EurekaRemediationTool:Grade6
Module1,TopicC
Tobecomemathematicallyproficient,studentsmustaccesson-gradelevelcontent.ThisdocumentaimstohelpteacherswhousetheEureka
curriculumtotargetremediationforstudentsneedingextrasupport
beforeandduringapproachingon-grade-levelwork,creating
opportunitiesforon-timeremediationdirectlyconnectedtothenew
learning.
AboutthisTopic
FocusStandards:
6.RP.A.2:Understandtheconceptofaunitratea/bassociatedwitharatioa:b
withb≠0,anduseratelanguageinthecontextofaratiorelationship.For
example,“Thisrecipehasaratioof3cupsofflourto4cupsofsugar,sothereis
3/4cupofflourforeachcupofsugar.”“Wepaid$75for15hamburgers,which
isarateof$5perhamburger.”
6.RP.A.3:Useratioandratereasoningtosolvereal-worldandmathematical
problems,e.g.,byreasoningabouttablesofequivalentratios,tapediagrams,
doublenumberlinediagrams,orequations.
b. Solveunitrateproblemsincludingthoseinvolvingunitpricingand
constantspeed.Forexample,ifittook7hourstomow4lawns,
thenatthatrate,howmanylawnscouldbemowedin35hours?
Atwhatunitratewerelawnsbeingmowed?
d. Useratioreasoningtoconvertmeasurementunits;manipulate
andtransformunitsappropriatelywhenmultiplyingordividing
quantities.
Topic Overview per the Eureka Curriculum
InTopicC,studentsapplytheirunderstandingofratiosandthevalueofa
ratioastheycometounderstandthataratiorelationshipof5milesto2
hourscorrespondstoarateof2.5milesperhour,wheretheunitrateisthe
numericalpartoftherate,2.5,andmilesperhouristhenewlyformedunitof
measurementoftherate(6.RP.A.2).ThroughoutTopicC,studentscontinue
tomakeuseoftherepresentationsanddiagramsofTopicsAandBasthey
investigatetheconceptsofthistopicwithinthecontextofreal-worldrate
problems.InLesson16,studentsdeveloptheirvocabularyandconceptual
understandingofrateastheyworkthroughanddiscussproblemsthatrequire
expressingsimpleratiosasratesusingphrasessuchas‘per’,‘foreach’and
‘forevery’.InLesson17,studentsreinforcetheirunderstandingastheysee
problemsforthefirsttimewheretheratiorelationshipisexpressedinrate
form.Studentsareaskedtoverbalizeanddepicttheunderlyingratio
relationshipasacollectionofequivalentratios.
InLesson18,studentsgeneralizetheprocessforfindingarateanddefinethe
termunitraterelatingittothevalueofaratio.Intheremaininglessonsof
TopicC,studentssolveunitrateproblemsinvolvingunitpricing,constant
speed,andconstantratesofwork(6.RP.A.3b).Theycombinetheirnew
understandingofratetoconnectandrevisitconceptsofconvertingamong
different-sizedstandardmeasurementunits(5.MD.A.1).Theythenexpand
uponthisbackgroundastheylearntomanipulateandtransformunitswhen
multiplyinganddividingquantities(6.RP.A.3d).InLessons19–20,studentsare
conscientiousconsumers,andcomparisonshopbycomparingunitpricesand
convertingmeasurementunitsasneeded.Forinstance,whencomparinga
10-ouncebagofsaladthatsellsfor$2.25toa1-poundbagofsaladthat
retailsfor$3.50,studentsrecognizethatinadditiontofindingaunitprice,
theymustconvertpoundstoouncesforanaccuratecomparison.
InLessons21–22,studentsconductreal-worldsimulationsthatgeneraterates
relatedtospeedandwork.Indoingso,studentsbegintoviewmathasatool
forsolvingreal-lifeproblems.TopicCconcludeswithLesson23,inwhich
studentsdrawupontheirexperiencesinpreviousmodelinglessonsto
demonstratetheirabilitytoproblem-solveusingrates,unitrates,and
conversions.
ThisEurekaRemediationToolisconsidereda“living”documentaswebelievethatteachersandothereducatorswillfindwaystoimprovethedocumentas
theyuseit.PleasesendfeedbacktoLouisianaTeacherLeaders@la.govsothatwecanuseyourinputwhenupdatingthisguide.
