EXPLORING NUMBER SEQUENCE AND ORDER · EXPLORING NUMBER SEQUENCE AND ORDER ... Ordinal numbers are...
Transcript of EXPLORING NUMBER SEQUENCE AND ORDER · EXPLORING NUMBER SEQUENCE AND ORDER ... Ordinal numbers are...
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EXPLORINGNUMBERSEQUENCEANDORDER
Itisperfectlypossibletoviewtheworldentirelythroughnumberprocessesandsystems.Arguablythisishowmathematiciansinterpretwhattheysee,hearanddo.Weneedtothinkaboutthehiddenmessageswesendchildreninrelationmaths.Isitsomethingwesilentlyshudderabout,ordowecelebratethejoy,understandingandpracticalbenefitsthatnumberhasbroughtintoourlives.Eitherway,itisimportantweempowerchildrentorecognisetheimpactofnumberandgivethemconfidencetousenumberprocessesasameanstolearnmoreabouttheworldinwhichwelive.Cardinalnumbersarethoserelatetothequantityofanobject,e.g.1=oneobject,2=twoobjects,etc.Theyaretheoneswhicharecommonlycounted.Theydonotincludefractions,decimalsorpercentages.Ordinalnumbersareaboutthepositionofobjects,e.g.1st,2nd,3rd,4th,etc.Theytellustheorderofobjects.Nominalnumbersarenumberswithoutvalueorposition.Examplesincludepostcodes,telephonenumbers,numbersonthebacksofteamplayers,e.g.thenumbersonrugbyshirts,ThomastheTankengine’snumber.Integersarenumberswhicharewholenumbers(i.e.nofractions)andincludecardinalnumbersandnegativenumbers–thosewhicharelessthanzero.Whetheryouintroducetheabovetermsisuptoyou.However,havinganunderstandingofdifferentsetsofnumberscanhelpuswhenweworkwithchildrensothatweareawareofwhatweneedtobedoingwithchildren.Forexample,lookingatweathertemperaturesonafrostydaycanhelpchildrenunderstandaboutnegativenumbers.Writingnegativenumbersonawatertraycanalsohelporonatransparenttubewhichisfilledwithwater.Otherrelatedvocabularyincludes:morethan,lessthan,inbetween,what’smissing,count,sort,order,recognise,match,numbers,digits,numerals,placevalue,units,tens,hundreds
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CountingonandbackwithbigsticksBeginwithsimpleroutinessuchascountingforwardsslowlytappingonestickonthegroundintimetoeachnumbersaidaloud.Encourageallchildrentojoininwithcountingaloudtoo.Workondevelopingasteadyrhythm.Variationsinclude:
Countonfromdifferentnumbers–letthechildrenchoosethestartingpoint Focusonbridging,e.g.startat88andcountonto105 Countbackwardsasmuchasforwards.Thishelpswithsubtraction With older children, count back from a positive number such as 5 andmove beyondzerointonegativenumbers
Developa“switch”andchallengechildrentobeginbycountingforwardsandthenwhensomeonecallsout“switch”youchangedirectionandcountbackwards
Countforwardsasyouwalkoutoftheclassroomtotheoutsidespace.Anotherextensionistohaveeachchildholdtwosticks.Thisallowsforchildrentotaptheleftstickfirst,followedbytherightstick.Thisworkswellforbuildinguptoworkonmultiplication.Sitdownonthegroundifshortsticksarebeingused.Yourclasswillneedtopractiseaslowsteadyrhythmasthetemptationistospeedup!Itcanbeextendedto:
3-tapsequence:Leftsticktap,rightsticktap,tapbothstickstogether 4-tapsequence:Leftsticktap,rightsticktap,tapbothstickstogethertwice Tappingoneverymultipleof3,or5orothernumber.Thiscanbeextendedtochantingthetablesorsimplecountingin2s,3s,10s,etcandtappingthesticksasyoudoso.
