Download - FINAL RCD UNIT 4 UPO 4th Grade Math · (See grade 4 Language standards 1 here for specific expectations.) L.4.3.a,cUse knowledge of language and its conventions when writing, speaking,

Mathematics ‐ Unit 4

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RigorousCurriculumDesignUnitPlanningOrganizer

Subject: Mathematics Grade: 4UnitNumber: 4 UnitName: MultiplyingFractionsandDecimalFractionsUnitLength Days:20 Mins/Day:60

UnitSynopsis

Inthisunit,studentswillextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.Studentswillalsosolvewordproblemsinvolvingmultiplicationofafractionbyawholenumber.Nextstudentswilllearntoexpressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.Theywillusedecimalnotationforfractionswithdenominators10or100.Finally,studentswilllearntocomparetwodecimalstohundredthsbyreasoningabouttheirsizeandrecognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Theywillrecordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheirconclusions.

PriorityStandards

MathCCSS StandardsforMathematicalPractice

4.NF.4‐Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.a.Understandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).b.Understandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)c.Solvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?4.NF.5‐Expressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100=34/100.4.NF.6‐Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.4.NF.7‐Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.

☒Makesenseofproblemsandpersevereinsolvingthem☐Reasonabstractlyandquantitatively☒Constructviableargumentsandcritiquethereasoningofothers☐Modelwithmathematics☐Useappropriatetoolsstrategically☒Attendtoprecision☒Lookforandmakeuseofstructure☐Lookforandexpressregularityinrepeatedreasoning

Supporting

Standards

MathCCSS ELACCSS NGELDStandards


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4.MD.2‐Usethefouroperationstosolvewordproblemsinvolvingdistances,intervalsoftime,liquidvolumes,massesofobjects,andmoney,includingproblemsinvolvingsimplefractionsordecimals,andproblemsthatrequireexpressingmeasurementsgiveninalargerunitintermsofasmallerunit.Representmeasurementquantitiesusingdiagramssuchasnumberlinediagramsthatfeatureameasurementscale.4.OA.1‐Interpretamultiplicationequationasacomparison,e.g.,interpret35=5×7asastatementthat35is5timesasmanyas7and7timesasmanyas5.Representverbalstatementsofmultiplicativecomparisonsasmultiplicationequations.

RI.4.1Refertodetailsandexamplesinatextwhenexplainingwhatthetextsaysexplicitlyandwhendrawinginferencesfromthetext.RI.4.4Determinethemeaningofgeneralacademicanddomain‐specificwordsorphrasesinatextrelevanttoagrade4topicorsubjectarea.RI.4.7Interpretinformationpresentedvisually,orally,orquantitatively(e.g.,incharts,graphs,diagrams,timelines,animations,orinteractiveelementsonWebpages)andexplainhowtheinformationcontributestoanunderstandingofthetextinwhichitappears.W.4.2.a‐eWriteinformative/explanatorytextstoexamineatopicandconveyideasandinformationclearly.W.4.10Writeroutinelyoverextendedtimeframes(timeforresearch,reflection,andrevision)andshortertimeframes(asinglesittingoradayortwo)forarangeofdiscipline‐specifictasks,purposes,andaudiences.SL.4.1.a‐dEngageeffectivelyinarangeofcollaborativediscussions(one‐on‐one,ingroups,andteacher‐led)withdiversepartnersongrade4topicsandtexts,buildingonothers'ideasandexpressingtheirownclearly.SL.4.2Paraphraseportionsofatextreadaloudorinformationpresentedindiversemediaandformats,includingvisually,quantitatively,andorally.SL.4.3Identifythereasonsandevidenceaspeakerprovidestosupportparticularpoints.SL.4.6DifferentiatebetweencontextsthatcallforformalEnglish(e.g.,presentingideas)andsituationswhereinformaldiscourseisappropriate(e.g.,small‐groupdiscussion);useformalEnglishwhenappropriatetotaskandsituation.(Seegrade4Languagestandards1hereforspecificexpectations.)L.4.3.a,cUseknowledgeoflanguageanditsconventionswhenwriting,speaking,reading,orlistening.L.4.4.a‐cDetermineorclarifythemeaningofunknownandmultiple‐meaningwordsandphrasesbasedongrade4readingandcontent,choosingflexiblyfromarangeofstrategies.L.4.5.cDemonstrateunderstandingofwordsbyrelatingthemtotheiropposites(antonyms)andtowordswithsimilarbutnotidenticalmeanings(synonyms).L.4.6Acquireanduseaccuratelygrade‐appropriategeneralacademicanddomain‐specificwordsandphrases,includingthosethatsignalpreciseactions,emotions,orstatesofbeing(e.g.,quizzed,whined,stammered)andthatarebasictoaparticulartopic(e.g.,wildlife,conservation,andendangeredwhendiscussinganimalpreservation).

