Alaska-DLM EssentialElementsand
InstructionalExamplesfor
Mathematics
Kindergarten
Revised for Alaska July, 2014
Thepresentpublicationwasdevelopedundergrant84.373X100001fromthe U.S.DepartmentofEducation,OfficeofSpecialEducationPrograms.The views expressedhereinare solelythoseoftheauthor(s),andnoofficialendorsement bytheU.S.Departmentshouldbeinferred.
ALASKA-DLMESSENTIALELEMENTSANDINSTRUCTIONEXAMPLESFORKINDERGARTEN
KindergartenMathematicsStandards:CountingandCardinality
AKGrade-LevelClustersAK-DLM
EssentialElements
Instructional Examples
Knownumbernames and thecountsequence.
K.CC.1.Count to100by onesand bytens.
EEK.CC.1. Startingwith one,countto10by ones.
Studentswill:
EEK.CC.1. Startingwithanynumbergreaterthanone,countto10by ones. Ex. Count numbersto 10startingwithoneandanynumbergreatthanone andless than10.
Ex. Count sequentiallyto10 startingwithone,independentof objects, pictures,orthings asastudent wouldrecitethealphabet.
Ex. Count withor withoutone-to-onecorrespondencenumbersbeyond
10.
Ex. Count groupsof10.
Ex. Count backwardsfrom10.
Studentswill:
EEK.CC.1. Startingwithone, count to10by ones. Ex. Countnumberto10verbally.
Ex. Count without one-to-onecorrespondenceto10 starting with oneby rote.
Ex. Sequentially singnumbersto10 startingwithone.
Studentswill:
EEK.CC.1. Startingwithone, count byonestofive. Ex. Count ownfingerstofiveverbally.
Ex. Sequentially,countsequencetofiveeither independentofobjects, pictures,orthings asastudent wouldrecitethealphabetorby pointing. Ex. Count without one-to-onecorrespondencetofive.
Ex. Sequentially singnumberstofive. Ex.Sing alongto counting song.
Studentswill:
EEK.CC.1. Countwithteacherfromonetotwo.
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
Ex. Count withtheteacherto two.
K.CC.2.N/A
K.CC.3.N/A
K.CC.4.Understandthe relationshipbetween numbers and quantities; connectcounting to cardinality.
Whencountingobjects,say thenumbernamesinthe standardorder,pairing
eachobjectwith one and only onenumbername andeachnumbername with oneand onlyone object.
Understandthat thelast numbernamesaidtellsthe
EEK.CC.2.N/A
EEK.CC.3.N/A
EEK.CC.4.Demonstrate one-to-one correspondence,pairing eachobjectwith one and only onenumberandeach name withonly oneobject.
Studentswill:
EEK.CC.4.Demonstrateone-to-onecorrespondencewith morethan one. Ex. Whencountingobjects,say thenumbernames instandardorder and pair eachobjectwithone andonly onenumbername.
Ex. Passpencils outto classmatesandcountthepencils aseachclassmate getsapencil.
Ex. Usesone-to-onecorrespondencewhencounting up to10 common objectsinthe classroom(crayons,blocks, buttons).
Ex. Count out10penniestoexchangeforadime.
Ex. Sing acountingsongandraisethecorrectnumberoffingerswitheach number.
Ex. Count dotson diceandmoveforwardcorrespondingnumberof spaces on gameboard.
Ex. Roundrobin countto10.
Studentswill:
EEK.CC.4.Demonstrateone-to-onecorrespondence,pairing eachobject with oneand onlyonenumberandeachname withonlyoneobject.
Ex. Useone-to-one correspondencewhencounting up tofivecommon objectsinclassroom(crayons,blocks, buttons).
AK Grade-Level ClustersAK-DLM
EssentialElements
numberofobjects counted.Thenumberof objectsisthesame regardlessof their arrangementorthe order inwhichthey were counted.
Understand thateach successivenumbername referstoaquantitythatis onelarger.
Instructional Examples
Ex.Createsets of objectstofive.
Ex. Placecorrespondingnumberofbeansinan eggcarton witheach sectionlabeled1-5.
Ex.Movebeadson an abacusasanotherstudentcountsonetofive. Ex. Givenan eggcarton,placefive stickersineachsection.
Studentswill:
EEK.CC.4.Demonstrateoneobject’scorrespondencewithoneobject.
Ex. Useone-to-one correspondencewhencountingup tothreecommon objectsinclassroom(crayons,blocks, buttons).
Ex.Givenbowls,placethree ballsineach.
Ex. Matchobjectsby pairing eachobjectwithoneandonlyoneother number.
Ex.Place“one”letterineachstudent’smailboxtogohome.
