Bearsinthecave
Annotation​
Moanaisableto​ one-to-onematchandcountsalltosolvethisadditionproblem.
Shepicturesthe​ firstfivebearsasshecountsthemfrom1,thencontinuesthecount​ usingthebearsfromthe
secondpottle.
Problem:​Bearsinthecave
Theteacherplaces​ infrontofthestudenttwosetsofbearshiddenbeneathtwoplastic​ pottlesandposesthis
problem:
Thereare5​ bearsinthiscaveand3inthiscave.Howmanyarethere​ altogether?
Student​response
Moanalookshardat​ thefirstpottlewhichsheleavesinplace,andnodsherhead5times​ saying,“1,2,3,4,5.”​
Sheuncoversthe​ setof3bears,looksatthemandnods3times.Shethenlooksback​ atthefirstpottle,nodding
andcounting“1,2,3,4,5”and​ thenmoveseachofthe3uncoveredbearssaying“6,7,8.”She​ thenlooksupand
says,“Thereare8bears.Icounted.”
Teacher:
Moana:
Howwouldyouwritethat?
Wellthere’sfivesoIcouldwrite5.Andthenthere’sthreeso​ Icanwrite3.Andallofthemis
eight,soIcanwrite8.
Poppingballoons
Annotation
Samunderstands​ thatthisisasubtractionproblem.Hecarefullychecks​ byone-to-onecountingeachfingeras
hesubtractsthecorrectamount​ andhechecksthathehasansweredthequestion,“howmanyleft?”
Problem:​Poppingballoons
Theteacher​ showsthisproblemtothestudentandreadsitwithhimasrequired:
Therewere10​ redballoons.4wentpop!Howmanyballoonswereleft?
Student​response
Samholdsup10​ fingers.Hecarefullyfoldsdown4fingers,countingaloudashe​ doesso.Hechecksagainthat4
havebeentakenaway.Hekeeps2​ hands(6fingers)intheairandcountseachofhis6remaining​ fingersmoving
eachashedoes,toindicatetohimselfthattheyhave​ beencounted.Hesays,“There’s6left.Itookawaythe4
and​ counted.”
Teacher:
Sam:
Teacher:
Sam:
Tellmewhatyouknowthathelpedyou.
I​ ​ knowIhavetotakesomeawaybecausetheypopped.
Howwouldyouwritethat?
I’d​ ​ write10becausethat’showmanytherewereatthestart.(He​ ​ draws10balloons.)Idoa
takeawaysignandfourbecausethat’s​ ​ howmanypopped(Hedeletes4balloonswithlines
toshowtheyhave​ ​ popped)andthenIwriteequalssixbecausethat’swhat’sleft.
Visitingthelibrary
Annotation
Amycountsallthe​ itemstosolvethischangeunknownadditionproblem,firstlyby​ accuratelycounting5and
thencounting4.​
Problem:​Visitingthelibrary
Theteachershows​ thisproblemtothestudentandreadsitwithherasrequired:
5childrenwere​ inthelibrary.Somemorecamein.Thereare9childrennow.How​ manymorecameintothe
library?
Student​response
Amyholdsupone​ hand,nodding5timesasshelooksateachofherfingersandsays,"5".Sheholdsupher
otherhandand,assheraises4more​ fingersoneatatime,shenods4timesandsays,“Six,seven,​ eight,nine.”
Shelooksateach​ ofher4fingers,nodding4timesandsays,“It’s4becauseI​ countedtheonesthatcamein.”
Teacher:
Amy:
Whatdoyouknowthathelpedyou?
IknewthatsomewerealreadytherebecauseIcouldcountthemall.
Ladybirds
Annotation
Courtney​ understandsthe‘startunknown’problemandsolvesthisby​ countingeachoftheladybirdsfrom1.​
Problem:​Ladybirds
Theteachershows​ thestudentthispictureandposesthisproblem:
Thereweresome​ ladybirdsonthisleaf.2flewawayandnowthereare5left.How​ manywereontheleaftostart
with?
Student​response
Courtneyasksfora​ pencilanddrawsthe2extraladybirds.Thenshecountsthe5onthe​ leafandthe2inher
drawing,pointingtoeachofthe7asshedoes​ so,saying,“Ithinkitmustbe7atthebeginning.”
Teacher:
Courtney:
Whatdoyouknowthathelpedyou?
Iknowithastobethose5thereandsomemore.SoIdrawedthe2thatflewawayandthenI
couldcountthemall.
HandyCounters
Annotation​
Ihakasolvesthis​ additionproblembycountingeachitemone-to-onetofindthetotal.
​Problem:​Handycounters
Theteacherplaces​ agroupofcountersineachofthestudent’shandsandposesthis​ problem:
Youhave7​ countersinthishandand4countersinthishand.Howmanycounters​ doyouhavealtogether?
Student​response
Ihakaopensboth​ hands.Hetipsthe7countersontothetableandcountsthemwith​ onehandfrom1.Hethen
openshisotherhandandkeepsthecount​ going,saying,“8,9,10,11.I’vegot11.Icountedthem.”
Teacher:
Ihaka:
Howwouldyouwritethat?
Likethis.That’sthatseven(pointing)andthat’sthat​ four(pointing)andthat’showmuchallof
themis(pointingto​ 11).