ELD.4.I.B.6(RI.4.1,RI.4.4,L.4.3)Readingcloselyliteraryandinformationaltextsandviewingmultimediatodeterminehowmeaningisconveyedexplicitlyandimplicitlythroughlanguage.ELD.4.I.B.7(L.4.3,L.4.5.c)ListeningactivelytospokenEnglishinarangeofsocialandacademiccontext.ELD.4.I.A.2(L.4.6)Interactingwithothersinwritinglanguageinvariouscommunicativeforms(print,communicativetechnology,andmulti‐media).ELD.4.I.C.10(W.4.2.d,W.4.10)Writingliteraryandinformationaltexttopresent,describe,andexplainideasandinformation,usingappropriatetechnology.

InterdisciplinaryStandards

UnwrappedPriorityStandards

Standard1: 4.NF.4‐Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.a.Understandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).b.Understandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)c.Solvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?


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Skills Concepts Bloom’s DOKMultiply Afractionbyawholenumberbyapplyingandextendingprevious

understandingofmultiplicationofafraction.3 2

Understand afractiona/basamultipleof1/b. Forexample,useavisualfractionmodeltorepresent5/4asthe

product5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).

2 1

Understand amultipleofa/basamultipleof1/b. 2 1Use thisunderstandingtomultiplyafractionbyawholenumber.

Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)

3 2

Solve wordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.

Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?

4 3

Standard2: 4.NF.5‐Expressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

Skills Concepts Bloom’s DOKExpress afractionwithdenominator10asanequivalentfractionwith

denominator1002 2

Use thistechniquetoaddtwofractionswithrespectivedenominators10and100.2

Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

3 2

Standard3: 4.NF.6‐Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.

Skills Concepts Bloom’s DOKUse decimalnotationforfractionswithdenominators10or100.

Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.

2 1

Standard4: 4.NF.7‐Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.

Skills Concepts Bloom’s DOKCompare twodecimalstohundredthsbyreasoningabouttheirsize. 4 3Recognize thatcomparisonsarevalidonlywhenthetwodecimalsrefertothe

samewhole.1 1

Record Recordtheresultsofcomparisonswiththesymbols>,=,or<. 2 2Justify theconclusions,e.g.,byusingavisualmodel. 4 3


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LearningProgressions

Standard1: Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.CCSS.Math.Content.4.NF.B.4.aUnderstandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).CCSS.Math.Content.4.NF.B.4.bUnderstandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)CCSS.Math.Content.4.NF.B.4.cSolvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?

PreviousGrade3NF.1,3NF.3c

CurrentGrade NextGrade5NF.2,4,6

Skills Concepts Skills Concepts Skills ConceptsUnderstand afraction1/basthe

quantityformedby1partwhenawholeispartitioned

intobequalparts;understandafractiona/basthequantityformedbya

partsofsize1/b

Understand afractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4

astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).

Solve wordproblemsinvolvingadditionandsubtractionof

fractionsreferringtothesamewhole,includingcasesof

unlikedenominators,e.g.,byusingvisualfractionmodelsorequationstorepresenttheproblem.Usebenchmark

fractionsandnumbersenseoffractionstoestimatementallyandassessthereasonableness

ofanswers.Forexample,recognizeanincorrectresult2/5+1/2=3/7,byobserving

that3/7<1/2.Express wholenumbersasfractions,

andrecognizefractionsthatareequivalenttowhole

numbers.Examples:Express3intheform3=3/1;

recognizethat6/1=6;locate4/4and1atthesamepointofanumberlinediagram.

Understand amultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)

Interpret theproduct(a/b)×qasapartsofapartitionofqintobequalparts;equivalently,astheresultofasequenceofoperationsa×q÷b.For

example,useavisualfractionmodeltoshow(2/3)×4=8/3,andcreateastorycontextforthisequation.Dothesamewith

(2/3)×(4/5)=8/15.(Ingeneral,(a/b)×(c/d)=ac/bd.)

