingwhattheysetouttodo

Lessonsareshortbutintense.Teacherleddiscussionisinterspersedwithshorttasksand/orpupiltopupilorpupiltoteacherdiscussion.

CreatingandThinkingCritically–Thinking• 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 Continuous–innumber,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 Keyconcepts–EarlyLearningGoal11NumberForExpectedachievement

• 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.

• Nurturechildren’snumbersensebydevelopingsubitising(Piaget)whichmeanstobeabletorecognisenumbersinsmallgroupswithouttheneedforcounting(e.g.usingdicepatterns,tensframes,Numiconetc.)

• Moveableobjectsarebestusedinitiallyforcountingtoencourage1:1correspondence

patternones,tens,digitscompare,order,sizefirst,second,third……last,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.

• Herearesomenumbers…e.g.7,8,10,11–whichoneismissing?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.‘Mybookof6’andtakingphotographs,stampingnumbersandobjectsin.

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

MoreorLess?ByStuartJMurphy,EqualScmequalbyVirginiaKroll

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

• Countingerrors–encouragechildrentochecktheircountingforsenseanderror.

Calculating Keyconcepts–EarlyLearningGoal11NumberForExpectedachievement

• 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/fairlyisonetoexplorewiththechildren–theyneedtoensurethattheshareawholeobject(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.• IfIhave5teddiesaltogetherandIneedtoputthemintotwoboxes.

HowmanycouldIputineachone?IstheremorethanonewayIcouldpackthem?Howmanywayscanyoufindaltogether?

• Practicalproblemsinvolvingaddition,subtractionandsharingsuchassnacktime,artwork,datacollection.

• Useeverydaypicturesforchildrentomakenumberstoriesforcalculating,similartothoseinJapaneseorShanghaiesetextbooksforgrade1.

• UsingapanbalanceandNumiconpieces,unifixcubese.g.“2cubesand3cubesintheredpanbalances5cubesinthebluepan”

• Usingatensframe• Countingon/backonanumberlineortrack–cardordicegames• Baking/Playdough–Canyousharethe_______equallybetween2or4?• Traditionalstorieswithcontextsforcalculating• RedRidingHood’sMathAdventurebyLalieHarcourt• AFairBearSharebyStuartJMurphy• TheDoorbellRangbyPatHutchins• HowManyLegsbyKesGray

Possiblemisconceptions Theychildrenmaythinkthatsubtractioniscommutativelikeaddition.Whencountingonorback,pupilsmaysaythenumberthattheystartone.g.countingonfrom8toadd8and3theymaysay“8,9,10”.Whenusingtheterm‘differencebetween’somepupilsmayassumetheeverydayuseandnotthemathematicalonee.g.“Thedifferencebetweenthe7and8isthat7hasstraightlinesand8hascurvedones”.Theremaybeconfusionbetweenthesymbols+-and=Avoidconfusionbylabellingpartssuchas“thebiggesthalfofthepizza”Avoidmisconceptionsbycalculatingwithavarietyofobjectsandamountstoexposechildrentocountinglargeobjectsandsmallerones–itisnotthesizeoftheindividualitembuttheircardinalvalue.

ExploringLength Keyconcepts–EarlyLearningGoal12Shape,spaceandmeasuresForExpectedachievement

• Childrenuseeverydaylanguagetotalkaboutsizeofeverydayobjects

• Pupilswillcomparequantitiesandobjects• Childrenwillusethelanguageofdistance

ThereisnoexpectationthatthechildrenuseanystandardmeasuresintheEarlyYearsFoundationstage.

Themes Possiblekeylearningpoints• Conservationoflength–sizedoesnotalterifobjectismoved• Prediction• Reasoningandjustifying

• Comparingthelengthsoftwoofthesametypeofobjects.Statingwhichislongest,whichistheshortest.

• Estimatingandorderingfamiliarobjectsbylengthandbycomparingdirectly• Understandingplacesthatarenearorclose• Understandingplacesthatarefaraway

MathematicalLanguage PedagogicalNotesMeasure,size,compare,guess,estimate,Enough,notenough,toomuch,toolittle,toomany,toofewNearly,closeto,aboutthesameas,justover,justunderLength,height,widthLong,short,tallHigh,lowWide,narrow,thick,thinLonger,shorter,taller,higherLongest,shortest,tallest,highestFar,near,close

• Thereisdistinctionbetweenlong(anyorientation)andtall(verticallength)soensurethatthechildrennotonlyknowthedifferencebutseeobjectsinavarietyoforientations.

