EurekaRemediationTool:Grade6
Module2,TopicB
Tobecomemathematicallyproficient,studentsmustaccesson-grade-levelcontent.Thisdocumentaimstohelpteacherswhouse
theEurekacurriculumtotargetremediationforstudentsneedingextrasupportbeforeandduringapproachingon-grade-levelwork,
creatingopportunitiesforon-timeremediationdirectlyconnectedtothenewlearning.
AboutthisTopic
FocusStandards:
6.NS.B.3:Fluentlyadd,subtract,multiply,anddividemulti-digit
decimalsusingthestandardalgorithmforeachoperation.
TopicOverviewpertheEurekaCurriculum
Priortodivisionofdecimals,studentsrevisitalldecimaloperations
inTopicB.Studentshavehadextensiveexperiencewithdecimal
operationstothehundredthsandthousandths(5.NBT.B.7),which
preparesthemtoeasilycomputewithmoredecimalplaces.
Studentsbeginbyrelatingthefirstlessoninthistopictomixed
numbersfromthelastlessoninTopicA.Theyfindthatsumsand
differencesoflargemixednumberscanbemoreefficiently
determinedbyfirstconvertingtoadecimalandthenapplyingthe
standardalgorithms(6.NS.B.3).Withindecimalmultiplication,
studentsbegintopracticethedistributiveproperty.Studentsuse
arraysandpartialproductstounderstandandapplythe
distributivepropertyastheysolvemultiplicationproblems
involvingdecimals.Placevalueenablesstudentstodeterminethe
placementofthedecimalpointinproductsandrecognizethatthe
sizeofaproductisrelativetoeachfactor.Studentsdiscoverand
useconnectionsbetweenfractionmultiplicationanddecimal
multiplication.
ThisEurekaRemediationToolisconsidereda“living”documentaswebelievethatteachersandothereducatorswillfindwaystoimprovethedocumentas
theyuseit.PleasesendfeedbacktoLouisianaTeacherLeaders@la.govsothatwecanuseyourinputwhenupdatingthisguide.
EurekaRemediationTool:Grade6
Module2,TopicB
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
EurekaModule2,TopicB
PartA:5.NBT.B.7Addition
1. Findthesum.Explainand/orshowyourwork.
0.34+0.05
2. Findthesum.Explainorshowyourwork.
2.1+1.4=
3. Findthesum.Explainorshowyourwork
3.08+8.94=
PartB.5.NBT.B.7Subtraction
4. Findthedifference.Explainorshowyourwork.
8.01–0.04=
5. 5.Findthedifference.Explainorshowyourwork.
0.76–4.8=
6. Findthedifference.Explainorshowyourwork.
4–0.38=
PartC.5.NBT.7Multiplication
7. 7.Findtheproduct.Explainorshowyourwork.
4x0.06=
8. 8.Findtheproduct.Explainorshowyourwork.
0.42x2=
9. 9.Findtheproduct.Explainorshowyourwork.
0.5x1.32=
DiagnosticAssessmentKey:Grade6
EurekaModule2,TopicB
Solutions:
1. 0.39
2. 3.5
3. 12.02
4. 8.03
5. 2.8
6. 3.962
7. 2.4
8. 0.84
9. 0.66
RemediationGuidance:Grade6
EurekaModule2,TopicB
PartAFocus:5.NBT.B.7–Add,subtract,multiply,anddividedecimalstohundredths,usingconcretemodelsordrawingsandstrategiesbasedon
placevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction;justifythereasoningusedwithawritten
explanation.
Whythisisimportantforcurrentgradelevelwork:
Inorderforstudentstobecomefluentwiththestandardalgorithmofaddingdecimalsingrade6,place
valueconceptsmustbeunderstood.Studentsshouldrecognizethatjustaswithwholenumber
addition,likeunitsmustbeaddedtogetherandbundledorcarriedtothenextplacewhenthereareten
ormoreofthatunit.Placevaluecharts,disks,and/orbasetenpiecesmaybeprovidedforstudentuse
whencompletingthediagnosticassessment.Mentalmathwithawrittenjustificationshouldbe
encouragedforhigherstudents.
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem1
Studentsshouldconnectthe
problemtoadditionofwhole
numbersbyaddinglikeunits,
tenths+tenths=tenths,and
hundredths+hundredths=
hundredths
Problem2
Studentsshoulddeterminethat
since13tenthsisafractionor
decimalgreaterthanone,it
mustbeconvertedtoonewhole
andthreetenths.After
converting,likeunitsshouldbe
added.
RemediationResourcesforTargeted
Instruction:
5thGrade,Module1,TopicD,
Lesson9
UsetheConceptDevelopmentportion
Problem3
oftheLessonandasamplingof
Takenoteastowhether
studentsareabletobundlelike problemsfromtheProblemSetthat
unitsandcarrytothenextplace. focusonconceptualunderstanding
Studentsmayalsousethepartial andproceduralskillandfluency.
summethodtoadd.
