Download - : Math Grade : 3 Grade : Week 1 - Upi Elementary …upielementaryschool.weebly.com/.../math_lp_3rd_qtr.pdfGuam District Level Lesson Plan Quarter _3_ Content: Math Grade/Course: 3rd

GuamDistrictLevelLessonPlan

Quarter_3_

Content:Math Grade/Course:3rdGrade Timeline:Week1Standard(s):3.OA.2Interpretwhole-numberquotientsofwholenumbers,e.g.,interpret56÷8asthenumberofobjectsineachsharewhen56objectsarepartitionedequallyinto8shares,orasanumberofshareswhen56objectsarepartitionedintoequalsharesof8objectseach.Forexample,describeacontextinwhichanumberofsharesoranumberofgroupscanbeexpressedas56÷8.LessonOverview:Students’masteryofthisskillwillincludeanunderstandingoftwotypesofcontextsthatcanberepresentedusingdivision.Oneisthat(forexample)56dividedby8isthenumberofobjectsineachsharewhen56objectsaredividedinto8equalshares.Theotheristhat56dividedby8isthenumberofshareswhen56objectsarepartitionedintosharesof8objectseach.Thesetwotypesofdivisioncontextsareoftendescribedas“partitive”and“quotative”,respectively.Whenconstructingdivisionproblems,teachersoftenleanheavilytowardstheformer;e.g.,“IfIhave15cookiesandwanttodividethemamongfivechildren,howmanycookiescaneachchildhave?”Itisimportantthatteachersalsointroducestudentstotheothertypeofdivisioncontext;e.g.,“IfIhave15cookiesandwanttomakegiftbagsof5cookieseach,howmanygiftbagscanImake?”Studentsshoulddescribeacontextinwhichanumberofsharesoranumberofgroupscanbeexpressedasadivisionstatement.Further,studentswilleventuallymaketheconnectionbetweendivisionandmultiplication.

LessonObjective(s):ICanStatements:

• Icanexplaindivisionasasetofobjectspartitionedintoanequalnumberofshares.

• Icanidentifypartsofdivisionequations(dividend,divisor,andquotient)

• ·Icaninterpretquotientsindivision(32÷4=8canbe4groupswith8itemsineachgroupor8groupswith4items)

Vocabulary:dividend,division,divisor,equalshares,groups,partition,quotient,equation,sharing,unknown/symbol,inverserelationship

FocusQuestion(s):WhatstrategiescanIusetohelpmeunderstandmathematicalproblemsinvolvingdivision?Howdopropertieshelptodivide?Whatistherelationshipbetweenmultiplicationanddivision?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Conceptbuilding:Whatisdivision?ShowtheonlinedemolessononLearnzillion:

https://learnzillion.com/resources/72522-interpret-whole-number-quotients-of-whole-numbers-3-oa-a-2

InstructionandStrategies:

• Startwithareal-worldproblemsuchas:"Ihaveeightkidswhowanttoplayvolleyball.Ineedtwoteamsofequalplayers.Howmanywillbeoneachteam?HowshouldI'divide'themup?"Discusstheproblemwithyourstudents,thenshowthemtheequationontheboardforthisproblem:8/2=4.Youcanalsodrawapictureofsomethingliketwelvecupcakesandfourfriends,andshowhowtheproblem12/4=3cupcakesforeachperson.

• Showthefactfamilytogowiththereal-worldproblemsandequationsyoudiscussedinStep2.Oncetheyunderstandwhatdivisionmeans,youcanshowthemhowtofigureouttheanswerquickly.Forexample,ifstudentsknowthat4x3=12,thentheycanseetherelationshipbetween12/4=3andthemultiplicationproblem.

Givestudentsaproblemsuchas20/4=?,andthenaskstudentstosolvethisproblemtofindthequotient:4x?=20.Explainthatwhatevernumeralreplacesthe?intheequation(inthiscase5)istheanswertothedivisionproblem.

• Discusshowsomedivisionproblemswillnotalwayshaveawholenumberfortheanswer.Forexample,giveyourstudentsarealisticproblemsuchas,"Ihave22cookiesand5cookiescanfitineachbox.HowmanyfullboxeswillIhave,andhowmanyleftovercookies?"Thenshowtheequation22/5=?.Workontheproblemtogetherwithillustrationsorevenmanipulativesuntilstudentsfigureouttheanswer4boxeswith2cookiesleftoveror4R2.Again,makesurestudentsunderstandwhattheRstandsfor(remainder)andwhatremaindermeans.Itisimportantforstudentstomakeconnectionswithmultiplicationandreal-lifeapplicationswhenlearningdivision.

Notes:• Studentsdevelopanunderstandingofthemeaningsofmultiplicationanddivisionofwholenumbersthrough

activitiesandproblemsinvolvingequal-sizedgroups,arrays,andareamodels;multiplicationisfindinganunknownproduct,anddivisionisfindinganunknownfactorinthesesituations.

• Theuseofdrawings,pictures,andmanipulativeobjectswillaidinstudents’understandingofdivisionastheprocessofmakingequalsharesfromawholenumber.

• Commoncontextsshouldbeusedthateasilylendthemselvestowholenumberquotientsthataretypicallypartitionedintoequalshares.Forexample,ifyouarepackagingbottlesofjuiceforaneventinto6-packs,andyouhave42bottles,howmany6-packsdoyouhave?Anotherexample:howmanydozensofeggsaretherein132eggs?132÷12=11.Athirdexample:42÷6=7.49daysishowmanyweeks?49÷7=7.

GuidedPractice:

• Workon3wordproblemswiththestudentsastheysolveontheirpersonalwhiteboards.UseActiveParticipationStrategiestocheckforunderstanding.(Think-Pair-Share,PartnerWork,ThumbsUp-ThumbsDown,etc.)

FormativeAssessment:

• Havethestudentsworkon3wordproblemsattheirdeskswiththeirpartners.

IndependentPractice:• QuickCheck/ExitTicket

Closure:LessonDebrief:Howdoesknowledgeofmultiplicationhelpyoudivide?Accommodations/Modifications:Modelthestepsinasmallgroup.Showthemultiplicationtableforvisualsupport.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,HowardCountyCommonCoreMath,ReadTennessee,3rdGradeMathFlipbookReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week1Standard(s):3.OA.3Usemultiplicationanddivisionwithin100tosolvewordproblemsinsituationsinvolvingequalgroups,arrays,andmeasurementquantities,e.g.,byusingdrawingsandequationswithasymbolfortheunknownnumbertorepresenttheproblem.LessonOverview:Studentswilldrawobjectsinarraysandequalgroupsandwriteequationstosolvedivisionwordproblems.Theywillexplaintheconnectionbetweentheirdrawingandtheequationstothedivisionwordproblems.