EurekaRemediationTool:Grade6
Module1,TopicC
Overview
EurekaRemediationToolsinclude:
1. adiagnosticassessmenttohelpteachersdetermine
themisunderstandingsorgapsinmathematical
knowledgerelatedtoaspecificTopicintheEureka
curriculum
2. guidanceforteacherstoanalyzestudentworkonthe
diagnosticassessment
3. suggestedmaterialsfortargetedremedialinstruction
Note:Theuseofthisguidanceisnot
intendedtodelaystudents’
engagementwithon-grade-level
learning.On-grade-levellearning
shouldbethefocusofinstructional
timeandbetreatedasanopportunity
forstudentsto“finish”learning
previousskillsanddeepenconceptual
understanding.
DiagnosticAssessment
Thediagnosticassessmentisdesignedtobeadministeredtotargetedstudentspriortobeginning
instructiononthegivenTopic.Whenappropriate,itisbrokenintoparts(PartA,PartB,andsoon);each
partaddressesadifferentprerequisitestandardandcontainsthreeproblems.Ifastudentcorrectly
answersatleast2outofthe3problems,itcanbeassumedthathe/sheisreadytoengagewiththenew
contentoftheTopicwithlittletonosupportneededpriortoengagingwiththeTopic.Thediagnostic
assessmentisdesignedinthiswaysothatteacherscandeterminethe“entrypoint”toremedial
instructionand/oropportunitiesforunfinishedlearningwithinthecontextofthenewlearning.Theentry
pointsandopportunitiesforunfinishedlearningwillvarybetweenstudents.
GuidanceforRemediation
TheRemediationGuidanceisdesignedforteacheruse.Itisalsobrokenintoparts(PartA,PartB,andso
on)andcorrelatestothepartsonthediagnosticassessment.Eachpartcontainsthefollowing:
1. Thefocusstandard:Thefocusstandardsarestrategicallychosentoaddressprerequisiteskillsand
arepurposefullyarrangedintheorderthatstudentstypicallymastertheskillsandknowledge.
2. Whythisisimportantforcurrentgradelevelwork:Thissectiondescribeshowtheworkofthe
prerequisitestandardrelatestothestandard(s)addressedintheTopicofinstruction.
3. Usingthediagnosticassessmenttoidentifygaps:Thissectionidentifiescommonerrorsstudents
makeonthediagnosticassessmentitems.
4. RemediationResourcesforTargetedInstruction:TheresourcespinpointspecificEurekalessons
andpartsoflessonsforteacherstousetoaddressgapsinmathematicalknowledge.UsingEureka
materialstoaddressremediationensuresalignmenttothestandards,consistencyinapproachto
learning,andsimilaritiesinstrategiesforsolvingproblems.
DiagnosticAssessment:Grade6
EurekaModule1,TopicC
PartA:5.MD.A.1:
Forthefollowingthreequestions,useamodeland/orshoworexplainhowyougotyour
answer.
1.Howmanymetersarein350centimeters?
2.Ifthereare20quartsin5gallons,howmanyquartsarein1gallon?
3.Suzyismakinganapplepieandherrecipecallsfor40ozofapples.Atthegrocerystore,
applesaresoldinpounds.Ifthereare16ouncesin1pound,howmanypoundsofapples
shouldSuzybuy?
PartB:5.NF.B.3
4.Writethefollowingfractionasawholenumber.Useadivisionsentencetoexplainhowyou
determinedyouranswer:
15
3
5.Alandscaperhas120bagsoffertilizerthathewilluseonbuildingflowerbedsforhis
customers.Ifthelandscaperhas25customers,howmanybagswillhebeabletouseforeach
customer?
6.Sarahismakingcookiesforherschoolparty.Therecipecallsfor9cupsofflourtomakefour
batchesofcookies.Ifeachbatchofcookiesusesanequalamountofflour,howmanycupsof
flourshouldSarahuseforeachbatchofcookies?
DiagnosticAssessmentKey:Grade6
EurekaModule1,TopicC
Solutions:
$
1. 3 %
2. 4
$
3. 2 %
4. 5;15dividedby3is5.
%&
(
%'
'
5. 4 or4 6.
)
(
$
or2 (
RemediationGuidance:Grade6
EurekaModule1,TopicC
PartAFocus:5.MD.A.1:Convertamongdifferent-sizedstandardmeasurementunitswithinagivenmeasurementandusetheconversionsin
solvingmulti-step,real-worldproblems(e.g.convert5cmto0.5m;9ftto108in).