Foreachapproach–tapping,passingorlistening,startsimpleandbuildupthecomplexityinlinewithwhatyourchildrencanmanageandwheretheyareatwiththeirmaths.Alittleandoftenworkswell.Feelfreetoaddmusicandbuilduprhythmgamestoo.Stickpassing(1msticksoranygatheredsticks)
Everyevennumberpassastick.Everyoddnumbertapitontheground. Countin3’s,passastickonthemultiplesof3 Playfuzzbuzzandpassstickstotheleftonmultiplesof5andtotherightonmultiplesof7.Staystillonmultiplesofboth
Sticktappingandlisteninggames(1msticksoranygatheredsticks)
Splitintotwogroups.Onegroupchoosesanumberbetween0and9andtapsthisout.Theothergrouprespondwiththenumberthatisneededtomake10.
Extendthisideatomultiplicationsumsandotheraddingortakingaway. Getthechildrentodevelopsystemsforexplainingdecimalpointsorfractitions.
Doublesticks
Usefortap-taponthegroundandsnap-snapintheair–thiscanallowforthinkingtime,keepingasteadyslowrhythmandsayingmultiplicationtablesinfull,e.g.2times2is4.
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Countingsticks(makeyourownandchildrencanmaketheirfroma1mstick–justaddmaskingtapeorpeelbarkringsat10cmintervals).Thesecanbeusedverticallyaswellashorizontallyandmakegreatwalkingandmeasuringstickstoo.Askchildrento:
Hold their stick vertically and touch each piece of tape in order as they count aloud.Withlittlechildren,countinones,thenmoveontotens,fives,twos,etc.
Remember to count backwards as well as forward. Make it fun by increasing anddecreasingthespeed.
Playshowmeactivitieswhichhelpwithroundingandestimation,e.g.showmeroughlywhere73,84,32,25is,etc.
BasketballmathsThisgameusesabasketballhooptopracticementalmathsstrategies.Ifyourschooldoesn’thaveahooporyourchildrenaretooyoung,thenuseabucketorplasticbox.Playersstandinalineacoupleofmetresfromthehoop.Theteacherholdsapileofadditionandsubtractionfactsandcallsouttheequations,oneatatime,e.g.“4+3”.Thefirstplayerinlinecalculatedtheanswerinherhead,thenbouncestheball7timesasshewalkstowardsthehoop.Whenshestops,shecallsouttheanswerandshoots.Thenthenextchildtakesaturn.Thisgamecanbeplayedwithawholeclasssplitintoteams.Encouragethewholeclasstocountthebounces.HopscotchIfyourschoolhasflagstonesorpavingthenhopscotchgridscanbequicklydrawnusingchalk.Aswellasusingnumbers0–10,withchildrenwhoaremoreconfidentthiscanbeextendedindifferentways,e.g.:
• 11-20• 31,32,33-40• 100,200,300–1000,etc
Thishelpschildrenunderstandandgainconfidencetalkingaboutandusingbiggernumbers.Yourclasscanalsoinvestigatethedifferenttypesofhopscotchmarkingsfoundaroundtheworldonline.Theymayenjoydevisingtheirownlayoutstoo.FindanumberThisworkswellforyoungerclasses.Findasuitableplacetogatherinacircle.Eachchildneedstomarkhisorherplace.Thiscouldbewithamat,acirclechalkedonthegroundorahoop.Askchildrentofindbetweenoneandtenofthesameobjectoutsidewhichtheycanholdintheirhand.Thismightbeleaves,gravel,daisies,etc.Askthechildrentoreturntothecircleoncetheyhavefoundtheirobjects.Fromthere,anumberofactionscanhappensuchas:
Sitdownifyouhavelessthan4objects Swapplaceswithsomeoneifyouhaveonly1object Standononelegifyouhavebetween3and7objects Findsomeonewiththesameobjectandfindthetotalofbothofyourobjects Shareoutyourobjectsequallywithafriend
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MathematicalpicturesThisblogpostlooksathowtocreatenumericalmathspicturesusingfoundmaterials:http://creativestarlearning.co.uk/early-years-outdoors/20-something-maths-pictures/Asimilarprocesscanbeappliedtoshapepictures,measuringpictures,symmetry,etc.