• Icanjustifyinwordstherelationshipbetweenadrawingandtheequationthatareusedtosolveadivisionwordproblem.

Vocabulary:partitiondivision,measurementdivision,distribution,division,equalarrays,equalgroups

FocusQuestion(s):Howdoesdrawingapictureandwritinganequationhelpyousolveadivisionwordproblem?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:PlaythevideoofthelessonfromLearnzillionasaspringboard/previewofthelesson:https://learnzillion.com/resources/72645-solve-multiplication-and-division-word-problems-3-oa-a-3InstructionandStrategies:

• Afterplayingthevideo,workaproblemwiththewholeclass,referringtothestrategieslearnedinthevideotohelpvisualizetheproblem.UseThink-Pair-Sharetoaskabouteachsteporstrategythattheylearned.

• Havethestudentswritethe“formula”forvisualizingequalgroups:#ofgroupsx#ineachgroup=totalThisisimportantforthemtounderstandthatbothmultiplicationanddivisionwordproblemsdealwithequalgroups.Thiswillalsohelpthemidentifywhatistheunknownineitheramultiplicationordivisionwordproblem.Moreover,such“formula”willhelpthemunderstandtheinverserelationshipbetweenmultiplicationanddivision.(Conceptbuilding)

GuidedPractice:

• Studentscanbegintopracticesimilarproblemsinpairsusingitems#3–5intheEqualGroupsworksheet.Facilitatetoensurethatstudentsareexplainingtherelationshipbetweentheirdrawingandtheequation.

• StudentswillrecordtheirjustificationontherelationshipbetweentheirdrawingandequationFormativeAssessment:

• Fingers-Upstrategy:Studentswillindicatetheirdegreeofunderstandingbyusinga1,2,3scale.(1:Don’tunderstand,2:Someunderstanding,butneedmoreclarification,and3:Gotit!)Usethisstrategyasyouask

studentsaboutspecificwordproblemsasyouaremovingthroughthislesson.

IndependentPractice:• QuickCheckandHomework

Closure:ApplicationCards—Studentsthinkofawaytoapplytheirnewknowledgeorskillintherealworldandwriteitdownonanindexcard.Collectthecardsandeithersharethemanonymouslywiththeclassorkeepthemtoreviewprivately.

Accommodations/Modifications:Providestudentswithmanipulativestorepresentgroups.Modelhowtousethemanipulativestorepresentgroupsbyseparatingcountersintodifferentnumberofgroupsinvarioussets.Peermodelingwillbeusedtoshowstudentshowtovisualizeandillustratedivisionequationsonpaper.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,learnzillion.com,HowardCountyCommonCoreMath,ReadTennessee,3rdGradeMathFlipbookTeacher-madepracticeworksheet,flowchart,manipulativesReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week2Standard(s):3.OA.4Determinetheunknownwholenumberinadivisionequationrelatingthreewholenumbers.LessonOverview:Asstudentsgainmorepracticeandfluencywithmultiplicationanddivisionproblems,theycanbegintorelatethreewholenumbers.Forexample,determinetheunknownnumberthatmakestheequationtrueineachoftheequations:8x?=48;5=?÷3;6x6=?


• I can determine the unknown number in division problems such as in the following examples: 8 x 9 = ?, 8 x ? = 48, ? x 3 = 27

• I can identify the parts and whole of an equation • I can identify symbols used for missing numbers\

.Vocabulary:equalsign,multiplicationequation,divisionequation,unknownvariable

FocusQuestion(s):Whatmultiplicationordivisionstrategymightapplytoasituation?Howdoyoudeterminethatthestrategyworked?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Teacherremindsstudentsofhowmathproblemscanberepresentedasanumbersentencewherestudentsmustfindthevalueofamissingnumberinthemiddle;forexample,subtractioncanberepresentedasanadditionnumbersentencewithamissingaddend,anddivisioncanberepresentedasamultiplicationnumbersentencewithamissingfactor,buttheconceptcanmanifestitselfinotherproblems,too.

Examples: 8×x=32 17-x=15

InstructionandStrategies:

• OnlineDemoLesson:https://learnzillion.com/resources/72854-determine-unknown-whole-numbers-in-multiplication-or-division-equations-3-oa-a-4

• Aconnectionto3.OA.4ismadetoextendbeyondthetraditionalnotionoffactfamilies,byhavingstudents

exploretheinverserelationshipofmultiplicationanddivision.Studentssolveproblemsanddetermineunknownsinequations.Studentsshouldalsoexperiencecreatingstoryproblemsforgivenequations.Whencraftingstoryproblems,theyshouldcarefullyconsiderthequestion(s)tobeaskedandansweredtowriteanappropriateequation.

• Studentsapplytheirunderstandingofthemeaningoftheequalsignas“thesameas”tointerpretanequationwithanunknown.

Whengiven4x?=40,theymightthink:• 4groupsofsomenumberisthesameas40.• 4timessomenumberisthesameas40.• Iknowthat4groupsof10is40,sotheunknownnumberis10.• Themissingfactoris10because4times10isequalto40.• Equationsintheformofaxb=candc=axbshouldbeusedinterchangeably,withthe

unknownindifferentpositions.Examples:

• Solvetheequation:24=?x6

• Rachelhas3bags.Thereare4marblesineachbag.HowmanymarblesdoesRachelhavealtogether?(3x4=m)

GuidedPractice:



• Havethestudentsworkon3problemsattheirdesksindependentlyfirst,thenhavethemcompareanswerswiththeirpartners.


Closure:LessonDebrief:Whatstrategiesdidyouusetosolvefortheunknownnumber?Howdidyoudeterminethatyourstrategyworked?Accommodations/Modifications:Modelthestepsinasmallgrouptoprovidemorefocusedinstruction.Usemanipulativesandmodels.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,HowardCountyCommonCoreMath,ReadTennessee,3rdGradeMathFlipbookReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week2Standard(s):3.OA.5Applypropertiesofoperationsasstrategiestomultiplyanddivide.LessonOverview:Justlikeinadditionandsubtraction,studentsneedavarietyofwaystosolvefornumbersentencesinvolvingmultiplicationanddivisionwithoutrelyingonrotememorization.Studentsshouldemployavarietyofsolutionmethodsthatdemonstratetheirunderstandingofthemeaningofmultiplication.Thesemethodsincludetheuseofthecommutativepropertyofmultiplication,theassociativepropertyofmultiplication,andthedistributivepropertyofmultiplicationoveraddition.


• I can explain the commutative, associative, and distributive property of multiplication.

• I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.