• Theremaybeopportunitytodiscusstheneedforauniform,non-standardunit.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Find5objectsthatarelongerthanyourthumb.Find5objectsthat

areshorterthanyourthumb.Findanobjectthatisaboutthesamelengthasyourthumb.

• NRICHEYFSLongCreatures• NRICHEYFSMakingCaterpillars• Buildingtowers,blocks,Lego• Measuringchildren,plantgrowth,leaves,paperorribbonforroleplaypostoffice,

• Joethinksthatthebluecrayonisthelongest.Ishecorrect?Howdoyouknow?• Usetheclasscharacterorpuppettomakelanguageandmeasuring

errorswhichthechildrenneedtocorrect.

measuringthedistanceofcarsrolleddownaslope• JimandTheBeanstalkbyRaymondBriggs• GoldilocksandtheThreeBears

Possiblemisconceptions • Childrenmaythinkthatthesamestickislongerwhenitisvertical

andshorterwhenitishorizontal• Whendirectlycomparingtwoobjects,childrenmaynotmatchthe

endstogethercorrectly,thusgivingafalseimpressionofwhichissmallerorlarger.

• Childrenmaynotseeacrookedlineislongerthanastraightlineeveniftheybeginandendatthesamepoint.

• Childrenmayconfuselengthandwidthe.g.theymaythinkawideribbonislongerthananarrowerone.

DescribingPosition Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Childrentouseeverydaylanguagetodescribeposition

Themes Possiblekeylearningpoints• Prepositions• Distance(nearandfar)• Estimatingandconjecturing• Justifying

• Tounderstandprepositions(selectafewatatimefromthelist,whilstembeddingalreadylearnedvocabulary)

• Touseprepositionscorrectly• Tounderstandtheconceptofnear/far

MathematicalLanguage PedagogicalNotesPositionOver,under,above,below,top,bottom,side,On,in,outside,inside,around,infront,behind,back,front,Beside,nextto,opposite,apart,between,middle,edge,cornerDirection,left,right,up,downForwards,backwards,sidewaysAcross,nextto,close,near,farAlong,through,to,from,towards,awayfrom

• ThereareseveralsynonymsforprepositionsintheEnglishLanguage–ensureyoudrawattentiontothiswiththechildrentoavoidconfusion.

• Theconceptofnearandfararerelativee.g.theseasideisfarawaybutnearerthanthemoon!Itmightbeworthaddingaquantifiablevaluee.g.howlongwouldittakeinacar?Howmanysteps?

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Usetheclasscharacterorpuppettomakelanguageandpositionerrorswhichthechildrenneedtocorrect.

• WearegoingonabearhuntbyMichaelRosen• Rosie’sWalkbyPatHutchins• NaughtyBusbyJanetteOke• Dinosaur’sDayOutbyNickSharatt• TheHokeyCokeysong(todistinguishleftfromright)• Smallworldplayresourcessuchascars,maps,cookingsituations,shops• Outdoororlargeplayequipmentsuchasbikes,trikes,obstaclecourses,treasurehunts• UsingLogoorBeebotsorotherprogrammabletoys• NRICH:Positionwithwellies• NRICH:Scooters,bikesandtrikes

Possiblemisconceptions • ChildrenmayhavelessdevelopedeverydaylanguageskillsonarrivalatschoolormaybeEAL.Therearesynonymsusedforeachposition.

• Manychildren(aswellasadults!)confuseleftandright.

ExploringWeight Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Childrenuseeverydaylanguagetotalkaboutweightofeverydayobjects

• Pupilswillcomparequantitiesandobjects• Childrenwillusethelanguageofweight

Themes Possiblekeylearningpoints• Prediction• Reasoningandjustifying

• Tounderstandwhattheterms‘light’and‘heavy’and‘weighsthesameas’mean• Tobeabletouseapanbalance• Tocomparetwoobjectsbytheirweight• Ordermorethantwoobjectsbytheirweight

MathematicalLanguage PedagogicalNotesMeasure,size,compare,guess,estimate,Enough,notenough,toomuch,toolittle,toomany,toofewNearly,closeto,aboutthesameas,justover,justunderWeigh,weighs,weighsthesameas,balances,heavy,light,heavierthan,lighterthan,heaviest,lightest,scales

• Childrenmayneedinstructionaboutwhatthepanbalancemeanse.g.theheavierobjectwillbenearerthetable/groundandthatthelighteronewillbeupintheair.

• Althoughthereisnoexpectationtousestandardweights,childrenmaybereadytobalanceobjectsandrecordsuchasthebookbalances25cubesetc.