N/A N/A Solve wordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwo

wholenumbers

Solve realworldproblemsinvolvingmultiplicationoffractionsandmixednumbers,e.g.,byusingvisualfractionmodelsorequationstorepresentthe

problem.


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Standard2: NF5Expressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100

=34/100.PreviousGrade

3NF3aCurrentGrade NextGrade

5NF5Skills Concepts Skills Concepts Skills Concepts

Understand twofractionsasequivalent(equal)iftheyarethesamesize,orthesamepointona

numberline.

Express afractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

Interpret

Comparing

Explaining

multiplicationasscaling(resizing),by:thesizeofaproducttothesizeofonefactoronthebasisofthesizeoftheotherfactor,withoutperformingtheindicatedmultiplication.whymultiplyingagivennumberbyafractiongreaterthan1resultsinaproductgreaterthanthegivennumber(recognizingmultiplicationbywholenumbersgreaterthan1asafamiliarcase);explainingwhymultiplyingagivennumberbyafractionlessthan1resultsinaproductsmallerthanthegivennumber;andrelatingtheprincipleoffractionequivalencea/b=(n×a)/(n×b)totheeffectofmultiplyinga/bby1

Standard3: NF6:Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.

PreviousGraden/a

CurrentGrade NextGrade5NF5a

Skills Concepts Skills Concepts Skills ConceptsN/A N/A Use decimalnotationfor

fractionswithdenominators10or100.Forexample,

rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberline

diagram.

Comparing thesizeofaproducttothesizeofone

factoronthebasisofthesizeoftheotherfactor,withoutperformingthe

indicatedmultiplication.

Standard4: NF7:Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,and

justifytheconclusions,e.g.,byusingavisualmodel.PreviousGrade

n/aCurrentGrade NextGrade

n/aSkills Concepts Skills Concepts Skills ConceptsN/A N/A Compare twodecimalstohundredthsby

reasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.

N/A N/A


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BigIdea(s) CorrespondingEssentialQuestion(s)4.NF.4–Wewillusevisualmodelsandequationstorepresentmultiplicationoffractions4.NF.5–Tenthsandhundredthscanbeusedwhenfindingequivalentfractionstoaddthemtogether.4.NF.6‐Decimalnotationforfractionswithdenominators10or100canberewrittenas0.1and0.01respectively.E.g.1/10and1/100willbewrittenas0.1and0.01.4.NF.7–Comparingtwodecimalsorfractionscanonlybecomparedwhentheyarereferencingthesamewhole

4.NF.4–Howdoyourepresentmultiplyingfractionswithwholenumbersincomputationandwordproblems?4.NF.5–Whencan10thsand100thsbeusedinterchangeably?4.NF.6–Howarefractionsof10thsand100thsrepresentedasdecimals?4.NF.7‐Whenarethecomparisonoftwoormoredecimalsorfractionsvalid?

UnitVocabularyWordsAcademicCross‐CurricularVocabulary(Tier2) Content/DomainSpecificVocabulary(Tier3)

ApplyUnderstandModelExpressRepresentDescribe

Compare/ComparisonsRecognizeRecord

Multiply/MultiplicationFraction

WholeNumberMultipleEquationProductSolve

WordProblemsVisualFractionModel

DenominatorEquivalent

DecimalNotationHundredthsTenthsSymbols

GreaterThanLessThanEqualTo

ResourcesforVocabularyDevelopment(Strategies,RoutinesandActivities)

21stCenturySkills☐CreativityandInnovation☒CriticalThinkingandProblemSolving☒CommunicationandCollaboration☐FlexibilityandAdaptability

☐InitiativeandSelf‐Direction☒SocialandCross‐CulturalSkills☐ProductivityandAccountability☒LeadershipandResponsibility

Costa&Kallick,2008

UnitAssessmentsPre‐Assessment Post‐Assessment

Pleasecheckwww.alvordschools.org/cfaforIDnumbers.

Pleasecheckwww.alvordschools.org/cfaforIDnumbers.