Vocabulary:equalsign,multiplicationequation,unknownvariable,commutative,distributive,associativeproperty

FocusQuestion(s):Whatmultiplicationstrategymightapplytoasituation?Howdoyoudeterminethatthemultiplicationstrategyworked?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Presentthisproblemtotheclass:

Kyshawnwasworkingonhishomeworkwhenhecametoamultiplicationproblemthathehasn’tlearnedyet.Theproblemwas6x5=______.Kyshawnhaslearnedsomemultiplicationfacts.Heknowsthat2x5=10and4x5=20.HowcanKyshawnusewhatheknowstofindthesolutiontohishomeworkproblem?Usedrawings,words,orequationstoexplain.

Callonvolunteerstoshowhowtheyfiguredouttheanswer.InstructionandStrategies:

• OnlineDemoLesson:https://learnzillion.com/resources/72372-apply-properties-of-operations-as-strategies-to-multiply-and-divide-3-oa-b-5

• Studentsshouldhaveavarietyofopportunitiestoworkwithnumbersentencesthataremissingoneofthewholenumbers.

• Continuedworkwithmultiplicationanddivisionfactfamilieswillaidstudentsinfindingsolutionsmuchfaster.• Studentsshouldlearnhowtosolveproblemsusingthefollowingstrategies:

§ Example:If6x4=24isknown,then4x6isalsoknown(commutativepropertyofmultiplication).§ Example:3x5x2canbefoundby3x5=15,then15x2=30,orby5x2=10,then3x10=30

(Associativepropertyofmultiplication).§ Example:Knowingthat8x5=40and8x2=16,onecanfind8x7as8x(5+2)=(8x5+(8x2)-40+16

+56(Distributiveporpertyofmultiplication).• WhilestudentsDONOTneedtousetheformaltermsoftheseproperties,theyshouldunderstandthat

propertiesarerulesabouthownumberswork;studentsdoneedtobeflexibleandfluentinapplyingeachofthem.

• Studentsrepresentexpressionsusingvariousobjects,pictures,words,andsymbolsinordertodeveloptheirunderstandingofproperties.Theymultiplyby1and0anddivideby1.Theychangetheorderofnumberstodeterminethattheorderofnumbersdoesnotmakeadifferenceinmultiplication(butdoesmakeadifferenceindivision).Giventhreefactors,theyinvestigatechangingtheorderofhowtheymultiplythenumbersto

determinethatchangingtheorderdoesnotchangetheproduct.Theyalsodecomposenumberstobuildfluencywithmultiplication.(Marzano:GeneratingandTestingHypothesis)

• Theassociativepropertystatesthatthesumorproductstaysthesamewhenthegroupingofaddendsorfactorsischanged.Forexample,whenastudentmultiplies7x5x2,astudentcouldrearrangethenumberstofirstmultiply5x2=10andthenmultiply10x7=70.

• Thecommutativeproperty(orderproperty)statesthattheorderofnumbersdoesnotmatterwhenaddingormultiplyingnumbers.Forexample,ifastudentknowsthat4x3=12,thentheyalsoknowthat3x4=12.Thearraybelowcouldbedescribedasa4x3arrayfor4rowsand3columnsor3rowsand4columns.Thereisno“fixed”waytowritethedimensionsofanarrayasrowsxcolumnsorcolumnsxrows.

• Studentsareintroducedtothedistributivepropertyofmultiplicationoveradditionasastrategyforusingproductstheyknowtosolveproductstheydon’tknow.Herearewaysthatstudentscouldusethedistributivepropertytodeterminetheproductof7x6.Again,studentsshouldusethedistributiveproperty,butcan

refertothisininformallanguagesuchas“breakingnumbersapart.”GuidedPractice:



• Havethestudentsworkon3problemsattheirdesksindependentlyfirst,thenhavethemcompareanswerswiththeirpartners.


Closure:LessonDebrief:Howcanyouillustrateeachproperty?Howdidyoudeterminewhichpropertywillwork?Accommodations/Modifications:Modelthestepsinasmallgrouptoprovidemorefocusedinstruction.Usemanipulativesandmodels.Resources(TextbookandSupplemental):Learnzillion.com,GuamDistrictCurriculumGuide,HowardCountyCommonCoreMath,ReadTennessee,3rdGradeMathFlipbookReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week3Standard(s):3.OA.7Fluentlymultiplyanddividewithin100,usingstrategiessuchastherelationshipbetweenmultiplicationanddivision(e.g.,knowingthat8×5=40,oneknows40÷5=8)orpropertiesofoperations.BytheendofGrade3,knowfrommemoryallproductsoftwoone-digitnumbers.LessonOverview:Asstudentsbecomemoresophisticatedwiththeirknowledgeofmultiplicationanddivision,theydevelopfluencytosolveawidevarietyofmultiplicationanddivisionproblems.

LessonObjective(s):

• I can multiply any two numbers with a product within 100 with ease by picking and using strategies that will get to the answer fairly quickly.

• I can instantly recall from memory the product of any two one-digit numbers.

Vocabulary:product,equalsign,multiplicationequation,unknown

FocusQuestion(s):Whatismultiplication?Whatmultiplicationstrategymightapplytoasituation?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Reviewoninterpretingmultiplicationequations:Havethestudentsmodelthefollowingequations:5x68x34x7Theycanuseequalgroups,array,areaofarectangle,jumpsonanumberlineorrepeatedaddition.Haveselectedstudentspresenttheirwork.Review:Whatdoesthesymbolxmean?Whatdoesthe=signmean?InstructionandStrategies:

• OnlineResources:https://learnzillion.com/lesson_plans/5649-understand-multiplication-with-0-and-1https://hcpss.instructure.com/courses/97/modules/items/22263

• “Knowfrommemory”doesnotmeanfocusingonlyontimedtestsandrepetitivepractice,butample

experiencesworkingwithmanipulatives,pictures,arrays,wordproblems,andnumberstointernalizethebasicfacts(upto9x9).TheCCSSdefinethewordfluentlyasaccuracy,efficiency(usingareasonableamountofstepsandtime),andflexibility(usingstrategiessuchasthedistributiveproperty).Instructionshouldfocusonbuildingfluencyovertime.(Marzano:ReinforcingEffortandProvidingRecognition)

• Strategiesstudentsmayusetoattainfluencyinclude:

MultiplicationbyzerosandonesDoubles(2sfacts),Doublingtwice(4s),Doublingthreetimes(8s)Tensfacts(relatingtoplacevalue,5x10is5tensor50)

Fivefacts(halfoftens)Skipcounting(countinggroupsof__andknowinghowmanygroupshavebeencounted)Squarenumbers(ex:3x3)Nines(10groupslessonegroup,e.g.,9x3is10groupsof3minusonegroupof3)Decomposingintoknownfacts(6x7is6x6plusonemoregroupof6)Turn-aroundfacts(CommutativeProperty)Factfamilies(Ex:6x4=24;24÷6=4;24÷4=6;4x6=24)Missingfactors

• GeneralNote:Studentsshouldhaveexposuretomultiplicationanddivisionproblemspresentedinbothverticalandhorizontalforms.