K.CC.5.Count toanswer “how many?”questions about asmanyas20things arrangedinaline,a rectangulararray,ora circle,orasmanyas10 thingsinascattered configuration;givena numberfrom1–20,count out thatmanyobjects.
EEK.CC.5. Countout up to threeobjectsfromalarger set,pairingeachobject with oneand onlyone numbernametotellhow many.
Studentswill:
EEK.CC.4. Withguidanceandsupport,countoneobject.
Ex.Place“one”letterineachstudent’smailboxtogohome. Ex. Putoneobjectin each sectionof an eggcarton.
Ex.Indicate“one”object whenasked,“Whereisone<nameoffamiliarobject>?”
Ex. Giveonepenciltoeach classmate.
Studentswill:
EEK.CC.5. Countfive objectsoutofagroupof morethanfiveobjects.
Count agivenset of fiveobjects,pairing eachobject withoneand onlyone numbernameandwhenasked,“howmany,”sayfivewithoutrecounting. Ex. Givenabox ofcrayons,selectfivecrayonsasrequestedbyteacher.
Ex. Givenasetof fiveobjects,countoutthreeobjects.
Ex.Froman arrayof fiveobjects,counteachobject inthegrouponlyone timeand tell howmanywasinthegroup withoutrecountingtheobjects. Ex. Countfivechildrenoutofallthechildrenonlyonetimeandtellhow manywithoutrecounting.
AK Grade-Level ClustersAK-DLM
EssentialElements
Studentswill:
Instructional Examples
EEK.CC.5. Countout up tothreeobjectsfromalargerset,pairingeach object withone andonlyone numbernametotell how many.
Ex. Givenan arrayof objects,countoutthreeof theobjects,countingeach objectonlyonceandtellhow many.
Ex. Givenabox ofcrayons,selectthreecrayonsasrequestedbyteacher. Ex. Count outthreecountingbearsfromagroupoffive.
Ex. Passoutthreepagestoeachstudentfromastackofpaper, counting
“one,two,three”eachtime,andtellhow manytheygavetothe students.
Studentswill:
EEK.CC.5. Count either one ortwoobjects outofagroup of fiveobjects. Ex.Givenaboxofcrayons,selecteitheroneortwocrayonsasrequested by teacher.
Ex. Count outtwo counting bearsfromagroupof five.
K.CC.6.Identifywhether
thenumberofobjectsin one group isgreaterthan, less than,orequaltothe numberofobjects in anothergroup,e.g.,by using matchingand countingstrategies.
EEK.CC.6. Identifywhether thenumberofobjectsin onegroupismoreorless than(whenthequantities are clearlydifferent)or equalto thenumberof objectsin anothergroup.
Studentswill:
EEK.CC.5. Identifyoneobjectoutofagroup of objects.
Ex. Identifybetweenaset with oneor twoapples whenasked,“show me oneapple”and makeachoice.
Ex. Go to theprizebox andpickoneobject.
Studentswill:
EEK.CC.6. Identifywhetherthenumberof objectsinonegroup ismoreor less thanor equaltothenumberofobjects inanothergroup.
Ex. Identifywhichgrouphas morefromtwogroups createdbytheteacher (e.g.,Theteachercreatestwogroupsof manipulativeobjectswhosetotal quantityiswithinthree.Giventwogroupsof blocks--forexample,one grouphassevenblocks andtheotherhasfour--the studentis ableto identify whichgrouphasmoreblocks.Theteacherasks whichgrouphas moreand thestudent identifiesit.
Ex. Giventwogroupsof blocks (one group haseightblocks andotherhas
five),identify whichgrouphaslessblocks.
Ex. Givenfivepaperstopass outtoagroupof eight students, indicatethat
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
thereareMORE studentsthan papersby countingthepeople andthen countingthepapers.
Studentswill:
EEK.CC.6. Identifywhetherthenumberof objectsinonegroup ismoreor less than(whenthequantities are clearlydifferent)orequalto the numberofobjects inanothergroup.
Ex. Givenachoice of twoboxesofblocks, oneboxwithnine blocks and onebox withfourblocks, identifywhichboxhasmoreblocks.
Ex. Givenachoice of twoboxesofblocks, oneboxwitheightblocks and onebox withfourblocks, identifywhichboxhasfewerblocks.
Studentswill:
EEK.CC.6. Giventwogroups of dramaticallydifferentquantitiesof objects, identifywhichgrouphasmore.
Ex. Whentwogroupsofobjectsare countedouttothestudent,identify which hasmoreobjectsthananothergroup(e.g.,using matchingand countingstrategies).
Ex. Giventwobowlsofsnackswith alargedifferencein quantity,identify
whichhasmore.
