Alaska-DLMEssentialElementsand
Instructional Examplesfor
Mathematics
FourthGrade
Revised for Alaska July, 2014
Thepresentpublicationwasdevelopedundergrant84.373X100001fromthe U.S.DepartmentofEducation,OfficeofSpecialEducationPrograms.The views expressedhereinare solelythoseoftheauthor(s),andnoofficialendorsement bytheU.S.Departmentshouldbeinferred.
AK-DLMESSENTIALELEMENTSANDCOMPLEXITYEXAMPLESFORFOURTHGRADE
FourthGradeMathematicsStandards:OperationsandAlgebraicThinking
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Use thefouroperations withwholenumbersto solveproblems.
4.OA.1.Interpreta multiplicationequationas acomparison,e.g., interpret35 =5×7asa statementthat35is5 timesasmanyas7and7 timesasmanyas5. Representverbal statementsof
multiplicativecomparisons asmultiplication
equations.
4.OA.2.Multiplyordivide tosolve wordproblems involvingmultiplicative comparison,e.g.,byusing drawingsandequations withasymbolfor the unknown numberto representtheproblem, distinguishing multiplicativecomparison fromadditivecomparison.
EE4.OA.1-2.Demonstrate theconnectionbetween repeatedadditionand multiplication.
Studentswill:
EE4.OA.1-2.Apply repeatedaddition tosolveamultiplicationproblem representedwithnumbers.
Ex.Presentedwithamultiplicationproblemsuchas3 x6,useeggcartons andconcreteobjectstocreatearrays(e.g.,sort threeobjects intosixegg slotsorsixobjectsintothreeslots).
Ex.Whenpresentedwithtwochoicesofarraysonthesmartboard and a multiplicationproblem,identify(i.e.,eyegaze)thecorrectarray.
Ex. Useskip counting on anumberline to solvemultiplicationproblems
(e.g.,movetwodigitsfive times fortheproblem2x 5).
Studentswill:
EE4.OA.1-2.Demonstratethe connectionbetweenrepeatedadditionand multiplication.
Ex.Skipcountbytwo,five, and10tosolve multiplicationproblems.
Ex. Using threegroupsof two objects,communicatethat 2+2+2isequal to3x 2.
Ex.Using plasticeggsandaneggcartontohold theeggsinplace,place an objectineachegg to illustrate6+6=12or6x 2= 12.
Ex.Representthechairsinaclass withthreerowsof fourchairs ineach
(e.g.,identify4 +4+4).
Studentswill:
EE4.OA.1-2.Demonstraterepeatedaddition tosums of10. Ex. Skipcountby twoandfiveto 10.
Ex. Add1+1+1. Ex. Add2+2+2. Ex. Add3+3+3.
Ex. Add2+2+2+2+2to equal10.
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Ex. Presentedwithapicture of two chairsinarowandgivenfour pictures ofindividualchairs,arrangetheadditionalfourchairsintoequalrowsand countallof the chairs.
4.OA.3.Solvemultistep word problemsposedwith whole numbers andhaving whole-numberanswers usingthefouroperations, includingproblemsin
whichremaindersmustbe interpreted.Represent theseproblemsusing equationswithaletter standingfortheunknown quantity. Assessthe reasonablenessofanswers usingmental computation andestimation strategies including rounding.
EE4.OA.3.Solve one-step real-world problems using addition or subtraction within 100.
Studentswill:
EE4.OA.1-2.Makeasetof10 and countto10. Ex. Usingfingerscount to 10.
Ex.Usinga10frame,placeacubeineachsquare. Ex. Usea switch to countto10.
Ex. Countlike objectstomakeasetof10.
Studentswill:
EE4.OA.3.Solve two-stepproblemsusing additionorsubtractionwhena number in theproblemis unknown (result,start,change,difference).
Ex.Useanumber linetosolvetwo-stepproblems.
Ex. Useahundredscharttosolve a two-stepproblem.
Ex.Solveatwo-stepwordprobleminvolvingaddition(e.g.,“IfAmyhas10 sheetsof paperandyouhave10 more sheetsthan Amy,how manysheets doyouhave?”[addition–comparetotalunknown]).
Ex.Solveatwo-stepwordprobleminvolvingsubtractions (e.g.,“Sandihas
10 catsand20 dogs –doesshehavemorecats ordogs? Howmany more?”[subtraction– comparedifferenceunknown]).
Studentswill:
EE4.OA.3.Solveone-stepproblemsusing additionorsubtraction. Ex. Usemanipulativestoaddor subtracttwogroups.
Ex. Usemanipulatives on anumber linetosolveaddition or subtraction
problems.
Ex.Solveone-stepwordproblem involvingaddition(e.g.,“If Samgave away10 applesandhasfive apples left,howmanydidhestartwith?” [addition–startunknown]).
Ex.Solveone-stepwordproblem involvingsubtractions(e.g.,“If Junehad
50 dollars and spentten,how muchdoesshehave left?” [subtraction–
classictakeaway]).
