reception mastery scheme of work - glow€¦ · mathematics overview: reception mastery of...
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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.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.