©2012NoyceFoundation
PerformanceAssessmentTask
LeapfrogFractions
Grade4taskalignsinparttoCCSSMgrade3
Thistaskchallengesastudenttousetheirknowledgeandunderstandingofwaysofrepresentingnumbersand
fractionsandtheirabilitytousemodels,benchmarks,andequivalentformsoffractionstoaddfractions.
Studentsmustbeabletoapplytheirunderstandingoftheconceptofonewholewhentryingtocombine
fractions.Studentsmustbeabletousetheirknowledgeoffractionsandtoolswithfractionstoconstructa
convincingargumentaboutrelativesizeoftotal.
CommonCoreStateStandardsMath‐ContentStandards
NumberandOperations
Fractions
Developunderstandingoffractionsasnumbers.
3.NF.1Understandafraction1/basthequantityformedby1partwhenawholeisportionedintobequalparts;
understandafractiona/basthequantityformedbyapartsofsize1/b.
3.NF.3Explainequivalenceoffractionsinspecialcases,andcomparefractionsbyreasoningabouttheirsize.
a. Understandtwofractionsasequivalent(equal)iftheyarethesamesize,orthesamepointonanumber
line.
b. Recognizeandgeneratesimpleequivalentfractions,e.g.½=2/4,4/6–2/3).Explainwhythefractions
areequivalent,e.g.byusingavisualfractionmodel.
d. Comparetwofractionswiththesamenumeratororthesamedenominatorbyreasoningabouttheir
size.Recognizethatcomparisonsarevalidonlywhenthetwofractionsrefertothesamewhole.Record
theresultsofcomparisonswiththesymbols,=,or,andjustifytheconclusions,e.g.byusingavisual
fractionmodel.
CommonCoreStateStandardsMath–StandardsofMathematicalPractice
MP.2
Reasonabstractlyandquantitatively.
Mathematicallyproficientstudentsmakesenseofquantitiesandtheirrelationshipsinproblemsituations.They
bringtwocomplementaryabilitiestobearonproblemsinvolvingquantitativerelationships:theabilityto
decontextualize–toabstractagivensituationandrepresentitsymbolicallyandmanipulatetherepresenting
symbolsasiftheyhavealifeoftheirown,withoutnecessarilyattendingtotheirreferents–andtheabilityto
contextualize,topauseasneededduringthemanipulationprocessinordertoprobeintothereferentsforthe
symbolsinvolved.Quantitativereasoningentailshabitsofcreatingacoherentrepresentationoftheproblemat
hand;consideringtheunitsinvolved;attendingtothemeaningofquantities,notjusthowtocomputethem;and
knowingandflexiblyusingdifferentpropertiesofoperationsandobjects.
MP.7Lookforandmakeuseofstructure.
Mathematicallyproficientstudentstrytolookcloselytodiscernapatternorstructure.Youngstudents,for
example,mightnoticethatthreeandsevenmoreisthesameamountassevenandthreemore,ortheymaysort
acollectionsofshapesaccordingtohowmanysidestheshapeshave.Later,studentswillsee7x8equalsthe
well‐remembered7x5+7x3,inpreparationforlearningaboutthedistributiveproperty.Intheexpressionx
2
+9x+14,olderstudentscanseethe14as2x7andthe9as2+7.Theyrecognizethesignificanceofanexisting
lineinageometricfigureandcanusethestrategyofdrawinganauxiliarylineforsolvingproblems.Theyalso
canstepbackforanoverviewandshiftperspective.Theycanseecomplicatedthings,suchassomealgebraic
expressions,assingleobjectsorbeingcomposedofseveralobjects.Forexample,theycansee5–3(x‐y)
2
as5
minusapositivenumbertimesasquareandusethattorealizethatitsvaluecannotbemorethan5foranyreal
numbersxandy.
AssessmentResults
ThistaskwasdevelopedbytheMathematicsAssessmentResourceServiceandadministeredaspartofa
national,normedmathassessment.Forcomparisonpurposes,teachersmaybeinterestedintheresultsofthe
nationalassessment,includingthetotalpointspossibleforthetask,thenumberofcorepoints,andthepercent
ofstudentsthatscoredatstandardonthetask.Relatedmaterials,includingthescoringrubric,studentwork,
anddiscussionsofstudentunderstandingsandmisconceptionsonthetask,areincludedinthetaskpacket.
GradeLevel Year TotalPoints CorePoints %AtStandard
Grade4 2009 7 3 36%