• Notethatmasteringthismaterialandreachingfluencyinsingle-digitmultiplicationsandrelateddivisionswithunderstandingmaybequitetime-consumingbecausetherearenogeneralstrategiesformultiplyingordividingallsingle-digitnumbersasthereareforadditionandsubtraction.Instead,therearemanypatternsandstrategiesdependentuponspecificnumbers.Soitisimperativethatextratimeandsupportbeprovidedifneeded.Suchfluencymaybereachedbybecomingfluentforeachnumber(e.g.,the2s,the5s,etc.)and

thenextendingthefluencytoseveral,thenallnumbers,mixedtogether.Organizingpracticesothatitfocusesmostheavilyonunderstoodbutnotyetfluentproductsandunknownfactorscanspeedlearning.GuidedPractice:

• FlashcardDrillwithteacher,thenwithpartners• MultiplicationFactGames


• TimedTestforMasteredTables• WorksheetPractice

IndependentPractice:

• Computer-assistedMultiplicationPractice• WritingFactsRepeatedly

Closure:Sitinacircle.CallonsomevolunteerstorecitetheirfavoriteTimesTable.Doaquickreviewofthetimestablefocusoftheday.Accommodations/Modifications:Providethemultiplicationtableasvisualaid.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,www.readtennessee.orgReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week3Standard(s):3.OA.8Solvetwo-stepwordproblemsusingthefouroperations.Representtheseproblemsusingequationswithaletterstandingfortheunknownquantity.Assessthereasonablenessofanswersusingmentalcomputationandestimationstrategiesincludingrounding.LessonOverview:Thislessonisfocusedondevelopingstrategiestosolvetwo-stepwordproblems.Studentsneedtobeexposedtomultipleproblem-solvingstrategies(usinganycombinationofwords,models,numbers,diagrams,physicalobjects,orsymbols)andbeabletochoosewhichonestouse.Thesizeofthenumbersshouldbelimitedtorelatedthirdgradestandards.


• I can choose the correct operation to perform the first computation, and

• I can choose the correct operation to perform the second computation in order to solve two-step word problems.

• I can write equations using a letter for the unknown number.

• I can decide if my answers are reasonable using mental math and estimation strategies including rounding.

Vocabulary:addition,estimationstrategies,mentalcomputation,commutativepropertyoveraddition,associativepropertyoveraddition,rounding,subtractionunknownvariable

FocusQuestion(s):Whataredifferentwaystorepresentagivenproblem?Whatmultiplicationstrategymightapplytoasituation?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Presentatwo-stepproblemtothestudents.Challengetheclasstosolveitontheirown.Thenhavethemsharetheirworkwithanelbowpartner.Callonseveralstudentswhouseddifferentstrategiestopresenttheirsolutionstotheclassusingthedocumentcamera(ifavailable).Thenusetheproblemasaspringboardtointroducethelessonandhighlighthowaproblemcanbesolvedusingdifferentstrategies.

InstructionalStrategies:• OnlineResource:

Howtoteachthestandard:https://learnzillion.com/lesson_plans/8632-solving-two-step-word-problems-using-a-model#fndtn-lesson

• Studentsgainafullunderstandingofwhichoperationtouseinanygivensituationthroughcontextualproblems.Numberskillsandconceptsaredevelopedasstudentssolveproblems.

• Theuseofpicturesanddiagramsisanimportanttooltoaidstudentswithproblem-solvingandisalsousefulforjustifyingaparticularanswer.

• Problemsshouldbepresentedonaregularbasisasstudentsworkwithnumbersandcomputations.(Researchersandmathematicseducatorsadviseagainstproviding“keywords”forstudentstolookforinproblemsituationsbecausetheycanbemisleading.)

• Studentsshouldusevariousstrategiestosolveproblems.Studentsshouldanalyzethestructureoftheproblemtomakesenseofit.Theyshouldthinkthroughtheproblemandthemeaningoftheanswerbefore

attemptingtosolveit.(CITW:IdentifyingSimilaritiesandDifferences)• Encouragestudentstorepresenttheproblemsituationinadrawingorwithcountersorblocks.Studentsshould

determinethereasonablenessofthesolutiontoallproblemsusingmentalcomputationsandestimationstrategies.(CITW:NonlinguisticRepresentations)

• Beginwithwordproblemsthatpromotemorethanonewaytosolveandencouragestudentstojustifytheirthinkingandbeabletoexplainsomeoneelse’swayofsolvingtheproblem.

• Whenstudentssolvewordproblems,theyshouldusevariousestimationskills,whichincludeidentifyingwhenestimationisappropriate,determiningthelevelofaccuracyneeded,selectingtheappropriatemethodofestimation,andverifyingsolutionsordeterminingthereasonablenessofsolutions.(CITW:GeneratingandTestingHypotheses)

• Estimationstrategiesinclude,butarenotlimitedto:o Usingbenchmarknumbersthatareeasytocomputeo Front-endestimationwithadjusting(usingthehighestplacevalueandestimatingfromthe

frontendmakingadjustmentstotheestimatebytakingintoaccounttheremainingamounts)o Roundingandadjusting(studentsrounddownorroundupandthenadjusttheirestimatedependingon

howmuchtheroundingchangedtheoriginalvalues)FormativeAssessment:

• Studentssolveagivenproblemontheirpersonalwhiteboards• PartnerPractice/TeamHuddle• QuickCheck


• Giveseveralproblemforindependentpractice.Closure:Havethestudentsanswerthefocusquestionsaftereachlesson.Accommodations/Modifications:Forstudentswhoneedintensivesupport,givesimplerproblemswithlowernumbers.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,EngageNY,HowardCounty,AboutEducation.com,ReadTenessee,3rdGradeMathFlipbook,http//www.learnzillion.comReflection:


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Content:Math Grade/Course:3rdGrade Timeline:Week4Standard(s):3.MD.7.bRelateareatotheoperationsofmultiplicationandaddition.b.Multiplysidelengthstofindareasofrectangleswithwhole-numbersidelengthsinthecontextofsolvingrealworldandmathematicalproblems,andrepresentwhole-numberproductsasrectangularareasinmathematicalreasoning.3.MD.7.cRelateareatotheoperationsofmultiplicationandaddition.c.Usetilingtoshowinaconcretecasethattheareaofarectanglewithwhole-numbersidelengthsaandb+cisthesumofa×banda×c.Useareamodelstorepresentthedistributivepropertyinmathematicalreasoning.3.MD.7.dRelateareatotheoperationsofmultiplicationandaddition.d.Recognizeareaasadditive.Findareasofrectilinearfiguresbydecomposingthemintonon-overlappingrectanglesandaddingtheareasofthenon-overlappingparts,applyingthistechniquetosolverealworldproblems.LessonOverview:Oncestudentshavemasteredtheconceptofarea,theyare ready to make calculations with arithmeticoperations. This standard has many parts: Studentsshould be able to find the areas of rectangles bymultiplication and know why the area of a rectanglewith whole-number side lengths is the product of theside lengths (because anm-unit byn-unit is composedofmxnarray of unit squares, which tile the rectanglewithout overlapping, thus the area of the rectangleismtimesn).Theyshouldthenbeabletorepresentanarbitrary product of whole numbersusingan areamodel,andtousethemodeltounderstanddistributivepropertyof multiplication. Finally, students should beable to find areas of rectilinear (characterized bystraight lines) figures by decomposing them intorectangles.