CarnumberplatesPleasetakecarewheninthecarparkoronthestreet.Keepaneyeoutformovingvehicles.Numberplatescanbeexploredinamultitudeofways.Itcanbeausefulexercisetogetyourclasstocomeupwithsomenumberplateactivitiesbasedonthecarsintheschoolcarparkoronalocalstreet.
Whatarethe largestandsmallestnumberplates inthecarpark?Howdidyoudecidethis?Whatcriteriadidyouuse?Takeaphotoornotedownthewinningnumberplates.
Mostcarnumberplateshaveareamixtureofnumbersandletters.Isitpossibletorankthenumbersinorder?Shouldcarsbeparkedaccordingtotheirranking?
Whichisthemostmathematicallyinterestingnumberplateandwhy?Numberbonds(upto20)Eachpairofchildrenhastwobasketsand10naturalobjects,e.g.stones.Thechildrenhavetodecidehowmanydifferentwaysthereareofputtingthestonesineachbasket.Thesecanbewrittendownonasheetofpaperorwhiteboard.Thenumberofobjectsvariesaccordingtothenumberbondbeingexplored.Therearemanyopportunitiesforpartitioningnumbersanddevelopinganunderstandingofadditionandsubtraction.Forexample,simplethrowinggamessuchasaimingforahooponthegroundwithasetof5beanbags.Howmanybagsmakeitintothehoopandhowmanyareoutsidethehoop?Skittlesgamesworkonthesameprinciple.Howmanygetknockedover?Howmanyarestillstanding?FlowerpotsumsTakeaflowerpotandsomecounters.Forchildrenwhostrugglewithmaths5counterswillbeenoughtobeginwith.Askthechildreninthegrouptoclosetheireyes.Hidesomeofthecountersunderneaththeflowerpot.Askthechildrentoopentheireyesandworkouthowmanycountersareundertheflowerpot.Repeatthegamebutleteachchildhaveagoathidingsomecounters.Manychildrenparticularlylikehidingallthecounters!Thisactivitycanbecompletedinpairsbychildrenwhoneedtopractisenumberbondsto20.Forchildrenworkingbeyond20withmentaladditionandsubtraction,thenusenumberpebbleswithplacevalueonit,e.g.10s,100’s,etc.Encouragechildrentoexplorefreelywiththenumbersandcomeupwithsuggestionsfortheiruse.
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QuickrecallusingnumberlinesforadditionandsubtractionEachchildcreatesasimplenumberlinefrom0to10usingchalkontheground.Thisworkswellifyouhavethespaceforthesetoradiateoutfromagatheringspacelikespokesonawheel.Alternatively,requestchildrencreatetheirnumberlinesinaline.Whatmattersisthatyoucanseeallthechildreneasily.Makingnumberlinesdoestaketimebutwithpractice,itgetseasier.Fromheregetthechildrentomovetothecorrectnumberintheirlinewhenyougivethemquickrecallquestions.Focusonspecific,e.g.wherethetotalis10orless,wherethetotalmakes10,questionswhichusethelanguageofaddition(andsubtraction)e.g.
Showmetheanswersto3+4,7+2,2+6,etc Whatmustbeaddedtothisnumbertomake10?6,5,7,etc. Swapplaceswithsomeoneifyouhaveonly
Numberlinescanalsobeusedbypairsofchildren,whereeachchildhastosteponanumber,e.g.