ScoringGuidesandAnswerKeys

EmbeddedwithinEADMS

EmbeddedwithinEADMS


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EngagingScenarioOverview(Situation,challenge,role,audience,productorperformance)

Description:TheFundraiserYourschoolishavingafundraiser.Youareinchargeofthedrinkandsnackstand.Youwillberesponsibleforsupplyingdrinksandsnackstosellduringparent‐teacherconferenceweek.Youwillbegivenachartwithpricesfromthreedifferentstores.Evaluatewhichstoresaregoingtobethebesttopurchaseyourproductsfrom.Youneedtobuy100drinksand100snacks.Theseamountsneedtobeshownasfractionswithadenominatorof100.Findthetotalyouwillspendondrinksandonsnacks.Basedonhowmuchyouspent,howmuchwillyouchargeforyourdrinks?Howmuchwillyouchargeforyoursnacks?Ifyousoldeverythingyoubought,wereyoursalesprofitable?Youwillresearchandgatheryourinformationindividuallyandplaceyourdataintoyourchart.

SuggestedLengthofTime

Days:20Mins/Day:60

EngagingLearningExperiencesSynopsisofAuthenticPerformanceTasks

AuthenticPerformanceTasks DescriptionSuggestedLengthofTime

Task1:SnacksatyourSale4.NF.4‐Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.a.Understandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).b.Understandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)c.Solvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?BigIdea–WewillusevisualmodelsandequationstorepresentmultiplicationoffractionsEssentialQuestion–Howdoyourepresentmultiplyingfractionswithwholenumbersincomputationandwordproblems?

Youhavepurchasedsnacksforyourweekofsales.Snackswereboughtinmixandmatchcasesof32itemseach.Yourcaseismadeupof popcorn,

chips, cookies,and crackers.Representeachofthesefractionsasafactorofthewholecase.

Days:3‐5Mins/Day:60

Task2:DrinksatyourSale4.NF.5‐Expressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100=34/100.BigIdea–Tenthsandhundredthscanbeusedwhenfindingequivalentfractionstoaddthemtogether.EssentialQuestion–Whencan10thsand100thsbeusedinterchangeably?

Youpurchasedacaseof100beveragestosell.Wateris ofthecase,juice

boxesare ofthecase,andsodais

ofthecase.Changethefractionsabovetofractionswithadenominatorof100tofigureouttheexactnumberofeachbeverageyouhavetosell.Attheendoftheweek,yousoldALLofthewater, ofjuiceand ofsoda.

Tellhowmanybeveragesyousoldasafractionwith100asadenominator.


Task3:FractionstoDecimalsThenCompare4.NF.6‐Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.4.NF.7‐Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.BigIdea‐Decimalnotationforfractionswithdenominators10or100canberewrittenas0.1and0.01respectively.E.g.1/10and1/100willbewrittenas0.1and0.01.BigIdea–ComparingtwodecimalsorfractionscanonlybecomparedwhentheyarereferencingthesamewholeEssentialQuestion–Howarefractionsof10thsand100thsrepresentedasdecimals?EssentialQuestion‐Whenarethecomparisonoftwoormoredecimalsorfractionsvalid?

Foreachdayofyoursale,youneedtohavesomechangetostartwith.Youhave3quarters,8dimes,12nickels,and7pennies.Representeachoftheseamountsasafractionof10(ifpossible),100,andasadecimalamount.Comparetheamountofeachtypeofmoneyyoustartthedaywith(i.e.pennies,nickels,dimes,andquarters),usingthesymbols>,=,or<.Determinewhichtypeofmoneyyouhavethemostof,leastof,etc.



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Task4:EngagingScenario Description:Yourschoolishavingafundraiser.Youareinchargeofthedrinkandsnackstand.Youwillberesponsibleforsupplyingdrinksandsnackstosellduringparent‐teacherconferenceweek.Youwillbegivenachartwithpricesfromthreedifferentstores.Evaluatewhichstoresaregoingtobethebesttopurchaseyourproductsfrom.Youneedbuy100drinksand100snacks.Theseamountsneedtobeshownasfractionswithadenominatorof100.Youcouldbuyanequalamountofeachdrinkorsnack,youcouldbuyhalfofonetypeofdrink/snackandhalfanother,youcouldbuyallofthesamedrink/snack,etc.Findthetotalyouwillspendondrinksandonsnacks.Representthatonthechartbelow.SeeExampleonpage14.