• InFoundationStageandKS1,Massandweightcanbetreatedasthesamealthoughinlateryearsmassistheamountofmatterwithinanobjectandweightistheamountofgravityactinguponit.

• Heremaybeopportunitytodiscusstheneedforauniform,non-standardunit.Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Whichdoyoupredictwillbetheheaviest/lightest?Why?• Usetheclasscharacterorpuppettomakelanguageandmeasuringerrorswhichthechildrenneedtocorrect.

• Howmany(cubes)doyouthinkwillbalance?Doyouwanttochangeyourmindnowthatweareaddingthecubestothebalance?Didyouguesstoomanyortoofew?

• Roleplay–market,postoffice,vets(weighinganimals)• Usingatoyorreallifesee-sawtoreinforcetheconceptofbalance/panbalance• Cooking/baking• NRICHEYFS:Balances• NRICHEYFS:Presents• MarvinWeighsInbyDaveBrowning

Possiblemisconceptions • Childrenmayconfusesizewithweightsoitisworthgivingexamplesoflarge,lightpackagesandsmall,heavyobjectsasitcannotbeperceivedvisuallyunlikeweightandlength.

ExploringCapacity Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Childrenuseeverydaylanguagetotalkaboutthecapacityofeverydayobjects

• Pupilswillcomparequantitiesandobjects• Childrenwillusethelanguageofcapacity

Themes Possiblekeylearningpoints• Prediction• Reasoningandjustifying

• Tounderstandfull,emptyandhalffull• Topredictandmeasurehowmanycupsfullwillittaketofillavarietyofcontainers

MathematicalLanguage PedagogicalNotesMeasure,size,compare,guess,estimate,Enough,notenough,toomuch,toolittle,toomany,toofewNearly,closeto,aboutthesameas,justover,justunderFull,empty,holds,container,halffull,holdsmore,holdsless

• ThereisadistinctionbetweenvolumeandcapacityaccordingtoNCETM“Volumeistheamountofspaceacontaineroccupiesandisalwaysthreedimensional.Itismeasuredincubicunitswhicharecommonlymetres,centimetresetc.Capacityistheamountacontainercanholdwhenitisfull–usuallymeasuredinlitresetc.“

• Encouragechildrentogetdowntoeyeleveltoaccuratelyjudgepartorfullcapacity.• Heremaybeopportunitytodiscusstheneedforauniform,non-standardunit.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Whichcontainerwillholdmore/less/aboutthesamethanthis

container?Howdoyouknow?• Usetheclasscharacterorpuppettomakelanguageandmeasuring

errorswhichthechildrenneedtocorrect.

• Usingwater,sand,rice,(uniformedornon-uniformedsizepebbles?),driedpastaorother‘pourable’materials

Possiblemisconceptions • Lotsofchildrenfinditdifficulttorealisethatashort,widecontainer

couldhavealargercapacitythanataller,narrowerone.• Whensuggestingittakes(x)amountofsmallcupstofillthebigger

cup,childrenmaynotconsistentlyfillthesmallercup,thusthemeasurementnotbeingaccurate.

• Childrenneedpracticalexperienceoffillingarangeofcontainersincludingmoreunusualcontainerswithdiagonaledgese.g.

UnderstandingTime Keyconcepts–EarlyLearningGoal12Shape,spaceandmeasuresForExpectedachievement

• Childrenuseeverydaylanguagetotalkaboutthepassingoftime.

• Pupilswillcomparequantitiesoftimeandobjectsrelatedtotime

Themes Possiblekeylearningpoints• Daysoftheweek• Sequencingeventsinaday• Unitsoftime–seconds,minutesandhours• Estimatingandpredicting• New/old• Comparingeventsandorderingbytheirduration• Readingaclocktothehour(o’clock)• Prediction• Reasoningandjustifying

• Tonamethedaysoftheweekinorder• Toorderanddiscusstheorderofeventsduringtheschoolday• Toordereventsinmylife• Tounderstand‘new’and‘old’• Tounderstand&usethelanguageofunitsoftime• ToestimateandmeasurehowmanytimeIcan_____in10secondsoraminute• Tocomparetwotimedurations(quicker,slower)• Tocomparetwoormoretimedurations(quickest,slowestetc.)• Tobeabletoreadthetimeontheclocktothehour(7o’clock)

MathematicalLanguage PedagogicalNotesTimeDaysoftheweek(Monday,Tuesdayetc.)Day,week,Birthday,holiday,morning,afternoon,evening,nightBedtime,dinnertime,playtime,Today,yesterday,tomorrow,Before,after,now,soon,early,lateQuick,quicker,quickest,quicklySlow,slower,slowest,slowlyOld,older,oldestNew,newer,newestTakeslonger,takeslesstime,hour,o’clockClock,watch,handsMeasure,size,compare,guess,estimate

• Themoreyoucanbuildtimeintoyoureverydayroutinesthebetter.Regularlydrawattentiontotheday,month,year,season,andtimeontheclock,birthdaysandroutines.