Showmetwonumberswhichtotal5,7,3,etc. Showmeapairofnumberswhichtotal6,4,8,etc. Showmeapairofnumberswhichmakes10.Nowshowmeadifferentpair
Usingtwonumberlinesforquickrecallcanbeextendedtonumberfactsto20.Remembertofocusonsubtractionactivitiestoo.NumbercyclesontyresThisactivityworkswellontyresoraroundanycircularobjectintheenvironment.Justmakesureitdoesnotmatterifmarkedwithchalk.Itisaboutdevelopingchildren’sabilitytorecallnumberfactsto10(oranyothernumber).Theaimistocreateacompletecircleofnumberfactsthatalllinktoeachother,sothatacompletecycleismadewherethefirstnumberbecomesthefinalnumber.Thisiswrittenonthetyrewithchalk.Childrencancompareandcheckeachothersnumbercyclesforaccuracy.Anexampleofanumbercycleis:
5+1=6-3=3+7=10-9=1+4=5Inasuccessfulnumbercycle,youshouldbeabletostartreadingitatanypointinthecircle.ShapehuntsandnumberfactsAniceextensiontoashapehuntistoaddinsomenumbers!Veryoftenthereisanexcessofshapestobefound,soincludinganelementofnumberworkbringsvarietytothistask.Whenthechildrenfindasquareorrectangle,thechallengeistocreateasumwithfournumbersthataddupto10,e.g.1+3+5+2.Thesearechalkedupontheshape:
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Thesameactivitycanbeundertakenfortrianglesoranyothershapeswithdefinedvertices.Naturallywithtriangles,thefocuswouldbetrios.Numberpatternscanalsobeexplored.Forexample,childrencanwritespecificnumbersinsquares,trianglesandothershapestheyfind,e.g.
Intriangles:0+0+0=0,1+1+1=3,2+2+2=6,3+3+3=9,etc Inquadrilaterals:0+0+0,1+1+1+1=4,2+2+2+2=8,3+3+3+3=12,etc
Itcanbeinterestingforthechildrentoworkoutthenumberpattern.Whatisthislinkedto?Whatwouldhappeniftheyfounda12-sidedshape?EvenandoddflowerpetalsArepetalsmainlyoddoreven?Pickaweedsuchasadaisyandusethistoinvestigate.Otherpossibilitiesincludebuttercups,speedwellandothercommonplayingfieldflowers.EvenandoddobjectsAskeachchildtofindupto5objectswhichtheycancarryintheirhands.NexttheyfindapartneranddecidewhoisAandwhoisB.IfthetotalofbothobjectsiseventhenAwins.Ifthetotalnumberofobjectsisodd,thenBwins.Eachpairshouldalsoseewhathappenswhentheobjectsaremultiplied.Swappartnersandrepeattheactivity.Dothisseveraltimesuntiltheclassseesapatternemergingintheresults.Whatdoesthissayaboutoddandevennumberswhenitcomestoadditionandmultiplication?Dotherulesworkforsubtractionanddivisiontoo?FourcornersThisworksbestforchildrenwhoarecompetentatunderstandingabstractnumberandcanusetheirfingersforaddingandsubtracting.Onanetballcourtorotherlargearea,tapedown,hanguporchalkanumberineachcorner.Havechildrenstandinthecentreofthecourt.Calloutdifferentinstructionsforthechildrentofollow,e.g.
• Findanumberbiggerthanfive• Thisisanumberrepresentsthenumberofhandsyouhave• Whatis3plus2?