Ex. Givenachoice of twoboxesofblocks withadifferencein quantity ofat leasttwicethe other,identifywhichhas more.
Studentswill:
EEK.CC.6.Exploregroupsthathavemoreandless.
Ex. Using sand/water/balltables withdrasticallydifferent quantities of materials,explorethequantitywhiletheteacheris talkingaboutthe languageof more.
Ex.Placesillybands/bangles/bellswithdrastically differentquantities on
thearmsor legsof the students and explorethequantity ofmorewhile theteacherusesthelanguage ofmore.
Ex. Giventwogroupsof buttonswithverydifferent amounts,identifythe groupthathas“more” bypointingtopicturesymbolsofmore/less, big/small.
KindergartenMathematicsStandards:OperationsandAlgebraicThinking
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
Understandadditionas puttingtogetherand addingto, andunderstand subtractionastakingapart andtakingfrom.
K.OA.1.Representaddition andsubtractionwith objects,fingers,mental images,drawings1,sounds (e.g.,claps),actingout situations,verbal explanations,expressions,
orequations.
EEK.OA.1.Represent additionas“putting together”orsubtractionas “takingfrom”ineveryday activities.
Studentswill:
EEK.OA.1.Representadditionas“puttingtogether”andsubtractionas
“takingfrom” withquantitiesto10.
Ex. Combinetwosets of objects,pictures,orthings tomakeoneset of 10 through theuseofassistivetechnologyor AACdevice.
Ex. Takeawayonesetofobjectsfrom10 anddeterminehow many remain.
Ex. Usingasimple storycontext andobjects,thestudentputstogether and takesfromasappropriatebydirectlymodelingtheproblemwithobjects, actions,orsymbols.
Ex. Followdirectionstogatherenough materialsfor everyoneand then
passthemouttoeach student.
Ex. Putacountingbearwith agrouptoadd ortakeawayacountingbear tosubtract.
Studentswill:
EEK.OA.1.Representadditionas“puttingtogether”orsubtractionas
“takingfrom”ineverydayactivities.
Ex. Identifythetotalnumberofcrayonswhenonestudenthasthree crayonsandanotherstudenthas two,andtheyputtheir crayonstogether to share.Describetheactionasput together.
Ex. Addtoagroupof crayonswhentoldtoaddtothegroup.
Ex.Takeawayfromagroupofcrayonswhentoldtotakeawayfromthe group.
Ex. Givenfivestickers,giveanotherstudentoneofthefivestickers,and
describetheactionastakeaway.
Ex.Joinlinkingcubestoshow action/processof puttingtogetheror addition.
1Drawingsneednotshowdetails,butshouldshowthemathematicsintheproblem.(ThisapplieswhereverdrawingsarementionedintheStandards.)
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
Ex. Breakapartlinkingcubes/snapblocks/bristleblocks/pop-beadsto showaction/process of taking fromorsubtraction.
Studentswill:
EEK.OA.1.Follow directionsto“puttogether”byaddingoneor “take from”bytaking one.
Ex. Givenabowlofcountingbears,addacountingbearto thebowl. The teachercalls theaction “puttingtogether”or addition.
Ex. Takeone when theteacherispassingoutsupplies anddirectsthe studentsto takeone.Theteachercallsthe action“takingaway”or subtraction.
Ex. PlacePopsiclesticksintoacircleand uselanguagetodescribeaddition
or“puttingtogether.”
Ex. Using cubes,createtowersby adding ortakingawayonecubeata time.
Ex. RemovePopsiclesticksfroma circleanduselanguagetodescribe subtraction or“takingfrom.”
Studentswill:
EEK.OA.1.“Puttogether”or “takefrom”withteacher.
Ex. Theteacherand studenttogetheradd ablockto a stackwhileteacher says,“puttogether.”
Ex. Theteacherand studenttogethertakeablockfromastackwhilethe teachersays,“takeaway.”
KindergartenMathematicsStandards:MeasurementandData
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
Describeandcompare measurableattributes.
K.MD.1.Describe measurableattributesof objects,such aslength or weight.Describeseveral measurableattributesof a single object.
K.MD.2.Directlycompare twoobjectswitha measurableattributein common,tosee which objecthas“moreof”/“less of”theattribute,and describethedifference.For example, directlycompare the heightsof twochildren and describeonechild as taller/shorter.
Classifyobjectsandcount thenumberofobjectsin eachcategory.
K.MD.3.Classifyobjects intogivencategories; count thenumbersof objectsineachcategory
EEK.MD.1-3.Classify objectsaccordingto attributes(big/small, heavy/light).
Studentswill:
EEK.MD.1-3.Orderobjectsaccording toattributes(big/smaller/smallest, heavy/lighter/lightest).