AuthenticPerformanceTask1

Name:Task1:PurchaseofProduct Suggested

LengthDays:3‐5Mins/Day:60

StandardsAddressed

PriorityStandards

CCSSMath StandardsforMathematicalPractice

Task1:PurchaseofProduct.4.NF.4‐Applyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.a.Understandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).b.Understandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)c.Solvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?BigIdea–WewillusevisualmodelsandequationstorepresentmultiplicationoffractionsEssentialQuestion–Howdoyourepresentmultiplyingfractionswithwholenumbersincomputationandwordproblems?

☐Makesenseofproblemsandpersevereinsolvingthem☒Reasonabstractlyandquantitatively☒Constructviableargumentsandcritiquethereasoningofothers☒Modelwithmathematics☐Useappropriatetoolsstrategically☒Attendtoprecision☐Lookforandmakeuseofstructure☐Lookforandexpressregularityinrepeatedreasoning

SupportingStandardsCCSSMath CCSSELA NGELD


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4.MD.2‐Usethefouroperationstosolvewordproblemsinvolvingdistances,intervalsoftime,liquidvolumes,massesofobjects,andmoney,includingproblemsinvolvingsimplefractionsordecimals,andproblemsthatrequireexpressingmeasurementsgiveninalargerunitintermsofasmallerunit.Representmeasurementquantitiesusingdiagramssuchasnumberlinediagramsthatfeatureameasurementscale.4.OA.3–Solvemultistepwordproblemsposedwithwholenumbersandhavingwhole‐numberanswersusingthefouroperations,includingproblemsinwhichremaindersmuchbeinterpreted.RepresenttheseproblemsusingequationswithaletterstandingfortheunknownquantityAssessthereasonablenessofanswersusingmentalcomputationandestimationsstrategiesincludingrounding.

RI.4.4Determinethemeaningofgeneralacademicanddomain‐specificwordsorphrasesinatextrelevanttoagrade4topicorsubjectarea.RI.4.7Interpretinformationpresentedvisually,orally,orquantitatively(e.g.,incharts,graphs,diagrams,timelines,animations,orinteractiveelementsonWebpages)andexplainhowtheinformationcontributestoanunderstandingofthetextinwhichitappears.L.4.4.a‐cDetermineorclarifythemeaningofunknownandmultiple‐meaningwordsandphrasesbasedongrade4readingandcontent,choosingflexiblyfromarangeofstrategies.L.4.6Acquireanduseaccuratelygrade‐appropriategeneralacademicanddomain‐specificwordsandphrases,includingthosethatsignalpreciseactions,emotions,orstatesofbeing(e.g.,quizzed,whined,stammered)andthatarebasictoaparticulartopic(e.g.,wildlife,conservation,andendangeredwhendiscussinganimalpreservation).

ELD.4.I.B.6(RI.4.1,RI.4.4,L.4.3)Readingcloselyliteraryandinformationaltextsandviewingmultimediatodeterminehowmeaningisconveyedexplicitlyandimplicitlythroughlanguage.ELD.4.I.B.7(L.4.3,L.4.5.c)ListeningactivelytospokenEnglishinarangeofsocialandacademiccontext.ELD.4.I.A.2(L.4.6)Interactingwithothersinwritinglanguageinvariouscommunicativeforms(print,communicativetechnology,andmulti‐media).ELD.4.I.C.10(W.4.2.d,W.4.10)Writingliteraryandinformationaltexttopresent,describe,andexplainideasandinformation,usingappropriatetechnology.ELD.4.II.A.1(W.4.2.d)UnderstandingTextstructure.ELD.4.II.A.2(W.4.2.d)Understandingcohesion

TeachingandLearningProgression

Suggestions:Teachstudentstoapplyandextendpreviousunderstandingsofmultiplicationtomultiplyafractionbyawholenumber.BY…a.Teachingthemtounderstandafractiona/basamultipleof1/b.Forexample,useavisualfractionmodeltorepresent5/4astheproduct5×(1/4),recordingtheconclusionbytheequation5/4=5×(1/4).b.Teachingthemtounderstandamultipleofa/basamultipleof1/b,andusethisunderstandingtomultiplyafractionbyawholenumber.Forexample,useavisualfractionmodeltoexpress3×(2/5)as6×(1/5),recognizingthisproductas6/5.(Ingeneral,n×(a/b)=(n×a)/b.)c.Teachingthemtosolvewordproblemsinvolvingmultiplicationofafractionbyawholenumber,e.g.,byusingvisualfractionmodelsandequationstorepresenttheproblem.Forexample,ifeachpersonatapartywilleat3/8ofapoundofroastbeef,andtherewillbe5peopleattheparty,howmanypoundsofroastbeefwillbeneeded?Betweenwhattwowholenumbersdoesyouranswerlie?