Thechildren shouldwalkor run to thecorrect corner. It canhelp somechildren if there isanumber line to look at to help check their calculations. To extend the game, add in morenumbers.MULTIPLICATIONANDDIVISION
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UsinghoopsScatteranumberofhoopsonthegrass.Whentheadultblowsawhistleorthemusicstops,theadultshoutsoutanumber,e.g.“3”.Thechildrenmustjumpinsideahoopsothatgroupsof3aremade.Thenchildrencanworkoutthesum,e.g.25childrenjumpedin8hoopsandonepersonwasleftover.Theleftoverchild/rencaneithergobackinthegameoritcanbeplayedasaprocessofeliminationwithchildrenwhoareout,collectinghoopsandcallingoutnumbersandcheckingthesumsarecorrect.Backintheclassthisactivitycanberevisedusingcounters.MultipleHop,SkipandJumpThisformofrelayracesprovidesagoodincentiveforchildrentolearntheirtablesorcountingin2s,3s,etc.Splittheclassintoteamsandhaveaconeforeachteamplacedapproximately12maway.Calloutacommandsuchas“Jumpby2s.”Thefirstplayerineachteamshouldjumptotheirconeandbacktotheirteam,countingintwoswitheachjump,e.g.2,4,6,8,etc.Atanytimecalloutanothercommandsuchas“Hopby3s”or“Skipby5s.”Thechildreninmotionhavetostartfromzerowitheachnewcommand.Whenthenextpersonintheteamistagged,theymustcontinuewherethelastchildleftoff.Aftertheraceisfinished,thewiningteamcanjumpforjoyastheycountin10s!HopscotchMathsIfyourschoolhasflagstonesorpavingthenhopscotchgridscanbequicklydrawnusingchalk.Forreinforcingmultiplicationtables,childrencanchalkin3,6,9,12,etcintotheirhopscotches.Thenthechildrencancountandplaythegame.Thegridscanbeextendedbeyond10spacestooformoreablechildren.Two-by-TwoChildrenneedtoworkinpairs,withoneball.Reviewcountingin2’s,3’s,etc.Thechildrenthrowtheballtoeachother,countingthepattern,e.g.2,4,6,8.Theactivitycanhavenumerousvariationssuchas:
Iftheballisdropped,thepairmuststartagain Onceanumberisreached,e.g.20ifcountingin2’s,thenthepaircansitdown Bouncepasses,chestthrowsorotherspecificpassescanbeemphasised.
BigstickmultiplicationAsawholeclass,practicetappingandpassingstickstoreinforcethetimestables.Inpairs,thiscanbeextendedwithchildrenmakinguptheirowntappingandpassingdanceroutines.BeanbagMultiplication
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Createa5x5gridwiththenumbers1to5alongthetopandlefthandside.Thechildrentakeitinturnstothrowabeanbagontothegridandworkouttheanswerforthesquareuponwhichitlands.Achildcentredalternativeistogeteachchildtothinkofmultiplicationsumandwriteitonapost-itnote.Putapost-itnoteineachsquareonthegrid.Childrenthencanthrowabeanbagatanysquareandgainapointfortheirteamforansweringcorrectly.Thiscanalsobeplayedbysimplydrawingcirclesorputtinghoops,tyresorothermarkersontheground.ThisactivitycanalsobeusedforpracticingsimpleadditionandsubtractionwithyoungchildrenArraysGet children into the habit of creating arrays from gatheredmaterials. Arraysworkwell for“Showme”activitiesespeciallybeyondtheearlyyears.Theconceptofanarrayisaboutlayingoutapatternofobjects,e.g.
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5x3array
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3x4array
Childrencanuseastickorpieceofstringtosectionoffthearray.Alternatively,objectscanbesimplyremovedandshown.Childrencandemonstrateanswerstoinstructionssuchas“Showme…”
Halfof12, Onethirdof15 Anotherarrayfor12,(e.g.4x3,2x6,6x2,etc.) Thesamenumberbutadifferentarrayfromthepeopleeithersideofyou.
Encouragechildrentoalsomakeup“Showme”challengesforeachothertocarryout.GatheringAcornsSquirrelsareverybusycreaturesinAutumngatheringacornsandothernutsandstashingtheminhidingplaces.Iftheywakeupduringwinterorearlyspringandfeelhungrytheythenhaveasupplyoffoodtoeat.Throwlotsofunifixcubesofdifferentcoloursoverpartoftheplayingfieldorasphalt.Thelargertheareathelongertheactivitytakes.It’sbesttostartsmall.Dividetheclassintosmallteamsofabout4or5children.Eachteamneedsahoop.Eachhoopshouldbeplacedatdifferentplacesaroundtheedgeoftheareasotheteamsarespacedout.Onthewhistle,thechildrenshouldbegincollectingtheunifixcubes.Eachchildmayonlygatheronecubeatatimeandbringitbacktotheirhoop.Ifyouhavechildrenwhofindthishard,givethemapairofchopstickstouseandremovethemtoahoopneartheteacher.