Whythisisimportantforcurrentgradelevelwork:
Whensolvingratioandrateproblems,studentswilllinktheirpriorknowledgeofmeasurement
conversionstoequivalentratiosbyusingratiotablesandtapediagramstodiscoverthemultiplicative
relationshipbetweenequivalentunits.Buildingupontheirunderstandingofmultiplicativecomparison
asitrelatestomeasurementconversionswillhelpstudentsunderstandthatthevalueofaratioisaunit
rate.Studentsshouldbetaughtthattheunitrateisanexpressionofallequivalentratiosasitrelatesto
theunitsandcanthereforebeappliedtoconvertbetweenthetwounitswhenonevalueisknown.For
example,usingtherateof12inchesperfoot,studentswilldeterminethevalueoftheratioof12:1is
12.Furthermore,ifthereare12inchesinevery1foot,thentheremustbe18inchesin1½feetbecause
18is1wholegroupof12and½ofagroupof12;therefore,18dividedby12is1½and18/12is11/2.
Itisimportantthatstudentscanconnecttherelationshipbetweenamultiplicationexpression,division
expressionandvalueoftheratio.amultiplicationexpression,divisionexpressionandvalueoftheratio.
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem1:
Looktoseeifstudentsusean
additivestrategyora
multiplicativestrategytofind
theequivalentmeasurement.
Studentsmayuseatape
diagramtodetermine
equivalence.
RemediationResourcesforTargeted
Instruction:
5thGrade,Module2,TopicD,
Lesson(s)13-15
Problem2
Problem3
UsetheConceptDevelopmentportion
Inproblem2,studentsshould
Looktoseehowstudents
divide20by5todeterminethat interprettheremainder.Dothey ofeachLessonandasamplingof
problemsfromtheProblemSetthat
thereare4quartsin1gallon.In roundupto3pounds,round
sixthgrade,thisisonestrategy
downto2poundsordotheysee focusonconceptualunderstanding
andapplication.
forfindingthevalueoftheratio theleftoverouncesaspartofa
and/ortheunitrate.Higher
wholepound.Studentsshould
studentsmayusetheir
determinethatifthereare16
knowledgefromTopicAandBto ouncesin1pound,then8
setupequivalentratiostofind
ouncesmustbe½ofapound.
thenumberofquartsper1
Alsotakenoteastowhether
gallon.
studentsleavethefractionas
8/16orconvertisto½.½ofa
poundismorerelativeforthe
contextofthissituation.
RemediationGuidance:Grade6
EurekaModule1,TopicC
PartBFocus:5.NF.B.3:Interpretafractionasdivisionofthenumeratorbythedenominator(a/b=a÷b).Solvewordproblemsinvolvingdivision
ofwholenumbersleadingtoananswerintheformoffractionsormixednumbers,e.g.byusingvisualfractionmodelsorequationstorepresent
theproblem.
Whythisisimportantforcurrentgradelevelwork:
InTopicCstudentsmovefromratiostoratestounitrates,leveragingtheirunderstandingoffractions
tocomputeunitrates(i.e.,thevalueofaratioa:bexpressedasa/b).Giventhatratiosrequire
quantitieswhichrequirecontextstudentsshouldbecomfortablesolvingwordproblemsinvolving
division.Thethreeproblemspresentedherearefoundationaltotheproblemspresentedtostudentsin
thisTopic.
**NOTE:ThisstandardisalsoafoundationstandardforModule1,TopicA.Whiletherearesome
differencesinthequestionsandtheimportanceforgradelevelworkasitrelatestoTopicC,Itmaynot
benecessarytoidentifygapsforthisstandardifyouhavealreadydoneso.
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem4
Payattentiontothemodeland
theexplanation.On-level
studentswillusedivisionor
informalproportionalreasoning.
Forexample,ifthereare15thirdsandevery3/3is1whole
then15/3is5wholes.If
studentsusedivision,takenote
astowhetheritisdueto
conceptualunderstanding
(similartoexamplestated
above)orbecausetheyare
followingaruleforconverting
betweenfractionsgreaterthan
St1andwholenumbers.
Problem5
Studentsshouldinterpretthe
remainderasafractionofabag
percustomer.Studentsmay
simplifythefractionto44/5or
leaveitas420/25.
RemediationResourcesforTargeted
Instruction:
5thGrade,Module4,TopicB,Lesson(s)
2-5
Problem6
Studentsshoulddeterminethat UsetheConceptDevelopmentportion
ofeachLessonandasamplingof
ninecupsofflourneedtobe
problemsfromtheProblemSet
dividedintofourequalgroups.
Studentsmayleavetheanswer focusedonconceptualunderstanding
andapplication.Lesson5issolely
as9/4=2¼cupofflourwhile
othersmaydivide9by4andget devotedtoapplication,usingitems
analogoustoitems4-6onthe
2¼.
diagnostic.