Resources:See4thGradeCaliforniaMathematicsFramework:http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradefour.pdfEngageNewYorkCommonCoreGeorgiaPerformanceStandards(CCGPS)www.learnzillions.comwww.commoncoresheets.comYouhavepurchasedsnacksforyourweekofsales.Snackswereboughtinmixandmatchcasesof32itemseach.Yourcaseismadeupof popcorn, chips, cookies,and crackers.

Representeachofthesefractionsasafactorofthewholecase.Youbought4casesofsnacksatthebeginningoftheweek.Attheendoftheweek,youhaveofyourpopcorn, ofyourchips, ofyourcookies,and ofyourcrackersleftover.

Representeachofthesefractionsasafactorofthewholeamountofsnacksyoubeganwith.

Bloom’s DOK2 1

ScoringRubric4–Thorough3–Adequate2–Partial1–Minimal

InstructionalStrategiesAllStudents SWD ELs Enrichment

CooperativeGroupingwithassignedroles

StudyBuddy

Graphicorganizers Differentiated

instruction


instruction

CooperativeGroupingwithassignedroles.

Morechallengingwork


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Think‐Pair‐Share Clearexpectationsand

examples Addressinglearning

modalities/Accommodatinglearningstylepreferences.

Repetition Manipulatives Modifiedcurriculum Additionaltime

www.alvordusdrcd.org

Repetition Manipulatives

aboveandbeyondgradelevel.

Tieredassignments.


Name:Task2:Denominatorsof10to100 Suggested


StandardsAddressed

PriorityStandards


Task2:Denominatorsof10to1004.NF.5‐Expressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.2Forexample,express3/10as30/100,andadd3/10+4/100=34/100.BigIdea–Tenthsandhundredthscanbeusedwhenfindingequivalentfractionstoaddthemtogether.EssentialQuestion–Whencan10thsand100thsbeusedinterchangeably?

☐Makesenseofproblemsandpersevereinsolvingthem☒Reasonabstractlyandquantitatively☒Constructviableargumentsandcritiquethereasoningofothers☒Modelwithmathematics☐Useappropriatetoolsstrategically☒Attendtoprecision☐Lookforandmakeuseofstructure☐Lookforandexpressregularityinrepeatedreasoning




ELD.4.I.B.6(RI.4.1,RI.4.4,L.4.3)Readingcloselyliteraryandinformationaltextsandviewingmultimediatodeterminehowmeaningisconveyedexplicitlyandimplicitlythroughlanguage.ELD.4.I.B.7(L.4.3,L.4.5.c)ListeningactivelytospokenEnglishinarangeofsocialandacademiccontext.ELD.4.I.A.2(L.4.6)Interactingwithothersinwritinglanguageinvariouscommunicativeforms(print,communicativetechnology,andmulti‐media).ELD.4.I.C.10(W.4.2.d,W.4.10)Writingliteraryandinformationaltexttopresent,describe,andexplainideasandinformation,usingappropriatetechnology.


Suggestions:Teachstudentstoexpressafractionwithdenominator10asanequivalentfractionwithdenominator100,andusethistechniquetoaddtwofractionswithrespectivedenominators10and100.Forexample,express3/10as30/100,andadd3/10+4/100=34/100.

Bloom’s DOK2 1ScoringRubric4–Thorough3–Adequate2–Partial1–Minimal


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Resources:See4thGradeCaliforniaMathematicsFramework:http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradefour.pdfEngageNewYorkCommonCoreGeorgiaPerformanceStandards(CCGPS)www.learnzillions.comwww.commoncoresheets.comYoupurchasedacaseof100beveragestosell.Wateris ofthecase,juiceboxesare

ofthecase,andsodais ofthecase.

Changethefractionsabovetofractionswithadenominatorof100tofigureouttheexactnumberofeachbeverageyouhavetosell.Attheendoftheweek,yousoldALLofthewater, ofjuiceand ofsoda.Tellhow

manybeveragesyousoldasafractionwith100asadenominator.