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Attheendofthedesignatedtime,thechildrencancountupthenumberofacornstheirteamhascollected.Thegamecanbemademorechallenginginmanyways:
Teamsmaybeallowedtostealacornsfromeachother’shoops.Thismayseemtoughbut this canhappen to squirrels. Theycanwakeupand find thatanother squirreloranimal has plundered their stash. Sometimes they forgetwhere they have put theiracornstoo!
Eachcolourcanbeworthdifferentpoints.Ifthisisarule,thenmakethegreen,brownand black ones worth more as they are harder to spot in grass. This increases thecomplexityofaddingandintroducesmultiplicationinaverypracticalway.Havepencilandpaperreadyfordoingthesums!Itcanalsobeundertakentoreinforceplacevalue,iftheunfixcubesareallocatedplacevalues,e.g.units,tens,hundreds,etc.
Decidewhethertosharethepointssystemfordifferentcolourswiththechildrenpriortobeginning the game. It canbean interesting twist for some classes, if theydonotknowthisuntilbeginningtocounttheirstash.
Use naturalmaterials like conkers, acorns, leaves and sticks. This game is great in awood,wherenaturehasnaturallyscatteredtheobjects!
Usedifferent lengthsandcolourofwool insteadof cubes. Thechildrenhave toknottogether the wool and then the class can decide whether it’s length or number ofstrandswhichismostimportant!
ZeroThe name “zero” comes from the Latin zephirum meaning empty or blank. The symbol “0”originatedinIndiainAD830.Itcausedconfusionforalongtimeastowhetheritwasanumberor a digit. If it stood for nothing, then surely it was nothing and did not need a symbol?Fibonacciprovidedananswer.Hesaid that zerocanbeusedasa“placeholder” toseparatecolumnsoffigures.Itcanalsobeusedtorepresentapositiononascale.Intemperaturescales,zerodegreesisavalidreading.Itdoesnotmean“notemperature”.Childrenthereforehavetolearnabouttheabstractandconcreteusesofzero.Thiscanworkbytakingawayorremovingitemsuntilthereare0objectsleft.Howeverlotsofpracticeisneededdevelopingtheconceptofzeroasaplaceholderthroughpracticalplacevaluework.Having a weather station and recording weather over the winter is a practical way ofdemonstratingwhywehavenegativenumbersandhowthesecanbeusedpractically.
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Somechildrenfindithelpfultohavealargenumberlinecreatedonthegroundandtobegivenpracticalsumstoseetheimpact.Forexample“Yesterday,thetemperaturewas1degreeabovefreezing.Overnightthetemperaturefellby4degrees.Whatwasthetemperatureintheearlyhoursofthismorning?”Likewise, a double-ended hopscotch can be drawn. Put zero in the middle and a negativenumberedhopscotchononeside(-1to-8),andapositivenumberedhopscotchontheotherside)+1to+8).Throwamarkeddieorspinaspinneronaspeciallymarkedpieceofcardwiththenumbers-3,-2,-1,1,2,3.Thepersonstartsonzeroandmoveseitherwayaccordingtothenumberspunorthrown.Everytimethepersonlandsinanumber,heorsheputsamarkthere.Theaimistojumpintoeverysquareonbothsidesofthehopscotch.Landheightisanotherscalewhereintegers(positiveandnegativenumbers)areused.Sealevelisconsidered0m.Onceyouareinthesea,yourfeetarebelowsealevel.Submarinesoperateatnegativealtitudes.N.B. Stocks and shares also trade innegative andpositive values. Theelectrical charge in anatomisalsomeasuredonanegativescale.