• I can use tiles to find the area of rectangles. • I can explain the relationship between tiling and

multiplying side lengths to find the area of rectangles.

• I can multiply adjacent side lengths of rectangles to solve word problems.

• I can use area models to explain the distributive property.

• I can decompose an irregular figure into non-overlapping rectangles.

• I can explain area as additive and use this understanding to solve word problems.

Vocabulary:area,closedfigure,length,rectangulararray,width,decompose,irregularshape,rectilinearfigure,squareunits,two-dimensional

FocusQuestion(s):WhatpropertiesbetweenadditiveanddistributivedoIuseinordertofindthearea?Howcanstudentsexplaintherelationshipofthedistributivepropertyincontextusingpictures,words,andnumberstosupporttheirreasoning?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Givestudentsarectanglewithwholenumbersidelengthsandaskthemtopredictthearea.Thenaskthemtomultiplythesidelengths,thentiletherectanglewithunitsquares.Askthemtoexplainwhythesetwoarethesame.InstructionandStrategies:

• OnlineDemoLessons:https://learnzillion.com/resources/73010-relate-area-to-the-operations-of-multiplication-and-additionhttps://learnzillion.com/resources/72595-recognize-area-as-additive-find-area-of-figures-by-decomposing-them-3-md-c-7dhttps://learnzillion.com/resources/72499-relate-area-to-multiplication-and-addition-using-unit-squares-and-arrays-3-md-c-7a-3-md-c-7b

• Studentsshouldbemovingontoproblemsinwhichtheyfindtheareaoflargerrectanglesby"seeing"thearrayofunitsquareswithinarectanglewithouthavingtophysicallycreateit.

• Askstudentstoexplainmultiplicationtosomeoneelseusinganareamodel.Askstudentswhethertheycanfindashortcuttomultiplyingaandb,multiplyingaandc,andaddingthetwoproducts;forexample,insteadofcomputing7x4+7x6bycomputingtwoseparateproductsandaddingtheresults,recognizethatthisis7x10=70.Havetheminterpretthisproblemusinganareamodel.Askstudentstocomeupwithamathematicaljustificationofthedistributiveproperty.

• Areaisadditive;perhapsaskstudentstocomputetheareaofafigurethatismadebyadjoiningtworectangles,andthenhelpthemseethattheareaofthisfigureisthesumoftheareasofthetworectangles(andcanbegottenbymultiplyingthesidelengthsofeachrectangle,andthenaddingtheproducts).

• Usingconcreteobjectsordrawings,studentsbuildcompetencewithcompositionanddecompositionofshapes,

spatialstructuring,andadditionofareameasurements.Studentslearntoinvestigatearithmeticpropertiesusingareamodels.Forexample,theylearntorotaterectangulararraysphysicallyandmentally,understandingthattheirareasarepreservedunderrotation,andthus,forexample,4x7=7x4,illustratingthecommutativepropertyofmultiplication.Studentsalsolearntounderstandandexplainthattheareaofarectangularregionof,forexample,12length-unitsby5length-unitscanbefoundeitherbymultiplying12x5,orbyaddingtwoproducts,e.g.,10x5and2x5,illustratingthedistributivepropertyasinthepreviousexample.

GuidedPractice:

• Havethestudentsworkontwoorthreeproblemsontheirpersonalboards,thencomparetheiranswerswiththeirelbowpartnersthenwiththeirteams.


• Worksheetonfindingtheareaofrectanglesandrectilinearareas.

IndependentPractice:• PerformanceTask:1. Giveeachstudentsquaremanipulativesor2cmgraphpaper(variedsizedwillalsowork).Thengiveeach

studentanareaamountthatcanbemadeinmultipleways.2. Havestudentseithercolorinthegraphpaperorusethesquaremanipulativestocreatetheareagiveninas

manywaysaspossible.3. Oncestudentshavebuiltthedifferentareamodelsofthegivennumber,havethemexplaintheirstrategy.

Closure:LessonDebrief:Havethestudentsanswerthefocusquestions.Accommodations/Modifications:ProvidethemultiplicationtableforDay3.Workwithasmallgroupwhoneedsextrasupport.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,HowardCountyCommonCoreMath,ReadTennessee,3rdGradeMathFlipbookReflection:


Quarter3

Content:Math Grade/Course:3rdGrade Timeline:Weeks6and7Standard(s):3.NF.1Understandafraction1/basthequantityformedby1partwhenawholeispartitionedintobequalparts;understandafractiona/basthequantityformedbyapartsofsize1/b.3.NF.2aUnderstandafractionasanumberonthenumberline;representfractionsonanumberlinediagram.a.Representafraction1/bonanumberlinediagrambydefiningtheintervalfrom0to1asthewholeandpartitioningitintobequalparts.Recognizethateachparthassize1/bandthattheendpointofthepartbasedat0locatesthenumber1/bonthenumberline.3.NF.2bUnderstandafractionasanumberonthenumberline;representfractionsonanumberlinediagram.b.Representafractiona/bonanumberlinediagrambymarkingoffalengths1/bfrom0.Recognizethattheresultingintervalhassizea/bandthatitsendpointlocatesthenumbera/bonthenumberline.LessonOverview:3.NF.1Grade3expectationsinthetwofractionstandardsarelimitedtofractionswithdenominators2,3,4,6,8.Studentsdevelopanunderstandingoffractions,beginningwithunitfractions.Studentsviewfractionsingeneralasbeingbuiltoutofunitfractions,andtheyusefractionsalongwithvisualfractionmodelstorepresentpartsofawhole.Studentsunderstandthatthesizeofafractionalpartisrelativetothesizeofthewhole.Studentsusetheirunderstandingoffractionsonthenumberlinetousearulertomeasurelengthstohalvesandquarterunits.3.NF.2Upuntil thispoint, studentshavehadvery limitedexposure to fractions. Now they will work with numbersthat exist between two whole numbers. Students learnthat a fraction is notonly a "part of awhole", but also apoint on the number line. This is significant becausestudentsoftenthinkoffractions(suchas3/8)asobjectsina completely separate category from whole numbers.Locating the fraction 3/8 on a number line shows that afraction can be thought of as between two wholenumbers.