StudyBuddy Think‐Pair‐Share Clearexpectationsand




instruction Repetition Manipulatives Modifiedcurriculum Additionaltime



instruction Repetition Manipulatives


Morechallengingworkaboveandbeyondgradelevel.

Tieredassignments.


Name:Task3:FractionstoDecimalsThenCompare Suggested


StandardsAddressed

PriorityStandards


Task3:4.NF.6‐Usedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100;describealengthas0.62meters;locate0.62onanumberlinediagram.BigIdea‐Decimalnotationforfractionswithdenominators10or100canberewrittenas0.1and0.01respectively.E.g.1/10and1/100will

☒Makesenseofproblemsandpersevereinsolvingthem☒Reasonabstractlyandquantitatively☒Constructviableargumentsandcritiquethereasoningofothers☒Modelwithmathematics


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bewrittenas0.1and0.01.EssentialQuestion–Howarefractionsof10thsand100thsrepresentedasdecimals?4.NF.7‐Comparetwodecimalstohundredthsbyreasoningabouttheirsize.Recognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Recordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheconclusions,e.g.,byusingavisualmodel.BigIdea–ComparingtwodecimalsorfractionscanonlybecomparedwhentheyarereferencingthesamewholeEssentialQuestion‐Whenarethecomparisonoftwoormoredecimalsorfractionsvalid?

☐Useappropriatetoolsstrategically☒Attendtoprecision☐Lookforandmakeuseofstructure☐Lookforandexpressregularityinrepeatedreasoning




ELD.4.I.B.6(RI.4.1,RI.4.4,L.4.3)Readingcloselyliteraryandinformationaltextsandviewingmultimediatodeterminehowmeaningisconveyedexplicitlyandimplicitlythroughlanguage.ELD.4.I.B.7(L.4.3,L.4.5.c)ListeningactivelytospokenEnglishinarangeofsocialandacademiccontext.ELD.4.I.A.2(L.4.6)Interactingwithothersinwritinglanguageinvariouscommunicativeforms(print,communicativetechnology,andmulti‐media).ELD.4.I.C.10(W.4.2.d,W.4.10)Writingliteraryandinformationaltexttopresent,describe,andexplainideasandinformation,usingappropriatetechnology.ELD.4.II.A.1(W.4.2.d)UnderstandingTextstructure.ELD.4.II.A.2(W.4.2.d)Understandingcohesion


Suggestions:Teachstudentstousedecimalnotationforfractionswithdenominators10or100.Forexample,rewrite0.62as62/100ORDescribealengthas0.62metersORLocate0.62onanumberlinediagram.

Bloom’s DOK

2 1ScoringRubric


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Resources:See4thGradeCaliforniaMathematicsFramework:http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradefour.pdfEngageNewYorkCommonCoreGeorgiaPerformanceStandards(CCGPS)www.learnzillions.comwww.commoncoresheets.comForeachdayofyoursale,youneedtohavesomechangetostartwith.Youhave3quarters,8dimes,12nickels,and7pennies.

Representeachoftheseamountsasafractionof10(ifpossible),100,andasadecimalamount.

Suggestions:Teachstudentstocomparedecimalstohundredthsbyreasoningabouttheirsizeandtorecognizethatcomparisonsarevalidonlywhenthetwodecimalsrefertothesamewhole.Studentsshouldbeabletorecordtheresultsofcomparisonswiththesymbols>,=,or<,andjustifytheirconclusionsbyusingavisualmodel.

Resources:

See4thGradeCaliforniaMathematicsFramework:http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradefour.pdfEngageNewYorkCommonCoreGeorgiaPerformanceStandards(CCGPS)www.learnzillions.comwww.commoncoresheets.comUsingtask3,comparetheamountofeachtypeofmoneyyoustartthedaywith(i.e.pennies,nickels,dimes,andquarters),usingthesymbols>,=,or<.

Determinewhichtypeofmoneyyouhavethemostof,leastof,etc.

4–Thorough3–Adequate2–Partial1–Minimal



StudyBuddy Think‐Pair‐Share Clearexpectationsand




instruction Repetition Manipulatives Modifiedcurriculum Additionaltime



instruction Repetition Manipulatives


Morechallengingworkaboveandbeyondgradelevel.