PlaceValueInmaths,childrenneedhelptounderstandtheconceptofplacevalue.Builduptheconceptsstepbystep.Manyinteractivemathsprogrammeshaveprogressionbuiltin.Childrenneedlotsofpracticeanddiscussionaboutnumberfactssuchas:1)PlacevalueandpositionWhenundertakingplacevalueworkoutside,reinforceconceptssuchas
48ismadeupof40and848is4tensand8units48isbetween47and49
2)Simpleadditionandsubtractionfacts 48is47+1 48is49-1 48is20add20add83)Numberfacts 48islargerthan47orsmallernumber 48issmallerthan49orotherlargernumbers 48isanevennumber.Itisnotanoddnumber4)Rounding 48roundedtothenearesttenis50
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148roundedtothenearesttenis150 148roundedtothenearest100is100PlacevaluesticktappingThesizeofthestickcanrepresentthequantityshown.Forexample,use1msticksfor100’s,10cmsticksfor10’sandwoodcookiesforunits.Workingintrios,childrencantapoutnumbersupto999foranothertriotoguess.PlacevaluegridsChildrenworkingroupssizeswhichmatchtheirunderstandingofplacevalue.Thiscouldbe
Pairs:tensandunitsTrios:hundreds,tensandunitsFours:thousand,hundreds,tensandunits
Etc.Eachchildassumesarole,e.ghundreds,tensorunitsandthegroupchalksorusesnumbercardsorstonestocreatea0-9grid,e.g.
Th H T U9 9 9 98 8 8 87 7 7 76 6 6 65 5 5 54 4 4 43 3 3 32 2 2 21 1 1 10 0 0 0
Whentheteachercallsoutanumber,e.g.1346,eachchildmuststandinthecorrectplaceontheirgrid.Thiscanbepractisedseveraltimesbeforebringinginadditionespeciallythatwhichinvolvesbridgingacrosstheunits,tensandhundreds.Thiscanbeextendedupto1million,withchildrenworkingcooperativelyingroupstoillustrateeachnumber.Suchgridsalsoworkwellforworkingindifferentbases.Remembertochangethevaluesineachgrid.Forworkinginbas5,youwouldneed:units,fives,twenty-fives,onehundredandtwenty-fives,etc.Collecting,sortingandexchangingmaterialsChildrenneedlotsofexperienceofcollecting,sortingandexchangingmaterials.Forexample,thiscouldbecountinggravelandputtingtheseintopilesoftens.Eachtencanthenbe
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exchangedforalargerstone.Oncetenstonesareachieved,thenthiscanbereplacedwithalargerocktorepresenthundreds.Atdifferenttimesoftheyear,dothiswithdifferentobjects,e.g.leavesintheautumn,conesinthesummer,conesinthewinter.Forexample,10smalllarchconescanbeexchangedforasitkaconethatrepresents10smallcones.Inturn,thesitkaconescanbereplacedbyalargesugarpineconetorepresentonehundred.Similarexchangescanhappenwithstonesofdifferentsizes.Itcanalsobedonethroughroleplay,e.g.usingshops,fairyland,etc.IntroducingotherbasesFormoreablechildren,consolidatingandapplyingtheirknowledgeofbase10tootherbasescanbeagoodwayofseeingiftheirplacevalueskillsaretransferable.Forexample:
o Binaryorbase2canbeexemplifiedthroughusingpineneedles(theygrowinpairs)
o Buttercupshavefivepetalssocanbeusedtoillustratebase5o Cloverleavescomeinthreesandthusareidealforlookingatbase3
Forbasework,usingthesheepcountingrhymesystemtraditionallyusedbyshepherdsinNorthernEnglandcanbeausefulinvestigationasitworksinbase5butarguablyalsoinbase20.Formoreinformationhavealookathttp://en.wikipedia.org/wiki/Yan_tan_tetheraAlsolookingatdifferentnumbersystemssuchasRomannumbersystemcanalsoaddtothediscussionsandinvestigationsarounddifferentbasesystemsandtheirvalue.
