EurekaRemediationTool:Grade4
Module1,TopicA
Tobecomemathematicallyproficient,studentsmustaccesson-grade-levelcontent.Thisdocumentaimstohelpteacherswhouse
theEurekacurriculumtotargetremediationforstudentsneedingextrasupportbeforeandduringapproachingon-grade-levelwork,
creatingopportunitiesforon-timeremediationdirectlyconnectedtothenewlearning.
AboutthisTopic
FocusStandards:
4.OA.A.1:Interpretamultiplicationequationasacomparisonandrepresent
Topic Overview per the Eureka Curriculum
verbalstatementsofmultiplicativecomparisonsasmultiplicationequations,
e.g.,interpret35=5x7asastatementthat35is5timesasmanyas7,and7
InTopicA,studentsbuildtheplacevaluechartto1millionand
timesasmanyas5.
learntherelationshipbetweeneachplacevalueas10timesthe
valueoftheplacetotheright.Studentsmanipulatenumbersto
4.OA.A.2:Multiplyordividetosolvewordproblemsinvolvingmultiplicative
seethisrelationship,suchas30hundredscomposedas3
comparison,e.g.,byusingdrawingsand/orequationswithasymbolforthe
thousands.Theydecomposenumberstoseethat7thousandsis
unknownnumbertorepresenttheproblem,distinguishingmultiplicative
thesameas70hundreds.Asstudentsbuildtheplacevaluechart
comparisonfromadditivecomparison.
intothousandsandupto1million,thesequenceofthreedigitsis
4.NBT.A.1:Recognizethatinamulti-digitwholenumberlessthanorequalto
emphasized.Theybecomefamiliarwiththebasethousandunit
1,000,000,adigitinoneplacerepresentstentimeswhatitrepresentsinthe
namesupto1billion.Studentsfluentlywritenumbersinmultiple
formats:asdigits,inunitform,aswords,andinexpandedformup
placetoitsright.Forexample,(1)recognizethat700÷70=10;(2)inthe
to1million.
number7,246,the2represents200,butinthenumber7,426the2represents
20,recognizingthat200istentimesaslargeas20,byapplyingconceptsof
placevalueanddivision.
4.NBT.A.2:Readandwritemulti-digitwholenumberslessthanorequalto1,000,000usingbase-tennumerals,numbernames,andexpanded
form.Comparetwomulti-digitnumbersbasedonmeaningsofthedigitsineachplace,using>,=,and<symbolstorecordtheresultsof
comparisons.
ThisEurekaRemediationToolisconsidereda“living”documentaswebelievethatteachersandothereducatorswillfindwaystoimprovethedocumentas
theyuseit.PleasesendfeedbacktoLouisianaTeacherLeaders@la.govsothatwecanuseyourinputwhenupdatingthisguide.
EurekaRemediationTool:Grade4
Module1,TopicA
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:Grade4
EurekaModule1,TopicA
PartA:3.OA.A.1:
1. Writeanumbersentencethatcouldbeusedtorepresentthetotalnumberofdotsin
themodelbelow.
2. Drawamodeltorepresent3×5.
3. Interpretandcomputetheproduct10×10.Useamodeltosupportyouranswer.
PartB:2.NBT.A.1:
4. Whatisthevalueofthe5in345?Drawamodelornumberbondtosupportyour
answer.
5. Whatisthevalueofthe5in456?Drawamodelornumberbondtosupportyour
answer.
6. Whatisthevalueofthe5in509?Drawamodelornumberbondtosupportyour
answer.
PartC:2.NBT.A.3:
7. Writethefollowingnumberinstandardform:
sevenhundredninety-five
8. Writethefollowingnumberinexpandedform:
980
9. Writethefollowingnumberinstandardform:
500+6
DiagnosticAssessmentKey:Grade4
EurekaModule1,TopicA
Solutions:
1. 4×3
2. modelswillvary
3. thetotalnumberofobjectsin10groupsof10objectseach;100(sample)
4. 5ones
5. 5tens(sample)
6. 5hundreds(sample)
7. 795
8. 900+80(sample)
9. 506
RemediationGuidance:Grade4
EurekaModule1,TopicA
PartAFocus:3.OA.A.1Interpretproductsofwholenumbers,e.g.,interpret5×7asthetotalnumberofobjectsin5groupsof7objectseach.For
example,describeacontextinwhichatotalnumberofobjectscanbeexpressedas5×7.