Ex. Giventwobackpacksofdifferentweight,describeordemonstrate whichone isheavier.
Ex. Giventwocubesof differentsizes, describeordemonstratewhichcube isbiggerand whichcubeissmaller.
Ex.Compareheightsof twoclassmatesto astandardsuchasameterstick. Ex.Comparesportsballs(baseball,basketball,tennisball, etc.)using variouslengths ofyarn.
Ex. Givenblocks ofvaryingsizes,identifywhich are heavier/lighterand
smaller/bigger.
Studentswill:
EEK.MD.1-3.Classifyobjectsaccording toattributes(big/small, heavy/light).
Ex. Givenabigbook andasmallbook,describeordemonstratewhichone isbiggerand whichoneissmaller.
Ex. Giventhe shoeof astudentandtheteacher,identifywhich one is biggerand whichone issmaller.
Ex.Sortheavyandlightobjectsaccordingto weight.
Ex. Giventhehand ofastudent inthe classandthehandof theteacher, identifywhichone isbiggerandwhichone issmaller.
Ex. Giventwoobjects of varyingweight,describeor demonstratewhichis heavy/lightorlarge/small.
Studentswill:
EEK.MD.1-3.Usingamodelor atemplate,sortobjectsbyone attribute
(big/smallorheavy/light).
Ex. Sortcountingbearsbysizeusingamodelortemplate.
AK Grade-Level ClustersAK-DLM
EssentialElements
andsortthecategoriesby count.2
Instructional Examples
Ex. Giventwoobjects,whereoneisat leasttwicethe sizeof theother, identifywhichone isbiggerandwhichone issmallerwithdescriptive promptsfromtheteacher.
Ex. Identifybiggerballwhenshown abeachballanda tennisball and listeningtotheteacherusevoice inflectionsandkinestheticmotionsto exaggeratebiggerandsmaller.
Ex. Identifythebiggerballwhenshown agolfballandbeachballand listeningtotheteacherusingvoice inflectionsand motionstoexaggerate. Ex. Sortobjects in the classroomintogroupsof heavyandlight(e.g., bowlingball,beach ball,andarock).
Ex. Giventwopicturesof real-lifeobjects,selectthebiggerone.
Studentswill:
EEK.MD.1-3.Matchobjectsby attributebigand small.
Ex. Touch alargeobject(such asa pumpkin)asteacherdescribesitas big whencompared toa smallerpumpkintoy.
Ex. Indicatesmallpumpkinasteacherdescribesit assmall whencompared with alargepumpkin.
Ex.Indicateif theywantthebigballorthesmallball.
2Limitcategorycountstobelessthanor equalto10.
Mathematics Standards: Geometry
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
K.G.2.Correctlyname shapesregardlessoftheir orientationsoroverallsize.
K.G.3.Identifyshapesas two-dimensional(lying ina plane,“flat”;or three- dimensional,“solid”).
EEK.G.2-3.Matchtwo- dimensionalshapes (circle, square,triangle).
Studentswill:
EEK.G.2-3.Matchtwo-dimensionalshapesthatvaryinsize (circle, square, triangle).
Ex.Givenanassortmentofshapesthatvaryinsize,matchtheshapes accordingtoshapeandsize.
Ex.Usingcomputersoftware,selectatriangleandmatch ittoatarget triangle thatisadifferentsize.
Ex. Givenacircle,goona“CircleHunt”tofindotherexamplesof circles around theschool.
Studentswill:
EEK.G.2-3.Matchtwo-dimensionalshapes (circle,square,triangle).
AK Grade-Level ClustersAK-DLM
EssentialElements
Instructional Examples
Ex. Givenacollection of pairs ofidenticallysizedshapes,matchthe shapes.
Ex. Matchshapesinaninteractivewhiteboardactivity.
Ex. Givenfourpokerchips andfourblocks, matchtheobjectsbasedon shape.
Studentswill:
EEK.G.2-3.Matchashape toitsduplicate.
Ex. Given oneshapeandshowntwoshapes,selectthematchingshape fromthe twochoicestooneofhers/his.
Ex. Matchacoloredconstructionpaper circletoanoutlineonpaper.
Ex.Completeashape-sortingbox.
Studentswill:
EEK.G.2-3.Repeatamodel tomatchshapes.
Ex. Matchshapedobjectswithteachermodel. Repeatafterobservinga teacher-directedmatchingactivityroutine involving shapes.
Ex. Matchshapedobjectswithteacherprompts.Repeatafterobserving theteachermatchthe correctshapedobjecttothe sameobject.
Ex. Repeatafterobservingtheteacherusepicturescutfrommagazines thatshow circlesandsquares.Teacherholdsup apictureandasks what shapeitis,thenplacesitonalargecircleorsquare mat.