Fractions,decimalsandpercentagesMuddyFaceswww.muddyfaces.co.uksellsquaremetresetsofstickscutinto:
1x1m 2x50cm 4x25cm 10x10cm
Thesecanbeusedtocreatesimplefractionswallsthatcanhelpexplaintherelationshipsbetweenfractions,decimalsandpercentages.ThereisalsoanexampleofhowaP6classusedgatheredstickstocreatetheirownfractionwalls:http://creativestarlearning.co.uk/maths-outdoors/outdoor-maths-using-sticks-to-understand-fractions/
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Startwithchallengingchildrentomake3linesofsticksthesamelengthastheone-metrestickandseehowthishappens.Encouragechildrento lookatothergroupsfor ideas. Ifanygroupmakesaperfectfractionwallthenshowthistotheothergroupsandaskthemtoexplaintheirdecision-makingbehindthis.Give the children time to invent their own games and activities that help reinforce theseconcepts.Youwillcommonlynoticethefollowingtypesofresponses:
Guessthestick–inabagorbehindaback,thechildrenfeelthesizeofastickandhavetoguessitslength
Countinglengths–thismightbemakingtowersofdifferentsizes,orplayingagameoflongjumpwherethechildrenusethesticktomeasurethejump.
Equivalencegames–thisinvolveschildrenrunning,hidingand/orfindingfractionsandtheirequivalent,e.g.showme0.5m(andchildrenrunandcollect2x25cmor5x10cmor1x50cmsticks)
Thepackisalsousefulforlookingatpracticalmeasurementintermsofthesespecificlengths.Ihave put the decimal value and the value in centimetres on each stick. I find that this aidsdiscussions.MathematicalPotionsChallengeyourclasstocreateamagicpotiontohelpyouunderstandfractions.Forexample,iftenthsarebeingintroduced,thensmallgroupsofchildrenmustfind:
• 10leaves• 10stones• 10smallflowers• 10otherinterestingobjects
Eachgroupshouldlaytheseingredientsonthegroundwheretheycanallseeandaccessthem.Eachchildneedshisownmixingcup,asplashofwaterandfoundtwig.Thegrouphastosplitthegatheredingredientsinawaythatensureseachpersonhasadifferentsmellingpotion.Eachpotionneedsanameandalistofingredientspresentedasafractionofthewhole,e.g.
Child1 Child2 Child3 Child4 Total
2leaves2stones2flowers2objects
1leaf4stones3flowers2objects
5leaves3stones3flowers2objects
2leaves1stone1flower2objects
10leaves10stones10flowers10objects
FractionFix FloppyFractionPotion
FartySmellyFractionPotion
FizzyFountain 40
Discussioncanbehadaboutwhousedthemostingredientsandwhetherthisaffectedthesmellinessofeachpotion.Thefinaltestcanbewhenallthepotionsaremixedtogethertomakeonehugepotion.
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ExpressionsandequationsEachchildwritesaseriesofnumbersonthegroundinchalk,e.g.:
Then,theygoroundvisitingotherchildren’snumbers.Onasheetofpaper,theycopydownthenumbersequenceandfillinthecorrectsymbolsfor>,=,<,etc.SomeorafewOtherquickgamescanbeplayed.Forexample,childrencanbeaskedtocollect“some”or“afew”stones fromagravelpath.Then thechildren findapartner, countout their stonesandfind out who has less than the other person or a number of stones greater than the otherperson. Ask children to swap partners when you call out “Change” and the children cancomparequantitieswiththeirnewpartner(thankstoJillO’Reillyforthisidea).HuntandhidesumsThechildrenworkinpairs.Anagreednumberofobjectsiscollectedorissuedsuchas10shellseach.Incoolerweather,thesecanbescatteredaroundanareaoftheplaygroundforchildrento gather. The children take turns to create number statements on the ground. Only theirpartner must not look whilst this is happening. The partner may only look once a numberpatternhasbeenmadeandpartofthesumiscoveredwithaflowerpot,e.g.2+ =10 or +8=10 or2+8=
AlgebraicequationsTheactivityabovecanbeextendedbyreplacingtheflowerpotandstones,simplywithonestoneoronestick.Usesticksandstonestoshowthe+,-,xand÷symbols.Usechalkorpaintedpebblesforthenumbers.HereanexampleofsomeP6work:http://creativestarlearning.co.uk/maths-outdoors/algebraic-equations/
A15 B10 C10 D12 E7