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Ex. Solveone-stepwordprobleminvolving addition(e.g.,“If Jessiehad20 cakesandbought five more,how manydoeshehavenow?” [additionjoin- part/part– whole]).
Ex.Solveone-stepwordproblem involvingsubtractions(e.g.,“If Sandy wantedto collect35cardsandshe alreadyhas15,how many moredoes sheneed?”[subtractiondeficitmissingamount]).
Studentswill:
EE4.OA.3.Solveone-stepaddition orsubtractionproblemswhenthereis anunknown(result,start,change,difference)up to10.
Ex. Givenagroup of fiveitems,determinehow manymoreareneededto make10.
Ex. Givenagroupofeightitems,determinehowmanyto takeawayto makefive.
Gainfamiliaritywith factors andmultiples.
4.OA.4.Findallfactorpairs for awholenumberin the range1–100.Recognize thatawholenumberis a multipleofeachofits factors.Determine
whetheragiven whole number in therange1–100 isamultiple ofagivenone- digitnumber.Determine whetheragiven whole
EE4.OA.4.Showoneway toarriveatproduct.
Studentswill:
EE4.OA.3.Addup tofive.
Ex.Givenagroupof two,addobjectstoatotaloffive. Ex. Givenagroup of three,addobjectstoatotaloffive.
Studentswill:
EE4.OA.4.Showmultiplewaysto arrive atthesameproduct.
Ex. Givenaproduct,usemanipulativesto creategroupsthatrepresentthe product.
Ex. Givenanumber(product) of the day,matchtheirfactorcardsto anotherstudent’sfactorcardtoequaltheproduct.
Ex. Givenan equationon adryeraseboard(e.g.,2x 4=8),makeequal groupstoshowpossiblefactorsforeight(e.g., onegroupofeight,two groupsof four,fourgroupsof two).
Studentswill:
EE4.OA.4.Show onewaytoarriveata product.
Ex. Usingagroupof manipulatives,separateintoequalgroups.
AKGrade-LevelClustersAK-DLM
EssentialElements
number in therange1–100 isprimeorcomposite.
InstructionalExamples
Ex. Providedwith counters,piecesof string, oryarn anda workmap,make equalsetstoarriveatthe product.
Ex. Giveneightobjects thatrepresenttheproduct, makeequalsets to representthefactors(e.g.,2+2+ 2+ 2) and counttoarriveatthe product (e.g.,8).
Studentswill:
EE4.OA.4.Makeequalsets andcount todeterminetheproduct.
Ex.Usingtwospinners, spinfirst spinnertodeterminethenumber of groupsandthesecond spinnertodeterminehow manyineachgroup. Supplythenumbersfromthespinnersasfactorsinthemultiplication
equation(e.g., x =).
Generateandanalyze patterns.
4.OA.5.Generatea numberor shapepattern thatfollowsagivenrule. Identifyapparent features ofthepatternthat were not explicitin therule itself.For example, given the rule“Add3” and the startingnumber1, generatetermsin the resultingsequenceand observethat theterms appearto alternate
EE4.OA.5.Userepeating patternstomake predictions.
Studentswill:
EE4.OA.4.Replicateonewaytoarriveataproduct.
Ex. Copy ateacher-createdmodelusingmanipulatives. Ex. Givenaset,replicatetheequalset.
Studentswill:
EE4.OA.5.Createapatternbasedon agivenruleandtheirpredictionof whatcomesnext.
Ex. Givenan AABCAABCrule,createapatternbasedon therule.
Ex. Givenadiewithplustwo,orplusthree,rollsthedieand createsa numberpattern basedontheoutcome.
Studentswill:
EE4.OA.5.Userepeatingpatternstomakepredictions.
Ex.Usinganumberline,predict what thenext numberwillbe whenyou applytherule “add2.”
Ex.Usingashapepattern(e.g.,squares,circles,triangles)predict whatwill comenextin the seriesofthreeshapes.
Ex.GivenasimpleABCABCpattern,indicate,“Whatcomesnext?”
Studentswill:
AKGrade-LevelClustersAK-DLM
EssentialElements
betweenodd and even numbers.Explain informally whythe numberswillcontinueto alternate in this way.
InstructionalExamples
EE4.OA.5.Replicateapattern.
Ex. Using woodenbeads,copyapattern. Ex.Rhythmicor tactilepatterns.
Studentswill:
EE4.OA.5.Differentiatebetweenapattern and anon-pattern. Ex. A pileof blocks vs.an ABABpattern of blocks.
Ex. Playlisteninggameto determinerhythmicpatternsversusnon- patterns.
FourthGradeMathematicsStandards:NumbersandOperationsin BaseTen
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Studentswill:
EE4.NBT.1.Comparenumberstoeachotherbasedon placevalue groups by composinganddecomposinggreaterthan50.
Ex. Givenanumberover50,useplacevalueblocks toindicatethevalue of eachdigit.
Ex. UsingPopsiclestickswith beans gluedtothemingroupsof10 and loosebeans,illustrateamulti-digit number.
Ex. Show anumberon thenumberlineandanswerthenumberof tens andonesinthegiven number.
Ex.Decomposenumbersto50inmultipleways(e.g.,36isthree10sand
six ones,ortwo10sand16 ones,or36 ones).
Studentswill:
EE4.NBT.1.Comparenumberstoeachotherbasedon placevalue groups by composinganddecomposingto50.
Ex. Givenatwo digitnumberupto50,useplacevalueblocks to indicate thetensvalueand theonesvalue.
Ex. Usemoney(dimesandpennies)torepresentplacevalue.
Ex. Decomposenumbersto50(e.g., 15 isone10andfiveones,22istwo
10sandtwo ones,36 isthree10s and six ones,41is four10sand aone,57 is five10s and sevenones).
Ex.Decomposenumbersinone way(e.g. 36isthreesetsof10 andsix ones).
Studentswill:
EE4.NBT.1.Compose anddecomposewhole numbersto20.
Ex. Given 15 pennies, createagroupofone10andagroup of fiveones. Ex. Useanumberbalance todeterminewhattwonumbersareneededto equalthenumberon theotherside.
Studentswill:
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
EE4.NBT.1.Identifywhole numbersto10. Ex. Givensets, pair withnumbers.
Ex.Givennumbers,matchtosets.
4.NBT.2.Read andwrite
EE4.NBT.2.Compare wholeStudentswill:
multi-digit wholenumbers usingbase-tennumerals, numbernames,and expandedform.Compare twomulti-digitnumbers based on meaningsofthe digitsineachplace, using
>,=,and <symbolsto
recordtheresultsof comparisons.
Numbers to 10 using symbols
(<,>, =).
EE4.NBT.2.Compare whole numbersusingsymbols(<, >,=).
Ex. Utilizeanumberlineto comparetwonumbersgreaterthan50and placeacard withthecorrectsymbol ontheline toshowtherelationship (<, >).
Ex.DuringP.E.,comparescoresof agametodeterminethe winner.Use
thesymboltoshowtherelationship betweenthescores.
Ex.Stateormatch meaningof>,<,and =asgreaterthan,lessthan, or equalto.
Studentswill:
EE4.NBT.2.Compare whole numbers(<,>,=).
Ex. Giventwogroupsof blocks, close orequalin value,determinewhich is greater,less,or equal.
Ex. Usingafloor numberline,twostudentsstandontwodifferent numbers and determinewhichis greateror less than.
Studentswill:
EE4.NBT.2.Compare whole numbers (<,, =)from0-20.
Ex. Giventwogroupsof objects,sevenblocks and10blocks, determine whichisgreateror whichisless.
Ex.Playafishgame:Onefishandtwoponds,each withacertainnumber of bugs,turnfish towardsthepond with the mostbugs.
Studentswill:
EE4.NBT.2.Compare whole numbers (<,) from0-10.
Ex.Usea10framewithtwotactiledotsand a10framewith 10 tactile dots,determinewhichismoreor less.
Ex. Giventwosetsof objects,determinewhich ismore.
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
4.NBT.3.Useplacevalue
EE4.NBT.3.Round any Studentswill:
understandingto round multi-digit wholenumbers toanyplace.
Use placevalue understandingand propertiesofoperations to performmulti-digit arithmetic.
4.NBT.4.Fluently add and
whole number 0-30 to the nearest ten.
EE4.NBT4. Addand subtractdouble-digit whole numbers.
EE4.NBT.3.Roundone- andtwo-digitnumbers,greaterthan50,to the nearest10.
Ex. Roll thedice tocountup the rounding tapeandstatethenearest10. Ex. Usingahundreds chart and agivennumberbetween50-100,roundto thenearesttens place.
Studentswill:
EE4.NBT.3.Roundsingleone-andtwo-digit wholenumbersfrom0-50to thenearest10.
Ex. Posterboards,distributedaroundtheroom,labeledbytens up to50,
be givenanumber,andasked togotothenearest10. Ex.Usingpenniesearned,exchangefor dimes.
Studentswill:
EE4.NBT.3.Round singleone-digitnumberstothenearest10.
Ex. Usingpaperplateslabeled zeroand 10,givenacardwitha number zeroto10,placeit on the correctplate.
Ex. Useanumber linetoroundtothenearest10.
Studentswill:
EE4.NBT.3.Identifynumbersthat aremoreorless than fiveona number line.
Ex. Placetheirfingers on fiveona numberlineandcounttofindanumber greaterthan five.
Ex.Shownfiveona numberline,identifyanumber thatislessthanfive.
Studentswill:
EE4.NBT.4.Addand subtractmulti-digitwholenumbers.
Ex. Givenbasetenpieces,makeexchangesto solve multi-digitaddition andsubtractionproblems.
Ex.Useacalculator and show howtheproblemissolved.
Studentswill:
AKGrade-LevelClustersAK-DLM
EssentialElements
subtract multi-digit whole numbersusingthe standardalgorithm.
InstructionalExamples
EE4.NBT.4.Addand subtractdouble-digit wholenumbers.
Ex. Useasortingboxdivided intotwosectionswith manipulativestoadd, subtract, and regrouptosolve additionand subtractionproblems.
Ex. Usebreak-apartnumbers (e.g.,20 +30=50,3+5=8, 40 + 8=48). Ex. Useanumber linetodemonstrateadditionbytens.
Studentswill:
EE4.NBT.4.Solveadditionwithnumbers20-50andsubtractionproblems with numbers0-20.
Ex. Use counterstoaddandsubtract.
Ex. Usenumberlinestoaddor subtract. Ex. Produceaddendsto10 fluently.
Ex.Theteacherorally states 14 –1=13 andusemagneticsymbolsto displaytheproblem.
Studentswill:
EE4.NBT.4.Solvesingle digit addition problemstoaddonetoanother number.
Ex .Use counterstoaddonetoanother number.
Ex .Usenumberlinestoaddone to anothernumber.
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
FourthGradeMathematicsStandards:Numberand Operations—Fractions14
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Extendunderstandingof fractionequivalenceand ordering.
4.NF.1.Explainwhya fractiona/b isequivalent toafraction(n ×a)/(n ×b) by usingvisualfraction models,withattentionto how thenumberandsize ofthepartsdiffereven thoughthetwofractions themselvesarethesame size. Usethisprincipleto recognizeandgenerate equivalent fractions.
4.NF.2.Comparetwo fractionswithdifferent numeratorsanddifferent denominators,e.g., by creatingcommon denominatorsor numerators,orby comparingtoabenchmark fractionsuchas1/2. Recognizethat
EE4.NF.1-2.Identify models of one half (1/2) and one fourth (1/4).
Studentswill:
EE4.NF.1-2.Understandtwofractionshavingunlike denominatorsare equivalent if theyrepresentthe samesizeportionofawhole.
Ex. Giventwosquares of paper,onescoredforhalvesandonescoredfor eighths, fold the eachpaperasscored,thenunfoldthepaper scoredfor thirds andcompareto the onefoldedinto 1/2to findthesamesize portion (e.g.,4/8=1/2).
Ex.Usetangrams.
Studentswill:
EE4.NF.1-2.Understand2/4=1/2.
Ex. Giventworectangles,cutone rectangleinto halfand a second into fourthsandcomparetherectanglestodeterminehow manyfourths equal ahalf.
Ex.Workingwithtwo rectanglesof thesamesize,foldone rectanglein halfand theotherin fourths and comparetofind how manyfourthsequal half.
Ex. Usingapictureof two circles,cut onein halfandtheotherin fourths
andcomparethemtofindhowmanyfourths equalhalf.
Studentswill:
14Grade4expectationsinthisdomainarelimitedtofractionswithdenominators2,3,4,5,6,8,10,12,100.
comparisonsarevalidonly whenthetwofractions referto the samewhole. Recordtheresults of comparisonswithsymbols
>,=,or<,andjustify the conclusions,e.g., byusing a visualfractionmodel.
Buildfractionsfromunit fractionsbyapplyingand extendingprevious understandingsof operationsonwhole numbers.
4.NF.3.Understanda fractiona/b witha 1 asa sumoffractions 1/b.
ƒUnderstand addition
andsubtractionof fractionsasjoining and separatingparts referringtothe same whole.
ƒDecomposeafraction
intoasumof fractions withthesame denominatorinmore thanoneway, recordingeach decompositionby an equation. Justify decompositions, e.g.,
EE4.NF.3.Differentiate betweenwholeand half.
EE4.NF.1-2.Understand4/4or 2/2=1.
Ex. Complete two-and four-piecepuzzles.
Ex.Filefoldergamewithself-stickingnon-adhesivepiecesthatmakea whole.
Studentswill:
EE4.NF.1-2.Understandthat twohalvesis equivalenttoonewhole.
Ex. Woodenshapesareseparatedintohalvesand putbacktogetherintoa whole.
Ex. Plastic eggs arebrokenintohalvesand putbacktowhole.
Studentswill:
EE4.NF.3.Differentiatefractionalparts lessthan1/4.
Ex. Withfractionbarslabeled1/2,comparethe1/2 tofractionbars less than.
Ex. Usingsquares,folditin1/2,1/4,1/8, . . .
Studentswill:
EE4.NF.3.Differentiatebetweenwhole,half,andfourth.
Ex. Usefraction stripsandfractiontilestoidentifywhole andhalf,and whichismore.
Ex. Usingsquares of paper, folditin 1/2and1/4andidentifytheparts.
Studentswill:
EE4.NF.3.Differentiatebetweenwholeandhalf.
Ex. Givenawholesandwichversusahalfsandwichcut horizontally, vertically,anddiagonally selectthewholeorhalf upon request.
Ex.Show thehalfwaypointonanumber line.
Ex. Withpicturescut intohalvesand picturesnotcut, sortthepicturesinto halvesandwholes.
Studentswill:
EE4.NF.3.Recognizethatfractionsarepartofawhole.
Ex. Usingaself-stickingnon-adhesiveshape,takeapartandput together fractionalpartsof awhole.
Ex. Utilize wooden shapes,separateintohalvesandputbacktogetherinto
by usingavisual fractionmodel. Examples:3/8=1/8+
1/8+1/8;3/8=1/8+
2/8;21/8=1+1+1/8
=8/8+8/8+1/8.
ƒAddandsubtractmixed
numberswithlike denominators,e.g., by replacingeachmixed number withan equivalent fraction, and/orby using propertiesof operationsandthe relationshipbetween additionand subtraction.
ƒSolvewordproblems
involvingadditionand subtraction of fractions referringtothe same wholeandhavinglike denominators,e.g., by usingvisual fraction models and equations to representthe problem.
whole.
Ex. Shownpictures of thewholeclass andpartof theclass,selectthe picture thatshowspartofthe classupon request.
FourthGradeMathematicsStandards:MeasurementandData
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Solveproblemsinvolving measurementand conversionof measurementsfroma larger unitto asmaller unit.
4.MD.1.Knowrelative
sizes ofmeasurementunits withinonesystemofunits includingkm,m,cm;kg,g; lb,oz.;l,ml;hr,min,sec. Withinasingle systemof measurement,express measurementsinalarger unitintermsofasmaller unit.Recordmeasurement equivalentsinatwo- column table. For example, knowthat1ft.is12times as long as 1in. Expressthe length ofa 4-ft.snakeas
48 in. Generatea conversiontable forfeet and inches listingthe numberpairs(1,12),(2,
24),(3, 36),. . .
EE4.MD.1.Identifythe smallermeasurementunitthatcomprises a larger unit within a measurement system (inches/foot, centimeter/meter, minutes/hour.)
Studentswill:
EE4.MD.1.Solveproblemsby demonstratingwhole unitscanbebroken intosmaller units.
Ex. Useaone-cupmeasuretopour waterintoapintjartodeterminehow manyplantscouldbewateredif eachplantneedsone cupof water.
Ex. Poursoilfroma1/2-cup measuringcupintoapint toseehow many starterpotscouldbefilledwithapintofsoil.
Ex.Determinewhichisbetterfor measuringadesktop,aruler ora yardstick.Measurethetablet,markthelength ontheruler,andcompare ittotheyardstick.
Ex. Pourtablespoonsofwaterintoa1/2 cupatablespoonatatimeand
determinehowmanyone-tablespoonportionsthereareinacup.
Studentswill:
EE4.MD.1.Identifythesmallermeasurementunits thatdivide alargerunit withinameasurementsystem.
Ex. Identifyhow manyinchesarethe smallerunits onaruler. Ex.Identifyhow manyfeetarethesmallerunitsonayardstick.
Ex. Identifyhow manycups arethe smallerunitsonapintmeasuringcup. Ex.Givenseveralmeasurementtools,matchthreerulerstoone-yard stick.
Studentswill:
EE4.MD.1.Identifystandardunitsofmeasurements.
Ex.Usedifferentmeasurementtoolstomeasuresandinatray.Ex. Usethe inchwormsonafootruleror yardstickto makethe connectionthat whiletheybothmeasure,oneunitis smallerthan the other.
Studentswill:
EE4.MD.1.Usemeasurementtools.
Ex. Comparethe lengthofarulertothelength ofabook.
Ex. Usea balance scaletocomparedifferent setsofobjectsto determine
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
whichobjectsare<,>,or=.
4.MD.2.Usethefour operationstosolve word problemsinvolving distances,intervalsof time, liquidvolumes,massesof objects,andmoney, includingproblems involvingsimplefractions
ordecimals,andproblems
that requireexpressing measurementsgivenina largerunit intermsofa smallerunit.Represent measurementquantities usingdiagramssuch as number linediagramsthat featurea measurement scale.
EE4.MD.2.a.Telltimeto thehalf hourusing adigital clock,or to thehour using ananalogclock.
EE4.MD.2.b.Measure mass or volume using standard tools.
Studentswill:
EE4.MD.2.a.Telltimetothequarterhourusing adigitalor analogclock. Ex. Indicatetimetothequarterhouron adigital clock.
Ex. Placeclockhandstoshow thequarterhour.
Studentswill:
EE4.MD.2.a.Telltimetothehalf hourusing adigitalclockorto thehour using ananalog clock.
Ex.Identifywhichclockshowsastatedtimeonadigitalclock(e.g., 2:30). Ex. Movehandsonaclock toshow astatedhalf hour.
Ex.Saythehouron an analogclock.
Studentswill:
EE4.MD.2.a.Relatetimetothehourtoactivities. Ex. Look at clock-2:00istimetogohome.
Ex. Identifyactivityonscheduleby matchingthehouron the scheduleto thehourontheclock.
Ex. Pointtohour fornextactivityonpersonalschedule.
Studentswill:
EE4.MD.2.a.Differentiateadigitalandanalog clockfromother measurementtools asatoolfortellingtime.
Ex.Givenadigitaloranalogclock andaruler,identifytheclock fortelling time.
Ex. Asked“How do we know whenit is timetogo tolunch?”, indicate a clock.
Studentswill:
EE4.MD.2.b.Usetheappropriate measurementtools tosolveproblems. Ex. Selectand usethe appropriatemeasuringtooltomeasuredifferent quantitiesforassignedtasks (e.g.,cup forliquidandpowder;scalefor solids).
AKGrade-LevelClustersAK-DLM
EssentialElements
EE4.MD.2.c.Use standard measurementto compare lengths ofobjects.
InstructionalExamples
Ex.Onafieldtrip tothegrocerystore, usethescale to determinehow muchabagof apples weighs.
Studentswill:
EE4.MD.2.b.Selectthe appropriate measurementtoolfromtworelated optionstosolveproblems.
Ex. Duringascience experiment,selectthebesttool touseto measure variousingredients(e.g.,tablespoonorcup, ruleroryardstick).
Ex. Givenabook,selectthe appropriate measuringtoolto useto measure itslength (e.g.,ruleror yardstick).
Studentswill:
EE4.MD.2.b.Selectthe appropriate measurementtoolfromtwounrelated optionstosolveproblems.
Ex. Given optionsof unrelatedmeasuringtools, choosethebesttoolfora particulartask (e.g.,“When makingcookies,which would youuseto measureflour, acup orruler?”).
Ex.Inafieldtrip tothe grocerystore, show whichmeasuringtoolshould beusedto weighabag ofapples. Allowstudentstopracticeby choosing otherfruits orvegetablestoweigh.
Studentswill:
EE4.MD.2.b.Identifymeasurementtools.
Ex. Sortnon-standardandstandardmeasurementtoolsinto twodifferent groups.
Ex. Usingpicturesof standardandnon-standardtools, identifywhichcan
beused tomeasuredifferentitems.
Studentswill:
EE4.MD.2.c.Usestandard measurementsto comparelengthofobjects andindicatehow manyeach is bystandard measures.
Ex. Givenapencilandbook,markthe lengthofeach on arulertotell whichis longer and approximatelyhow manyeachisby inches.
Ex.Givenatapemeasure,markthelength of a bookcaseand theteacher’s
AKGrade-LevelClustersAK-DLM
EssentialElements
EE4.MD.2.d.Identify objectsthathave volume.
InstructionalExamples
deskon thetape measuretoshow whichis longerand approximatelyhow manyeachis byfeet.
Studentswill:
EE4.MD.2.c.Usestandard measurementto comparelengths ofobjects. Ex. Givenapencilandbook,markthe lengthofeach on arulertotell whichislonger.
Ex.Givenatapemeasure,markthelength of a bookcaseand theteacher’s deskon thetape measuretoshow whichislonger.
Studentswill:
EE4.MD.2.c.Measurelengthof objectsusingstandardtools, such as rulers,yardsticks,andmetersticks.
Ex. Givenan objectandameasuringtool,usethetooltomarkthelength oftheobject.
Ex. Givenarulerandsandinabucket,markthedepthof thesandona
ruler.
Ex. Givenayardstick,measuredifferentlengths or widthsoftheroomand recordthe lengthon theyardstickinnumberof yardsticks.
Studentswill:
EE4.MD.2.c.Identifyitemsas long orshort.
Ex. Giventwodifferentitems,onemuchlongerthanthefirst,indicate long/short.
Ex.Aftertravelingtosomewherein theclassroomandsomewhereoutside ofroom,indicateeachdistance aslongorshort.
Studentswill:
EE4.MD.2.d.Determinevolumeofacubeby countingunitsof measure. Ex. Use cubestofillabox (small number,how many)and countthe numberofcubesneededtofillthebox.
Ex.Useliquidtofillbowl(how much,onecup,etc.).
Studentswill:
AKGrade-LevelClustersAK-DLM
EssentialElements
EE4.MD.2.e.Identifycoins (penny,nickel,dime, quarter)andtheirvalues.
InstructionalExamples
EE4.MD.2.d.Identifyobjectsthathavevolume.
Ex. Givenagroup of pictures(cup,rock,fork),choose whichonecanbe filled.
Ex.Identifyobjectsinthe room thatcanbefilled(cup,fish tank,etc.). Ex. Givenasquareanda cube,indicate cube.
Studentswill:
EE4.MD.2.d.Demonstratesolidorfull,emptyandpartfull.
Ex. Givenapieceof paperandacube,indicate,“Which onetakesupmore space?”
Ex.Fillacuphalffullfromthe waterfountain.
Ex.Asthe teacherisfilling acup,saystopwhenitishalf full.
Studentswill:
EE4.MD.2.d.Identifyvocabularyrelatedtovolume(full,empty). Ex. Matchpictureof unopenedbottleof soda to“full.”
Ex.Identifyan“empty”cup.
Ex.Indicate whichisfulland/or whichis emptywhenholding/feelingafull can of sodaandanemptycanofsoda.
Studentswill:
EE4.MD.2.e.Identifyrelativevalueof differentcollectionsof coins.
Ex. Whenasked whatisworthfivecents,chooseanickel.Whenasked whatisworth25cents,chooseaquarter.