RemediationGuidance:Grade6
EurekaModule2,TopicB
PartBFocus:5.NBT.B.7–Add,subtract,multiply,anddividedecimalstohundredths,usingconcretemodelsordrawingsandstrategiesbasedon
placevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction;justifythereasoningusedwithawritten
explanation.
Whythisisimportantforcurrentgradelevelwork:
Inorderforstudentstobecomefluentwiththestandardalgorithmofsubtractingmulti-digitdecimalsin
grade6,theroleofplacevalueconceptsinsubtractionmustbeunderstood.Studentsshouldrecognize
thatjustaswithwholenumbersubtraction,likeunitsmustbetakenfromlikeunits.Studentsshould
haveaconceptualunderstandingofre-groupingunitsandrecognizethattheminuenddoesnotchange
whenithasbeenregrouped.Placevaluecharts,disks,and/orbasetenpiecesmaybeprovidedfor
RemediationResourcesforTargeted
studentusewhencompletingthediagnosticassessment.Mentalmathwithawrittenjustification
Instruction:
shouldbeencouragedforhigherstudents.
UsingtheDiagnosticAssessmenttoidentifygaps:
5thGrade,Module1,TopicD,
Problem4
Problem5
Problem6
Lesson10
Whenstudentswritethe
Studentsmayuseamentalmath Studentsmayuseamental
standardnumbersentence,
method,suchascounting-upby strategytosolvethisproblem.
UsetheConceptDevelopmentportion
makesuretheyhaveplaceda0
firstchanging4.8to48-tenths
Since38-hundredthsand62oftheLessonandasamplingof
inthetenthsplaceforeach
andcountingupfrom48–tenths hundredthsmakeawhole,then problemsfromtheProblemSetthat
number.Itisnotnecessaryfor
to76-tenths,calculating28thedifferenceis3wholesand
focusonconceptualunderstanding
studentstouse0asa
tenths,thenconverting2862-hundredths,3.62
andproceduralskillandfluency.
placeholderinthesubtrahend.
tenthsto2.8.Ifstudentsusethe
Studentsmaycomputethis
standardalgorithm,makesure
problemmentallyandexplain
theyhaveconverted78-tenths
thatbecausetheonlything
to7.8andlined-uptheir
beingsubtractedwas4decimalscorrectly.
hundredths,theonesplace
wouldnotchange.
RemediationGuidance:Grade6
EurekaModule2,TopicB
PartCFocus:5.NBT.B.7–Add,subtract,multiply,anddividedecimalstohundredths,usingconcretemodelsordrawingsandstrategiesbasedon
placevalue,propertiesofoperations,and/ortherelationshipbetweenadditionandsubtraction;justifythereasoningusedwithawritten
explanation.
Whythisisimportantforcurrentgradelevelwork:
Relatingdecimalmultiplicationtowhole-numbermultiplicationwillsupporttheconnectionbetween
thestandardalgorithmofwhole-numbermultiplicationtothestandardalgorithmofdecimal
multiplication.Afocusonthedistributivepropertyandtheareamodelcanhelpstudentsuseplace
valueunderstandingtodecomposeunitsandmultiplyusingplacevalueconcepts.Estimationstrategies
arealsoimportantindeterminingdecimalplacementandthereasonablenessofananswer.Placevalue
charts,disks,and/orbasetenpiecesmaybeprovidedforstudentusewhencompletingthediagnostic
assessment.Mentalmathwithawrittenjustificationshouldbeencouragedforhigherstudents.
UsingtheDiagnosticAssessmenttoidentifygaps:
RemediationResourcesforTargeted
Instruction:
5thGrade,Module1,TopicE,
Lesson(s)11-12
Problem7
Problem8
Problem9
Studentsshouldrelatethis
Studentsshouldrelatethis
Studentmayviewthenumberas UsetheConceptDevelopmentportion
problemtowhole-number
problemtowhole-number
132hundredthsandthen
ofeachLessonandasamplingof
multiplication,knowingthatfour multiplicationandreasonif2
decomposeitandusethearea
problemsfromtheProblemSetthat
copiesof6-onesis24ones,4
groupsof42is84,then2groups modeland/ordistributive
focusonconceptualunderstanding
copiesof6-tenthsis24-tenths
of42-hundredthsis84propertytomultiplymentally
andproceduralskillandfluency.
whichis2.4.Studentsmaywrite hundredthsor.84.
andaddthepartialproducts.½a theiranswerasamixednumber.
groupof100is50,½agroupof
30is15and½agroupof2is1.
30-hundredths+15-hundredths
+1hundredthis66-hundredths
or.66.