Whythisisimportantforcurrentgradelevelwork:
Lesson1focussesoninterpretingamultiplicationequationasacomparison,leadingtorepresenting
verbalstatementsofmultiplicativecomparisonasmultiplicationequations.Inordertorepresenta
verbalstatementofmultiplicativecomparisonasamultiplicationequation,studentsmustrecognize
thatmultiplicationdeterminesthetotalnumberofobjectswhenthereareaspecificnumberofgroups
withthesamenumberofobjectsineachgroup.Whenwehaveequalgroups,multiplicationisamore
efficientwaytofindthetotalthanrepeatedaddition.Thethreeproblemsshowstudentunderstanding
ofmultiplicationandscaffoldindifficulty.
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem1:
Studentswhocreateanaddition
sentencethataccuratelymodels
thetotalnumberofdots(e.g.,
! + ! + ! + !)maynothavea
completeunderstandingof
multiplication.
Problem2:
Lookformodelsthatshow3
groupsof5objectsineach
group.Modelsthatdonotshow
5identicalobjectsineachgroup
maybeasignthatstudentshave
agapintheirfundamental
understandingofunits,which
couldleadtogreaterproblems
downtheroad.
Problem3:
Lookforstudentswhodonot
knowwhat“interpret”means
and/ordonotprovidean
interpretation,onlya
calculation.Theunderstanding
displayedinthisproblemisthe
sameunderstandingleveraged
inLesson1tointroducenew
placevalues.
RemediationResourcesforTargeted
Instruction:
3rdGrade,Module1,TopicA,
Lesson(s)1-3
UsetheConceptDevelopmentportion
ofeachLessonandasamplingof
problemsfromtheProblemSet
focusedonconceptualunderstanding.
RemediationGuidance:Grade4
EurekaModule1,TopicA
PartBFocus:2.NBT.A.1Understandthatthethreedigitsofathree-digitnumberrepresentamountsofhundreds,tens,andones;e.g.,706equals
7hundreds,0tens,and6ones.Understandthefollowingasspecialcases:
a) 100canbethoughtofasabundleoftentens—calleda“hundred.”
b) Thenumbers100,200,300,400,500,600,700,800,900refertoone,two,three,four,five,six,seven,eight,orninehundreds(and0
tensand0ones).
Whythisisimportantforcurrentgradelevelwork:
Inordertoextendtheirunderstandingofplacevaluerelatedtomultiplyinganddividingbymultiplesof
10,studentsmustbefamiliarwithanduseplacevalueastheyworkwithnumbers.Conceptual
RemediationResourcesforTargeted
understandingof“100”beingthesameamountas10groupsoftenaswellas100oneslaysthe
Instruction:
groundworkforthestructureofthebase-tensysteminfuturegrades.Theproblemsscaffoldindifficulty
fromtheonesplacetothehundredsplace.
2ndGrade,Module3,TopicA,
Lesson1
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem4:
Problem5:
Problem6:
UsetheConceptDevelopmentportion
Lookformodelsthatcorrectly
Lookforstudentswhoidentify
Lookforstudentswholeavethe ofthisLessonandasamplingof
representthevalueofeachdigit the5asrepresenting50ones.
hundredsplaceoutinthemodel. problemsfromtheProblemSet
inthenumber,e.g.,3hundreds, Althoughthisisnotincorrect,it Itisimportantforunderstanding focusedonconceptualunderstanding.
4tens,and5ones.
maybeasignofagapintheir
thatallplacesareincluded.
understandingofplacevalue.
RemediationGuidance:Grade4
EurekaModule1,TopicA
PartCFocus:2.NBT.A.3Readandwritenumbersto1000usingbase-tennumerals,numbernames,andexpandedform.
Whythisisimportantforcurrentgradelevelwork:
Lessons3and4explicitlybuildoffofthisGrade2understandingtohelpstudentsmastertheGrade4
expectationorreadingandwritingnumbersto1,000,000.Itisimportanttonotethatthereisno
analogousstandardinGrade3,requiringstudentstoreachbacktotheirunderstandingdevelopedin
Grade2.
UsingtheDiagnosticAssessmenttoidentifygaps:
Problem4:
Lookforstudentswhowritea
four-digitnumber,treatingthe
“seven”and“hundred”as
separatenumbers.Thisshowsa
gapintheirunderstandingof
wordform.
Problem5:
Lookforstudentswho
misrepresenttheplacevalueof
eachofthegivennon-zero
digits.Thismayshowagapin
students’understandingofand
abilitytoreadnumbersusing
numbernames,connectingthem
toplacevalue.
Problem6:
Lookforstudentswhowritea
two-digitnumberinsteadofa
three-digitnumber.Thismay
showagapinstudents’
understandingofexpanded
form.
RemediationResourcesforTargeted
Instruction:
2ndGrade,Module3,TopicC,
Lesson(s)5-7
UsetheConceptDevelopmentportion
ofeachLessonandasamplingof
problemsfromtheProblemSet
focusedonconceptualunderstanding.