ESTIMATIONANDROUNDING
Vocabulary:guess,estimate,overestimating,underestimating,count,some,few,many,lots,a
little,aweebit,approximately,roughly,roundabout,etc.
Simple rounding activities can begin very early on. Make a measuring stick with every 10cm
markedwithapieceofmaskingtape.Thiscanbeusefulforquickestimatesandroundingtothe
nearest 10cm. Likewise children can make their own one-metre measuring worm and the
stripescanrepresent10cmintervals.
Likewisethecomplexityofsomeestimationtaskssuchasdeterminingtheapproximateheight
ofabuildingwhichistootalltomeasurecanbemadeascomplexasneeded.Thusmostofthe
activitiesinthissectioncanbetweaked,changedandadaptedforeachlevel.
Estimationisanaturalpartofinvestigativemathsworkespeciallythatwhichinvolvesnumber,
sizeandquantity.Childrenneedlotsofpracticeatestimatingsothattheyareabletomake
reasonableguessesbaseduponexperienceandknowledgeratherthanwild,randomestimates.
Itisabasicstrategyforproblemsolvingandenquirywork.
Beingoutsideprovidesarealcontextforestimating.Itishardtotellthenumberofbirdsina
flock,bricksinawallorexactlyhowlongitwilltaketowalktotheshops.Sothereisaconstant
needforeveryonetobemakingestimatesofquantityandactivitybaseduponourown
experiences.
Practitionerscanbringestimationintodiscussionsinanincidentalwayandcanencourage
childrento:
Number-Haveaguessbeforecountingobjects
Matching–Anticipatewhethereveryglovehasapair
Distance-Estimatehowfarawaythenearestshopis
Volume-Thinkaboutthevolumeofwaterinonebucketcomparedtoanother
Shape–Estimatingthenumberofverticesinacuboid
Weight-Wonderhowmuchfoodbirdswilleat
Time-Considerhowlongitwilltakeforaconetoclosewhensoakedwithwater
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Probabilityandchance-Calculatewhetheracoinwilllandheadsortailswhenoutfora
pennywalk
Childrenintheirplaywillbemakingestimatesaboutalotofdifferentmatters.Whenobserving
children,listenandlookforevidenceofchildren’sabilitytoestimate.Itisanindicationoftheir
understandingofnumberandquantitytobeabletomakeareasonableguess,e.g.
Talkingabouthowmanymorebricksareneededtomakeatower
Tellinganotherpersonhowfartheycankickorthrowaball
Thinkingaboutwhetheritispossibletowalkallthewayalonganarrowtreetrunk
Whatisimportantisforpractitionerstoreinforceisthatacorrectanswerisnotneeded.This
oftenworksbestwhenanexactanswerisnotknownorcannotbedetermined.Agoodtacticis
alsotogetagrouptomakeajointestimationsothatnoonepersonisrightorwrong.
Muchoftheworkinvolvesconversationsaroundestimation.Adultscanmodellinesofthought
andwaysofmakingareasonableguess.Thiscaninclude:
Workingondirectcomparisons
Undertaking activities such as filling up a transparent tube with stones. Challenge a group of
children to release half the amount of stones and count them. This can then become the
estimatefortheotherhalfofthestonesleftinthetube.Thesecanberemovedandcounted.It
can be worth having a tape measure or metre stick that extends to 100 for this sort of
estimationwiththerangeofestimatespeggedormarkedonit.
Workingwithnonstandardmaterials
Havefunestimatingquantitiesofnaturalobjectsinrelationtolength,e.g.
Thelengthofapersonlyingonthegroundasmeasuredwithpinecones
Howmanyshellswillfitonasquiggledrawninthesandonabeach
Whichfeatheristhesamesizeasmyhand(andisthisthelengthorwidthofmyhand)
fromaboxfuloffeathers
Rounding
There are lots of specific tasks or challenges that can be developed which involve rounding
numbers.Forexample,estimate:
The daily air temperatures, before checking with a thermometer or digital weather
station.
Howfaranobjecthasbeenthrownbeforemeasuringit.
Thelengthofpathsaroundtheschool.
Giving children a few minutes to make the biggest pile of sticks in a wood. Then the
childrenhavetoestimatethenumberofsticksinthepilebeforeplayingpickupsticksto
removeandcounthowmanyarethere.
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Chunking
Breaking up large quantities into smaller chunks, e.g. “There are 10 leaves on this branch. I
reckonthereisabout20branchesonthistree,soitmusthaveabout200leaves.”
Linkingestimatestoplacevalue
Learningtogroupitemsintoquantitiesof10,then100,then1000isusefulasawayintoplace
valueandlearningtoroundupordowntotensandhundredsisamethodofquickcalculation.
Thiscanworkwellwhenestimatingtheamountofgravelonatrolleyorthenumberofleaves
inapile.
Veryoftenchildrenstrugglewhenitcomestoroundingupordownoncetheyareworkingwith
numbersbeyond100.Forexamplerounding387upto390(nearest10)or400(nearest100).
Roundingwithdecimalsalsorequiresextrareinforcement.
Outdoors,alevelofestimationmayalsoberequiredasfeaturesatadistancesmaybetoofar
awayortoohightophysicallymeasure.Alsothelevelofcomplexitycanbequiteachallenge.
Estimatethenumberofleavesinanareaontheforestfloor
Findanareawithleavespileofpreferablydryleaves.Dryleavesareeasiertorake,areless
messyandmorefuntoplaywithattheend.Ifleavesarescattered,markoutwithstringorthe
areayouwanttoestimate.Youcanevenusechildrentomakeforcornersinasquaresurface
area.Haveeachchildmakeaninitialestimateindividuallyoftheleaves.(Writethesedownso
youcanaverageafterwards).
Nowaskthechildrenhowtheycameupwiththeirestimate?Discusswaystomakethe
estimatemoreaccurate-suchascountingtheleavesinsmallareaandmultiplyingtomakeup
alargerarea.Redoestimates.Takeanaverage.Iftime(andenoughhelpers)raketheleavesup
andmakeanactualcounttocompare.Putleavesintopilesof10s,100s,and1000attheend.
Note:Donotmaketheareatoolarge.
Nowapplytheskillstobiggerchallenges…
Thefollowingchallengesaresurprisinglycomplexinthatlotsofdiscussionwillbeneeded.Use
acooperativelearningorCriticalSkillsapproachtogroupworkandactivitiesbasedontheseor
similarsuggestions:
Estimatethenumberofsticksonatree.
Estimatethenumberofstonesonabeach.
Estimatetheamountofgravelonapath.
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Howmanybrickswereusedtobuildtheschool(orjustonewall)?
If your school building has a wall with visible bricks, this is good practice for estimation.
Childrencandiscusshowtheyaregoingtoworkthisout.Forexample,onemethodistocount
thenumberofbricksinonelineandthencountthenumberoflines.
Howcanyouestimatethenumberofbricksintheschoolbuilding?Whatstrategycanyouuse
asagrouptogainthemostaccurateestimate?
Howcanwemeasuretheheightofaschoolbuildingorthetallesttreeintheschoolgrounds?
Thereareseveralwaysofdoingthis,butitcanbeinterestingforchildrentotryouttheirown
ideas.Havealookatthemeasurementsectionofthishandout.
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