• Icanexplainanyunitfractionasonepartofawhole.

• Icanexplainanyfraction(a/b)as"a"(numerator)beingthenumbersofpartsand"b"(denominator)asthetotalnumberofequalpartsinthewhole.

• Icanrepresentafractionandexplainmyrepresentation.

• I can explain and show how 1/b can be represented on a number-line in two ways (1) as a number that is located a distance of 1/b to the right of 0, and (2) as the size of each of the parts when a whole is partitioned into b equal parts.

• I can explain and show how a/b can be represented on a number line in two ways: (1) as a number that is located a distance a/b to the right of 0, and (2) as the size of a parts when a whole is partitioned into b equal parts.

• I can represent a unit fraction (1/b) on a number line between 0 and 1.

• I can represent any fraction (a/b) on a number line.

Vocabulary:denominator,equalparts,fairshares,fraction,numerator,one-eighth;1/8,one-fourth;¼,one-half;½,one-sixth;1/6,one-third;1/3,partitioned,unitfraction,whole,divide,fractionalparts,numberlinediagram,numerator

FocusQuestion(s):HowwillIshowafractionusingconcretemodels?Whatdoesthenumberinanumeratormean?Howdoyoupartitionpartsofawholetorepresentafraction?Howdoyoupartitionanumberlinetorepresentafraction?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Showapictureoradrawingofapizza.Poseaproblem:

Iffourfriendswanttosharethepizzaequally,howwouldyoucutthepizza?Whatdoyoucallthepartthateachpersongetsafterdividingitequally?Usethisproblemtopresentthewordfractionandwhatitmeans.InstructionandStrategies:

• OnlineResource:https://learnzillion.com/resources/72250-understand-fractionshttps://learnzillion.com/resources/72626-represent-fractions-on-a-number-line-3-nf-a-2

• Thefractionstandardsshouldrefertothesharingofawholebeingpartitionedorsplit.Fractionmodelsinthird

gradeincludearea(partsofawhole),models(circles,rectangles,squares),andnumberlines.Somerepresentations,suchasarectangle,areeasiertopartition,thansay,acircle.Usevariouscontextsfamiliartostudents,suchascandybars,fruit,andcakes.Setmodels,anothertypeofmodeling(partsofagroup),arenotexploredinthethirdgradecurriculum.In3.NF.1,studentsshouldfocusontheconceptthatafractionismadeup(composed)ofmanypiecesofaunitfraction,whichhasanumeratorof1.Forexample,thefraction3/5iscomposedof3piecesinthateachofthethreepieceshasasizeof1/5.(Marzano:CooperativeLearning,IdentifyingSimilaritiesandDifferences,NonlinguisticRepresentations)

• Someimportantconceptsrelatedtodevelopingunderstandingoffractionsinclude:§ Understandfractionalpartsmustbeequal-sized§ Thenumberofequalpartstellshowmanymakeawhole(thedenominator).§ Asthenumberofequalpiecesinthewholeincreases,thesizeofthefractionalpiecesdecreases(1/6is

smallerthan1/3);thisisoftenconfusingtostudents.Theyseelargerwholenumbersasbiggernumbersandwanttoassumethesameistrueforfractiondenominators;emphasizebypartitioningthesamesizewholeintodifferentpiecesforcomparison.Forthesamesizerectangularcake,ask:“Ifyoulikecake,whichpiecewouldyouprefer,1/10or1/6?”Havestudentsmakeaconjectureaboutunitfractionsandrelativesizeddenominators.

§ Thesizeofthefractionalpartisrelativetothewhole.Thenumberofchildreninonehalfofaclassroomisdifferentthanthenumberofchildreninone-halfofaschool.(Thewholeineachsetisdifferent,thereforethehalfineachsetwillbedifferent.)Anotherexample:1/2ofthepaintinasmallbucketcouldbelesspaintthan1/3ofthepaintinalargerbucket,but1/3ofaribbonislongerthan1/5ofthesameribbonbecausewhentheribbonisdividedinto3equalparts,thepartsarelongerthanwhenthesamelengthribbonisdividedinto5equalparts.

§ Whenawholeiscutintoequalparts,thedenominatorrepresentsthenumberofequalparts.(Awholeiscutintofoursamesizeparts,thefunctionofthedenominator;eachpartrepresents1/4ofthewhole.)Initially,studentscanuseanintuitivenotionof“samesizeandsameshape”(congruence)toexplainwhythepartsareequal.Forexample,whentheydivideasquareintofourequalsquaresorfourequalrectangles.Studentscometounderstandamoreprecisemeaningfor“equalparts”as“partswithequalmeasurements.”Forexample,whenarulerispartitionedintohalvesorquartersofaninch,theyseethateachsubdivisionhasthesamelength.Inareamodels,theyreasonabouttheareaofashadedregiontodecidewhatfractionofthewholeitrepresents.

§ Thenumeratorofafractionisthecountingnumberofequalparts.Therefore,¾meansthatthereare3one-fourths.Studentsshouldcountastheywouldforwholenumbers,1,2,3,...butnowcountfractionpartsofawhole:one-fourth,two-fourths,three-fourths...

§ Givenashape,studentspartitionitintoequalparts,recognizingthatthesepartsallhavethesamearea.Theyidentifythefractionalnameofeachpartandareabletopartitionashapeintopartswithequalareasinseveraldifferentways.

• Activity:Studentsthinkallshapescanbedividedthesameway.Presentshapesotherthancircles,squares,orrectanglestopreventstudentsfromovergeneralizingthatallshapescanbedividedthesameway.(Marzano:NonlinguisticRepresentations)Forexample,havestudentsfoldatriangleintoeighths.Provideoraldirectionsforfoldingthetriangle:

§ Foldthetriangleinhalfbyfoldingtheleftvertex(atthebaseofthetriangle)overtomeettherightvertex.

§ Foldinthismannertwomoretimes.§ Havestudentslabeleacheighthusingfractionalnotation.Then,havestudentscountthefractionalparts

inthetriangle(one-eighth,two-eighths,three-eighths,andsoon).

• Studentstransfertheirunderstandingofpartsofawholetopartitionanumberlineintoequalparts.Therearetwonewconceptsaddressedinthisstandardthatstudentsshouldhavetimetodevelop.

• Onanumberlinefrom0to1,studentscanpartition(divide)itintoequalpartsandrecognizethateachsegmentedpartrepresentsthesamelength.