Tieredassignments.


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Task 4 (Engaging Scenario)

DetailedDescription(situation,challenge,role,audience,productorperformance)Description:Yourschoolishavingafundraiser.Youareinchargeofthedrinkandsnackstand.Youwillberesponsibleforsupplyingdrinksandsnackstosellduringparent‐teacherconferenceweek.Youwillbegivenachartwithpricesfromthreedifferentstores.Evaluatewhichstoresaregoingtobethebesttopurchaseyourproductsfrom.Youneedbuy100drinksand100snacks.Theseamountsneedtobeshownasfractionswithadenominatorof100.Youcouldbuyanequalamountofeachdrinkorsnack,youcouldbuyhalfofonetypeofdrink/snackandhalfanother,youcouldbuyallofthesamedrink/snack,etc.Findthetotalyouwillspendondrinksandonsnacks.Representthatonthechartbelow.SeeExample.

Drinks Snacks

PricePerSoda

PricePerJuiceBox

PricePerGatorade

PricePerWaterBottle

PricePerPackofPopcorn

PricePerBagofChips

PricePerPackofCookies

PricePerPackofCrackers

Costco $0.25 $0.20 $0.80 $0.10 $0.99 $0.75 $0.70 $0.75

Wal‐Mart $0.50 $0.15 $0.75 $0.30 $0.95 $0.85 $0.65 $0.75Vons $0.75 $0.25 $0.75 $0.20 $0.99 $0.99 $0.80 $0.75

Drink FractionBought Store PricePerType AmountBoughtTotalForEach

DrinkSoda JuiceBoxes Gatorade Water

TotalofAllDrinks:

Snacks FractionBought Store PricePerType AmountBoughtTotalForEach

SnackPopcorn Chips Cookies Crackers

TotalofAllSnacks: ForExample:

Drink FractionBought Store PricePerType AmountBought TotalForEachDrink

Soda 25/100 Costco $0.25 25 $6.25JuiceBoxes 25/100 Walmart $0.15 25 $3.75

Gatorade 25/100 Vons $0.75 25 $18.75Water 25/100 Costco $0.10 25 $2.50

TotalofAllDrinks: $31.25Snacks FractionBought Store PricePerType AmountBought TotalForEach

Snack

Popcorn 25/100 Walmart $0.95 25 $23.75Chips 25/100 Costco $0.75 25 $18.75

Cookies 25/100 Walmart $0.65 25 $16.25Crackers 25/100 Vons $0.75 25 $18.75

TotalofAllSnacks: $77.50

Basedonhowmuchyouspent,howmuchwillyouchargeforyourdrinks?Howmuchwillyouchargeforyoursnacks?Ifyousoldeverythingyoubought(100drinks,100snacks),wereyoursalesprofitable?Forexample:IfIcharge$0.50oneachdrink,Iwillmake$50whichisaprofitof$18.75.IfIcharged$1.00foreachsnack,Iwillmake$100whichisaprofitof$22.50(Allinformationisbasedontheexamplechartabove.)Youwillresearchandgatheryourinformationindividuallyandplaceyourdataintoyourchart.Youwillthenmeetinsmallgroups,shareyourinformation,andvoteonthesalesthatyourgroupfindstobethemostprofitable.Yourgroupwillneedtopresentyourreporttoyourclassandmakeanargumentastowhyyoupickedthepricesyoudid,whetheryoursalewasprofitable,andhowmuchmoneyyoumade/lost.


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CooperativeGroupingwithassignedrolesStudyBuddyThink‐Pair‐ShareClearexpectationsandexamplesAddressinglearningmodalities/Accommodatinglearningstylepreferences.

GraphicorganizersDifferentiatedinstructionRepetitionManipulativesModifiedcurriculumAdditionaltime


GraphicorganizersDifferentiatedinstructionRepetitionManipulatives

CooperativeGroupingwithassignedroles.Morechallengingworkaboveandbeyondgradelevel.Tieredassignments.

FeedbacktoCurriculumTeamReflectontheteachingandlearningprocesswithinthisunitofstudy.Whatweresomesuccessesandchallengesthatmightbehelpfulwhenrefiningthisunitofstudy?

Successes Challenges

StudentPerspective

TeacherPerspective