• Itisaveryabstractconcept,onewhichchildrenneedtoseevisuallyusingsandtimers,stopwatches,clocks(useavariety),calendarsetc.

• Mostclassroomdisplayssuchasthedaysoftheweekandmonthsoftheyeararedisplayedinalinearway.Itwouldbebettertodisplaysuchinformationinacirclesothatchildrenarefamiliarwiththecyclicandrepetitivenatureoftheseunitsoftime.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Howmanyclapsorhopsorstarjumpsdoyouthinkyoucandoin1minute?Wereyoucorrect?

• Usetheclasscharacterorpuppettomakelanguageandmeasuringerrorswhichthechildrenneedtocorrect.

• Songscanbehelpfulwhenlearningthedaysoftheweekandmonthsoftheyearsothatthechildrencanrecitethemwithease.Itisnoteasyotherwisebecausethereisnologicalordertorememberingthem!

• Visualtimetables• Play‘What’sthetime,MrWolf?’• Sequencingeventsofastoryoreventsrelevanttothechildren’slife• Writingarecountofvisitoreventinliteracy• Timingeventsortasks• TheTimeitTookTombyStephenTucker• What’sTheTimeMrWolf?ByDebiGliori• CluckO’ClockbyKesGray• NRICHEYFSTiming

Possiblemisconceptions • Inaveryyoungchild’sunderstanding“yesterday”mayrelatetoanyeventthatisinthepast.

• Similarly,theymaynotbeabletounderstandfutureeventssuchasnextweek,nextmonthetc.

• Whentellingthetimeonananalogueclock,childrenmaysay3o’clockis“12to3”or“3to12”etc.

UsingMoney Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Childrenuseeverydaylanguagetotalkaboutmoney• Theycancomparequantitiesandobjects

Themes Possiblekeylearningpoints• Understandingtheconceptofmoney• Usingandapplyinginreallifesituations• Sortingandclassifying• Explainingandreasoning

• Tounderstandwhatmoneyis,whatitisforandthedifferentformsofmoney• TorecognisecoinsoftheUK• Toordercoinsbytheirvalue• Tosortcoinsbydenomination(&thenbyowncriteria)• Tousemoneyinplayandreallifesituationse.g.totalling,change,exchanging• Tosolveproblemswithmoney

MathematicalLanguage PedagogicalNotesMoneyCoin,penny,pence,poundPrice,costBuy,SellSpend,spent,pay

• Themostrecentcoinsincirculationdonotsaythedenominationinnumeralsonsochildrenwillneedlotsofexperienceofhandlingandidentifying(realnottoy)moneybyitscomparativesizeandshape.

• Donotusetheterm‘pennies’asageneraltermformoney,especiallyiftherearemixeddenominationsofcoins.

• Aswearelivinginatechnologicalworld,childrenmaynotseeadultsphysicallyhandovercashorevencardsinthecaseofcontactlesspayments.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Wouldyouratherhave51pencecoinsor32pencecoins?Why?• ShowmeNOTa10p,NOTa2p.• Howmanywayscanyoumake5pence?Howdoyouknowyouhavethemall?

• Usetheclasscharacterorpuppettomakecountinganddefiningerrorswhichthechildrenneedtocorrect.

• Visitarealshoporsupermarketwherechildrencanphysicallyhandovercashandevenreceivechange–itmightbeanewexperienceforthem!

• TheGreatPetSalebyMickInkpen• Jackandthebeanstalk/3littlepigstraditionaltales• Moneysong–5currentbuns• ItisanidealtolinkwithPSHE–thefeelingsandmoralsrelatedtomoneyandspending.Pfeg(PersonalFinanceEducationGroup)havesomegood,crosscurricularresources

• EYFSNRICH• PIRATEPOUNDLAND• Roleplay–shops,postoffice,banketc.

Possiblemisconceptions • Childrenmaynotunderstandthattotallingcoinsdoesnotmean• Countingthenumberofcoins(unlesstheyareonly1pcoins)andoftenfeelconfusedthat2p=21pencecoinsetc.

• Theymayalsothinkthata2pencecoinisworthmorethana5pencecoinbecauseitisphysicallylarger

DescribingPatterns Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Torecognise,createanddescribepatterns• Touseeverydaymathematicallanguagetodescribethem

Themes Possiblekeylearningpoints• Recognisingandextendingpatterns• Creatingpatterns• Usingandapplyinginreallifesituations• Sortingandclassifying• Explainingandreasoning• Generalising

• Torecognisea2steppattern• Toextend/createa2steppattern• Torecognisea3+steppattern• Toextend/createa3+steppattern• Tounderstandandrecognisesymmetry(ornot!)• Tocreatesymmetricalpatterns

MathematicalLanguage PedagogicalNotesCount,sort,group,set,listPattern,puzzle,repeatingpattern,Bigger,larger,smallerSymmetricalWhatcouldwetrynext?Howdidyouworkitout?Recognise,describe,draw,compare

• Educationalresearchshowsthatthebasisforlater,morecomplicatedalgebrahasrootsinspottingpatternsandrulesandmakingconnections.

• Opportunitytoexploreandextendpatternshouldbegivenfornumberandshapeinavarietyofcontexts.

• Itmaybeanopportunitytolinksymmetrywithfractionsforexample,givingchildrenonehalfofapatternandaskingthemtocompleteitonapegboard.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Whichoneoftheseisinthewrongplace?Howdoyouknow?• Canyoumakeapatternsimilartothis?• Canyouextendthispattern?• Usetheclasscharacterorpuppettomakelanguageandcreatingpatternerrorswhichthechildrenneedtocorrect.

• NRICHEYFS:MakingaPicture• AliensLoveUnderpantsbyClaireFreedman• Makingartworkinpaint,clayorcollage• DayandNight(PatternsinNature)byMargaretCHall• AndyGoldsworthyisanartistwhomakespatternsinnature–photographyonanaturewalk

Possiblemisconceptions • Somechildrenmaycontinueacolourornumberpatternbycopyingthepatternfromthebeginningratherthanlookingatwheretheinitialpatternended.

DescribingShapes Keyconcepts–EarlyLearningGoal12Shape,spaceandMeasuresForExpectedachievement

• Toexplorecharacteristicsofeverydayobjectsandshapes• Touseeverydaylanguagetodescribeobjectsandshapes

Themes Possiblekeylearningpoints• Usingandapplyinginreallifesituations• Sortingandclassifying• Explainingandreasoning

• Torecogniserectangles,includingsquares• Torecognisecircles• Torecognisetriangles• Toexplorecharacteristicsof2-Dshapesincludingcornerandsides

• Tosortandclassify2-Dshapes

• Torecognisecubes• Torecognisepyramids• Torecognisespheres• Torecognisecones• Toexplorecharacteristicsof3-Dshapesincludingface,edgeandvertices

MathematicalLanguage PedagogicalNotesCount,sort,group,set,list2DshapesCorner,side,rectangle(includingsquare),Circle,triangle3DshapesFace,edge,vertex,verticesCube,pyramid,sphere,cone

• Practitionersshouldbeawareoftheshiftbetween3Dshapesand2Drepresentationsofthem.Itisbesttoworkwiththephysical,concreteinavarietyofsizesandwitheverydayitemswhicharethatshape.

• Childrenfindittrickytounderstandthatasquareisaspecialrectangle.SomepeoplefinditusefultoadoptthepolicyofusingOblongwhichisanon-squarerectangle.

• Preciselanguagechoiceisvitalinthistopic(althoughincrediblyimportantinallareas).Propertiesof2Dand3Dshapesneeddefiningwithaccuracyandlanguagestructuresmodelledbyadults.

Reasoningopportunitiesandprobingquestions Suggestedactivitiesorstorieswithamathematicalcontext• Showmea________,showmeNOTa_____________.• Whichshapeisinthewrongplaceonthissortingtable?Howdoyouknow?

• Usetheclasscharacterorpuppettomakelanguageandsortingerrorswhendealingwithshapes,whichthechildrenneedtocorrect.

• NRICHEYFS:Shapesinthebag• NRICHEYFS:Exploring2Dshapes• NRICHEYFS:BuildingTowers• CaptainInvincibleandTheSpaceShapesbyStuartJMurphy• TheShapeofMyHeartbyMarkSpeering• TheShapeGamebyAnthonyBrowne

Possiblemisconceptions • Childrenmaynotrecogniseshapesiftheyareconstantlygiventhesameshapeinthesameorientation–theclassexampleisthesquareonitspoint,somechildrenwillsayitisadiamond.