GuidedPractice:

• Activity:Studentsthinkallshapescanbedividedthesameway.Presentshapesotherthancircles,squares,orrectanglestopreventstudentsfromovergeneralizingthatallshapescanbedividedthesameway.(Marzano:NonlinguisticRepresentations)Forexample,havestudentsfoldatriangleintoeighths.Provideoraldirectionsforfoldingthetriangle:

§ Foldthetriangleinhalfbyfoldingtheleftvertex(atthebaseofthetriangle)overtomeettherightvertex.

§ Foldinthismannertwomoretimes.§ Havestudentslabeleacheighthusingfractionalnotation.Then,havestudentscountthefractionalparts

inthetriangle(one-eighth,two-eighths,three-eighths,andsoon).FormativeAssessment:

• WhiteBoardExercises• Worksheetsonidentifyingfractionsfromgivenshapesandonthenumberlline(withandwithoutpartner)


• QuickChecks• Worksheets• Homework

Closure:LessonDebrief:Havethestudentsanswerthefocusquestions.Accommodations/Modifications:Providemanipulativesandfractionchartsandnumberlinesonthewallforreference.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,HowardCountyCommonCoreMath,learnzillion.com,ReadTennessee,3rdGradeMathFlipbookReflection:


Quarter_3_

Content:Math Grade/Course:3rdGrade Timeline:Week7Standard(s):3.NF.3.aExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.a.Understandtwofractionsasequivalent(equal)iftheyarethesamesize,orthesamepointonanumberline.3.NF.3.bExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.b.Recognizeandgeneratesimpleequivalentfractions,e.g.,1/2=2/4,4/6=2/3).Explainwhythefractionsareequivalent,e.g.,byusingavisualfractionmodel.3.NF.3.cExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.c.Expresswholenumbersasfractions,andrecognizefractionsthatareequivalenttowholenumbers.Examples:Express3intheform3=3/1;recognizethat6/1=6;locate4/4and1atthesamepointofanumberlinediagram.3.NF.3.dExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.d.Comparetwofractionswiththesamenumeratororthesamedenominatorbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualfractionmodelLessonOverview:Thesestandardscallforstudentstousevisualfractionmodels(areamodels)andnumberlinestoexploretheideaofequivalentfractionsandcomparingfractions.Itisimportantthattheyareabletojustifytheirreasoning.Studentsshouldonlyexploreequivalentfractionsusingmodels,ratherthanusingalgorithmsorprocedures.


• Icanusemodelstoshowandexplainequivalentfractions.

• Icanlocateequivalentfractionsonanumberline.• Icanusemodelstoshowandexplainwhole

numbersasfractions.• Icanlocatewholenumbersasfractionsona

numberline.• Icanusemodelstocomparetwofractionsand

recordthecomparisonusing<,>,or=.• Icanexplainhowthesizeofequalpartscanbe

usedtocomparetwofractionswiththesamenumerator,andexplainhowthenumberofequalpartscanbeusedtocomparetwofractionswiththesamedenominator.

Vocabulary:compare,equivalent/equivalency,numerator,plot,whole,denominator,equalparts,equivalent,fraction,numberline,numerator,visualfractionmodel,wholenumber,greaterthan(>),lessthan(<)

FocusQuestion(s):WhatmethodsorstrategieswillIusetoshowtheequivalencyofafraction?Whenaretwofractionsequivalent?Whatdoesitmeanfortwofractionstobeequivalentandhowwouldyoushowthistobetrue?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:Drawanumberlinefrom0to1.Putatickmarkinthemiddleofthenumberlineandaskthestudentswhatfractionisshownbythetickmark.(Studentsshouldbeabletosay½)Write½underthetickmarkandaskthestudentstoexplainwhyitis½.

Underyourfirstnumberline,drawanothernumberlineexactlythesamelength.Puttickmarkstodividethenumberlineintofourths.Havethestudentsidentifythefractionsshown.(¼2/4¾)“Lookingatthetwonumberlines,whattwofractionsareequivalentorthesameamount?(1/2and2/4).Howdoyouknow?”(Theyareexactlythesamelengthonthenumberlines.)

SettheobjectivesbyreadingyourICanStatementsonequivalentfractions.

InstructionalStrategies:

• Step-by-StepWebDemoLessons:https://learnzillion.com/lessons/1731-identify-equivalent-fractions-using-fraction-models

• WebResourceonpartitioningandunderstandingfractions:http://arb.nzcer.org.nz/supportmaterials/maths/concept_map_fractions.php#Partitioning

Havestudentsexploreseveralimportantideasabouttheseconceptsinthesestandards:• Animportantconceptwhencomparingfractionsistolookatthesizeofthepartsandthenumberoftheparts.

Forexample,1/8issmallerthan1/2becausewhen1wholeiscutinto8pieces,thepiecesaremuchsmallerthanwhen1wholeiscutinto2pieces.

• Studentsshouldrecognizehowtowritewholenumbersasfractions.Theconceptrelatestofractionsasdivisionproblems,wherethefraction3/1is3wholesdividedintoonegroup.Thisstandardisthebuildingblockforlaterworkwherestudentsdivideasetofobjectsintoaspecificnumberofgroups.Studentsmustunderstandthemeaningofa/1.Example:If6browniesweresharedbetween2people,howmanybrownieswouldeachpersonget?

• Studentscancomparefractionswithorwithoutvisualfractionmodelsincludingnumberlines.Experiencesshouldencouragestudentstoreasonaboutthesizeofpieces,thefactthat1/3ofacakeislargerthan1/4ofthesamecake.Sincethesamecake(thewhole)issplitintoequalpieces,thirdsarelargerthanfourths.

• Studentsshouldalsoreasonthatcomparisonsareonlyvalidifthewholesareidentical.Forexample,1/2ofalargepizzaisadifferentamountthan1/2ofasmallpizza.Studentsshouldbegivenopportunitiestodiscussandreasonaboutwhich1/2islarger.

• Studentsbuilduponpreviousideasfromearliergradestocomparefractionswiththesamedenominator.Theyseethatforfractionsthathavethesamedenominator,theunderlyingunitfractionsarethesamesize;wholeshavebeendividedintothesamenumberofequalparts.Sothefractionwiththelargernumerator,ormoreofthesamesizeparts,isthelargerfraction.Forexample:2/5<4/5thefractionwiththegreaternumeratorisgreaterbecauseitismadeofmoreunitfractions.Foranotherexample,thesegmentonanumberlinefrom0to3/4isshorterthanthesegmentfrom0to5/4becauseitmeasures3unitsof1/4asopposedto5unitsof1/4,therefore3/4<5/4.