Ex. Giventwocoins,identifythevalueofeachand indicatewhichismore. Ex. Given 14 pennies and twodimes, indicate whichsetis worthmore.
Studentswill:
EE4.MD.2.e.Identifycoins (penny,nickel,dime,quarter)andtheirvalues. Ex. Giventwocoins,choose correctcoin bynameand value.
Ex.Shownacoin,namescoin.
Ex. Show relativevaluesofpenny,nickel,dime,quarterbyarrangingthem in orderfromleasttomost.
AKGrade-LevelClustersAK-DLM
EssentialElements
Studentswill:
InstructionalExamples
EE4.MD.2.e.Matchcoinsthatarealike(penny,nickel,dime,quarter). Ex. Givenagroup ofcoins,matchcoinsthatare alike.
Ex. Givenapictureofaquarter,choose a quarterfromagroupof coins.
4.MD.3.Apply theareaandEE4.MD.3.Determine
Studentswill:
EE4.MD.2.e.Selectobjectsthatareusedfor money.
Ex. Giventhreepictures(twonon-coinsandone coin),identifywhich one isacoin.
Ex. Giventwochoices,identifywhich one is a coin.
perimeterformulasfor rectanglesinreal-world andmathematical problems.For example, find the width ofa
rectangularroom giventhe areaofthe flooring and the length,by viewingthe area formula as a multiplication equation with an unknown factor.
Representandinterpret data.
4.MD.4.Makealineplot to display adata set of measurementsinfractions ofa unit(1/2,1/4, 1/8). Solveproblemsinvolving additionandsubtractionof fractionsbyusing
the area of a square or rectangle by counting units of measure (unit squares).
EE4.MD.4.a.Represent data on a picture or bar graph given a model and a graph to complete.
Studentswill:
EE4.MD.4.a.Insertdataintoagraphtorepresentadata set withascale equalto10(0to10by ones).
Ex. Usingabar graph,enterone unitforeachstudenttoshow their favoriteactivityin thecorrectcategory(lunch,physical therapy,music, P.E.)todeterminemostpopularand least popular.
Ex. Goto the lostand found,categorizeandcounttypesof itemsand graphthemtodeterminemostandleast.
Studentswill:
AKGrade-LevelClustersAK-DLM
EssentialElements
informationpresentedin lineplots.For example, froma lineplotfind and interpretthedifferencein length betweenthe longest and shortestspecimens in aninsectcollection.
EE4.MD.4.b.Interpretdata fromavarietyofgraphsto answer questions.
InstructionalExamples
EE4.MD.4.a.Insertdataintoapreconstructedbargraphtemplate.
Ex. Clean outdesks; sortobjectsfoundintoreusable,recyclable,reducible, ortake-homeitems;andgraph resultswithone bar foreach–reuse, recycle,reduce,ortakehome.
Ex. Givenapreconstructedbargraphanddata,enterthedataonthebar graphby shadingoneunitof thebarfor eachpieceof data.
Studentswill:
EE4.MD.4.a.Identifyanappropriatescalefor thedataset.
Ex. Identifyifit is appropriatetousedegreesorouncesona weather graph.
Ex.Determineif it isappropriatetouseinchesorpoundsonaheight graph.
Studentswill:
EE4.MD.4.a.Givenatopic,identifyappropriatedatatocollect.
Ex. Usingaweathergraph,identify appropriatedata giventhechoice betweenapictureof thesun andapictureof ashoe.
Ex. Giventhetopic ofsnacks,determinewhetherjelly beansorbooks are appropriateforthegraph.
Studentswill:
EE4.MD.4.b.Createtheirownquestionsthatcanbe answeredbythedata onapictureandbargraph.
Ex. Cutsimple graphsfromnewspapers/magazinesandgluethemonto cardstock,createquestions/answersbased on thegraph.
Ex.Createtheirownquestions/answersbased on theinformationfroma graphshowingclasspreferencesbetweentwodifferentactivities.
Studentswill:
EE4.MD.4.b.Interpretdata fromavarietyofgraphstoanswerquestions. Ex. Answerquestionsbasedoninformationprovidedinapictureschedule. Ex. Tellhowmanysunnydaystherewereinamonth,basedonaweather graph.
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Studentswill:
EE4.MD.4.b.Makeobservationalstatementsaboutdatainapictureand bargraph.
Ex.Tellyou whatthey observeon agraphofstudents’eyecolors.
Ex. Show studentsagraph oftheBig12football teamsandaskthemwhat theythinkit is about.
Geometricmeasurement:
EE4.MD.5.Recognize
Studentswill:
EE4.MD.4.b.Demonstrateawarenessthatsymbolsmaybeused to representobjects and events.
Ex. Understand thatapictureof icecreamrepresentsafavorite flavor. Ex. Understand thatapictureof snow representsasnowyday.
Studentswill:
understandconceptsof angleandmeasure angles.
4.MD.5.Recognizeangles asgeometricshapesthat are formedwherevertwo raysshareacommon endpoint, and understand conceptsof angle measurement:
ƒAnangleismeasured
with referencetoa circlewithitscenterat thecommonendpoint oftherays,by consideringthefraction ofthecirculararc betweenthepoints wherethetworays
anglesingeometricshapes.EE4.MD.5.Labeldifferenttypesofanglesingeometricshapes.
Ex. Constructgeometricshapesusingcountingsticks.Thendetermine whetherangles arerightangles ornot.
Ex. Givenasquare,determinewhethertheanglesarerightanglesornot andstateasquarehasfourangles.
Studentswill:
EE4.MD.5.Recognizeanglesingeometricshapes.
Ex.Drawan arcto identifytheanglesafterteacherdrawsageometric shapeon awhiteboard.
Ex. Givenpicturesof differentgeometricshapesandanglesthatmatchthe shapes,overlayshapeswithmatchingangles.
Studentswill:
EE4.MD.5.Identifyanangle.
Ex. Wipe awaytheshapethatdoesnot containan angle whenteacher drawsashapewithanangle and acircle.
Ex.Identifyasmanyanglesastheycanseeorfeelontheplayground.
Ex.Givenan angle template,holdit to shapesin theclassroomandtellifit
AKGrade-LevelClustersAK-DLM
EssentialElements
intersectthecircle.An
matches.
InstructionalExamples
anglethatturns through 1/360of a circleiscalleda“one- degreeangle,” andcan beusedtomeasure angles.
ƒAnanglethatturns
through n one-degree anglesissaid tohave anangle measureof n degrees.
4.MD.6.Measureanglesin whole-numberdegrees usingaprotractor.Sketch anglesofspecified measure.
EE4.MD.6.Identifyangles aslargerand smaller.
Ex. Givenasetof fourshapes(onewithangles andthreewithnoangles), indicatethe shapewithangles.
Studentswill:
EE4.MD.5.Identifyshapesthat contain angles.
Ex. Givenasquareanda circle,identifythe square.
Ex.Findan objectthat isshapedlike asquarein theclassroom.
Studentswill:
EE4.MD.6.Constructanglesofvarioussizes. Ex. Constructrightandacute angles.
Ex.Replicateanglesfromgeometricshapes containingrightand acute angles.
Studentswill:
EE4.MD.6.Identifyanglesaslargerandsmaller.
Edž͘'ŝǀĞŶ ĂŶ ĂŶŐůĞƐŚĂĚĞĚ ƚŽ ůĞƐƐƚŚĂŶϰϱ϶ĂŶĚ ŽŶĞƐŚĂĚĞĚƚŽ ŵŽƌĞƚŚĂŶ
ϭϮϬ϶͕ŝŶĚŝĐĂƚĞ ͞tŚŝĐŚŝƐůĂƌŐĞƌ͍͟
Ex. Giventwofractionpuzzlespieces,one containing asignificantlylarger anglethan theother,indicate“Whichissmaller?”
Studentswill:
EE4.MD.6.Differentiateanglesinshapes.
Ex. Givenan angleandacircle,indicates“Whichis anangle?” Ex. Givenaballand acube, indicate “Which hasan angle?”
Studentswill:
EE4.MD.6.Replicateanangle.
Ex.Usepopsiclestickstoreplicateagivenangle. Ex. Bendapipe cleanerto replicateagivenangle.
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
FourthGradeMathematicsStandards:Geometry
AKGrade-LevelClustersAK-DLM
EssentialElements
InstructionalExamples
Draw andidentifylines andangles,andclassify shapesbypropertiesof theirlinesandangles.
4.G.1.Drawpoints,lines, linesegments,rays,angles (right,acute,obtuse),and perpendicularand parallel lines.Identifytheseintwo- dimensionalfigures.
4.G.2.Classifytwo- dimensionalfiguresbased
EE4.G.1.Recognize parallel lines and intersecting lines.
EE4.G.2.Describe the defining
Studentswill:
EE4.G.1.Createarepresentationof parallelandintersectinglines. Ex.UsingPopsiclesticks,createparallelandintersectinglines.
Ex.Play“SimonSays”toillustrateparallelandintersectinglineswitharm movements(oreyegazeapictureof students makingthecorrect movements).
Studentswill:
EE4.G.1.Distinguishbetweenparalleland intersectinglines.
Ex.Usingaroadmaprug,traceovertheparallellinesandthentraceover theintersectinglines.
Ex. Usingamap of theschoolon aninteractivewhiteboard,tracethe classroomsthatareinaparallellineandthehallwaysthat intersect. Ex. Findparallel linesinshapes.
Studentswill:
EE4.G.1.Identifyan intersectingline.
Ex.Usesidewalk chalk todrawanintersectingline.
Ex. Goon an environmenthuntand identifyintersectinglines. Ex. Traceintersectinglines(e.g.,roadsorhallways)onamap.
Studentswill:
EE4.G.1.Identifyaline.
Ex. Using yarn,stretchandgluealineon paper. Ex.Drawaline whendirected.
Ex. Walkonalinetapedtothefloorwhendirected. Ex.Givenalineandacircle,indicate whichistheline.
Studentswill:
EE4.G.2.Classifyshapesaccordingtoattributes.