exploring number sequence and order · exploring number sequence and order ... ordinal numbers are...

©JulietRobertson,CreativeSTARLearningLtd,2016www.creativestarlearning.co.uk 1

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


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.


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


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.


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:

13

10


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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


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


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.

xxxxxxxxxxxxxxx

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.


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.


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


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


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/


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


2leaves1stone1flower2objects


FractionFix FloppyFractionPotion

FartySmellyFractionPotion

FizzyFountain 40

Discussioncanbehadaboutwhousedthemostingredientsandwhetherthisaffectedthesmellinessofeachpotion.Thefinaltestcanbewhenallthepotionsaremixedtogethertomakeonehugepotion.


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

exploring number sequence and order · exploring number sequence and order ... ordinal numbers are...

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