• Forunitfractions,studentsalsoseetheonewiththelargerdenominatorissmaller,byreasoning,forexample,thatinorderformore(identical)piecestomakethesamewhole,thepiecesmustbesmaller.Fromthistheyreasonthatforfractionsthathavethesamenumerator,thefractionwiththesmallerdenominatorisgreater.Forexample,2/5>2/7,because1/7<1/5,so2lengthsof1/7islessthan2lengthsof1/5.Aswithequivalenceoffractions,itisimportantincomparingfractionstomakesurethateachfractionreferstothesamewhole.

GuidedPractice:(onPersonalWhiteBoards)

• Havestudentsmodeltwofractionsthatareequivalentusingnumberlinesandshapes.FormativeAssessment:

• Worksheetsforpractice• DailyQuickChecks

IndependentPractice:• WorksheetsandPerformanceTasks(HowardCountyThirdGradeMath)

Closure:LessonDebrief:Answerthefocusquestionsattheendofthelesson.

Accommodations/Modifications:Providestudentswithpairsofshapesornumberlinesthatarealreadypre-partitioned.Provideconcretemodelsorvisuals.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,Websites:HowardCountyCommonCoreMath,ReadTennesseeThirdGradeMath,www.learnzillion.comReflection:


Quarter_3_

Content:Math Grade/Course:3rdGrade Timeline:Week8Standard(s):3.NF.3.cExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.c.Expresswholenumbersasfractions,andrecognizefractionsthatareequivalenttowholenumbers.Examples:Express3intheform3=3/1;recognizethat6/1=6;locate4/4and1atthesamepointofanumberlinediagram.3.NF.3.dExplainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.d.Comparetwofractionswiththesamenumeratororthesamedenominatorbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualfractionmodelLessonOverview:Thesestandardscallforstudentstousevisualfractionmodels(areamodels)andnumberlinestoexploretheideaofequivalentfractionsandcomparingfractions.Itisimportantthattheyareabletojustifytheirreasoning.Studentsshouldonlyexploreequivalentfractionsusingmodels,ratherthanusingalgorithmsorprocedures.


• Icanusemodelstoshowandexplainwholenumbersasfractions.

• Icanlocatewholenumbersasfractionsonanumberline.

• Icanusemodelstocomparetwofractionsandrecordthecomparisonusing<,>,or=.

• Icanexplainhowthesizeofequalpartscanbeusedtocomparetwofractionswiththesamenumerator,andexplainhowthenumberofequalpartscanbeusedtocomparetwofractionswiththesamedenominator.

Vocabulary:compare,equivalent/equivalency,numerator,plot,whole,denominator,equalparts,equivalent,fraction,numberline,numerator,visualfractionmodel,wholenumber,greaterthan(>),lessthan(<)

FocusQuestion(s):WhatmethodsorstrategieswillIusetoshowtheequivalencyofafraction?Whenaretwofractionsequivalent?Whatdoesitmeanfortwofractionstobeequivalentandhowwouldyoushowthistobetrue?

DescriptionofLesson(IncludingInstructionalStrategies):AnticipatorySet:(SeelinkonLessonPlansonlearnzillionforexcellentideasforanticipatoryset.)

SettheobjectivesbyreadingyourICanStatementsonequivalentfractions.

InstructionalStrategies:

• Step-by-StepOnlineDemoLessonsandLessonPlans:

https://hcpss.instructure.com/courses/97/pages/3-dot-nf-dot-3-learnzillion-resources

Havestudentsexploreseveralimportantideasabouttheseconceptsinthesestandards:• Animportantconceptwhencomparingfractionsistolookatthesizeofthepartsandthenumberoftheparts.

Forexample,1/8issmallerthan1/2becausewhen1wholeiscutinto8pieces,thepiecesaremuchsmallerthanwhen1wholeiscutinto2pieces.

• Studentsshouldrecognizehowtowritewholenumbersasfractions.Theconceptrelatestofractionsasdivisionproblems,wherethefraction3/1is3wholesdividedintoonegroup.Thisstandardisthebuildingblockforlaterworkwherestudentsdivideasetofobjectsintoaspecificnumberofgroups.Studentsmustunderstandthemeaningofa/1.Example:If6browniesweresharedbetween2people,howmanybrownieswouldeachpersonget?

• Studentscancomparefractionswithorwithoutvisualfractionmodelsincludingnumberlines.Experiencesshouldencouragestudentstoreasonaboutthesizeofpieces,thefactthat1/3ofacakeislargerthan1/4ofthesamecake.Sincethesamecake(thewhole)issplitintoequalpieces,thirdsarelargerthanfourths.

• Studentsshouldalsoreasonthatcomparisonsareonlyvalidifthewholesareidentical.Forexample,1/2ofalargepizzaisadifferentamountthan1/2ofasmallpizza.Studentsshouldbegivenopportunitiestodiscussandreasonaboutwhich1/2islarger.

• Studentsbuilduponpreviousideasfromearliergradestocomparefractionswiththesamedenominator.Theyseethatforfractionsthathavethesamedenominator,theunderlyingunitfractionsarethesamesize;wholeshavebeendividedintothesamenumberofequalparts.Sothefractionwiththelargernumerator,ormoreofthesamesizeparts,isthelargerfraction.Forexample:2/5<4/5thefractionwiththegreaternumeratorisgreaterbecauseitismadeofmoreunitfractions.Foranotherexample,thesegmentonanumberlinefrom0to3/4isshorterthanthesegmentfrom0to5/4becauseitmeasures3unitsof1/4asopposedto5unitsof1/4,therefore3/4<5/4.

• Forunitfractions,studentsalsoseetheonewiththelargerdenominatorissmaller,byreasoning,forexample,thatinorderformore(identical)piecestomakethesamewhole,thepiecesmustbesmaller.Fromthistheyreasonthatforfractionsthathavethesamenumerator,thefractionwiththesmallerdenominatorisgreater.Forexample,2/5>2/7,because1/7<1/5,so2lengthsof1/7islessthan2lengthsof1/5.Aswithequivalenceoffractions,itisimportantincomparingfractionstomakesurethateachfractionreferstothesamewhole.

GuidedPractice:(onPersonalWhiteBoards)

• Havestudentsmodeltwofractionsthatareequivalentusingnumberlinesandshapes.FormativeAssessment:

• Worksheetsforpractice• DailyQuickChecks

IndependentPractice:• WorksheetsandPerformanceTasks(HowardCountyThirdGradeMath)

Closure:LessonDebrief:Answerthefocusquestionsattheendofthelesson.Accommodations/Modifications:Providestudentswithpairsofshapesornumberlinesthatarealreadypre-partitioned.Provideconcretemodelsorvisuals.Resources(TextbookandSupplemental):GuamDistrictCurriculumGuide,Websites:HowardCountyCommonCoreMath,ReadTennesseeThirdGradeMath,www.learnzillion.comReflection: