Post on 05-Apr-2018
7/31/2019 Math Grade 8
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Grade8Mathematics 1 CommonCoreSampleQuestions
New York State
Testing Program
MathematicsCommon Core Sample Questions
Grade
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7/31/2019 Math Grade 8
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Grade8Mathematics 2 CommonCoreSampleQuestions
Domain:FunctionsItem:CR
A trainer foraprofessional football teamkeeps trackof theamountofwater
playersconsumethroughoutpractice.Thetrainerobservesthattheamountof
water consumed is a linear function of the temperature on a given day. The
trainerfinds
that
when
itis90F
the
players
consume
about
220
gallons
of
water,andwhenitis76Ftheplayersconsumeabout178gallonsofwater.
1
PartA: Writealinearfunctiontomodeltherelationshipbetweenthegallonsofwaterconsumedandthetemperature.
PartB: Explainthemeaningoftheslopeinthecontextoftheproblem.Key:
PartA: y=3x
50
PartB: Foreveryonedegreeincreaseintemperature,thenumberofgallonsconsumedincreasesby3.
AlignedCCLS: 8.F.4Commentary:ThisquestionalignstoCCLS8.F.4becauseitassessesastudentsabilitytoconstruct a function that models a linear relationship from a description of a
relationshipbetweentwovalues(x,y)andinterprettherateofchange.
Rationale:Thecorrectanswer indicates theability toconstructa function tomodelalinear relationship. Given thatwater consumption is a function of temperature, the
valuescitedintheproblemareunderstoodascoordinatepairsthatcanberelatedbya
linearfunction.
PartA:3
14
42
7690
178220
y=3x+b
220=3(90)+b
50=b
PartB: Theslopeindicates3gallonsperdegree(1
3),whichshowsthatforevery
temperatureincreaseinonedegree,thenumberofgallonsofwater
consumedwouldincreasebythree.
7/31/2019 Math Grade 8
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Grade8Mathematics 3 CommonCoreSampleQuestions
Domain:ExpressionsandEquationsItem:MC
Whichofthefollowingexpressionsisnotequivalentto ?25
12
A 15355B 15151C 1535D 15254
Key:DAlignedCCLS:8.EE.1Commentary:ThisquestionalignstoCCLS8.EE.1becauseitassessesastudentsabilitytoapplypropertiesofexponentstorewriteexponentialexpressions.
Rationale: Selecting Option D could indicate that student recognizes the incorrectaddition of exponents or confusion on the concept of equivalence
(54x5
2=25).OptionsA,B,andC involvethecorrectapplicationofthepropertiesof
integerexponents.
7/31/2019 Math Grade 8
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Grade8Mathematics 4 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:CR
Acomputercando1000operationsin4.5106
seconds.Howmanyoperations
canbe
done
by
this
computer
in
one
hour?
Express
your
answer
in
scientific
notation.
3
Key:81011AlignedCCLS:8.EE.4Commentary:ThisquestionalignstoCCLS8.EE.4becauseitassessesastudentsability
toperformoperationswithnumbersexpressedinscientificnotation.
Rationale:Thecomputerworksattherateofthe1000operationsin4.5106seconds,or 22. 10
8multiplicationspersecond(1000/4.510
6).Applicationoftheconversion
of1hour=3600seconds[( 22. 108)x3600]givesthenumberofoperations(810
11)
thecomputercancompleteinonehour.
7/31/2019 Math Grade 8
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Grade8Mathematics 5 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:MC
x y8 42
3 17
0 2
6 28
Ifalinecontainsthepointsinthetableabove,theequationofthelineis4
A y=2x+5B y=2x5C y=5x2D y=5x2
Key:CAlignedCCLS:8.EE.6Commentary:ThisquestionalignstoCCLS8.EE.6becauseastudentusesy=mx+btowritetheequationofalinegivenitsslopeandtheyintercept.
Rationale: Option C is correct. The equation of a line can be represented in slopeinterceptform(y=mx+b)iftheslopeandyinterceptisknownorcanbefound. The
slope, m, canbe foundby performing the followingwith any twopairs of the given
points: 56
30
06
)2(28
m . The yintercept, b, is given in the table as 2 (0,2).
Accuratelysubstitutingthesevaluesintotheslopeinterceptformoftheequationgives
y=5x2. OptionCcanalsobedeterminedbytestingeachoftheoptionstodeterminewhichequationissatisfiedbythesetofpointsinthetable.SelectingOptionAindicates
confusionintheproperlocationofthesetwovaluesinaslopeinterceptform.Selecting
Option B also indicates confusion in the proper location of these two values in a
slopeinterceptform,aswellaspossiblesignerrorsforthevaluesofboththeslopeand
theyintercept.SelectingOptionD indicatesan incorrectcalculationofslopefromthe
giventable.
7/31/2019 Math Grade 8
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Grade8Mathematics 6 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:MC
Ifalinepassesthroughthetwopointsabove,theequationofthelineis
5
A y=2x+5B y=2x5C y=5x2D y=5x2
Key:CAlignedCCLS:8.EE.6Commentary:ThisquestionalignstoCCLS8.EE.6becauseastudentusesy=mx+btowritetheequationofalinegivenitsslopeandtheyintercept.
7/31/2019 Math Grade 8
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Grade8Mathematics 7 CommonCoreSampleQuestions
Rationale:OptionCiscorrect.Thestudentcandeterminetheslopegraphicallyoralgebraicallyandcanidentify(0, 2)astheyinterceptfromthegraph.Algebraicallythe
slopecanbedeterminedby 52
10
02
)2(8
m .Accuratelysubstitutingthesevalues
intotheslopeinterceptformofalinearequationgivesy=5x2.
7/31/2019 Math Grade 8
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Grade8Mathematics 8 CommonCoreSampleQuestions
Domain:Geometry/ExpressionsandEquations
Item:CR
Inthediagrambelow, ABCissimilarto ART.6
PartA: Whatisthescalefactorfrom ABCto ART?PartB: IftheslopeofACis2,whatisthevalueofxforcoordinateC?PartC: UsingtheinformationfrompartsAandB,whatisthelengthofRT?
Key:PartA:
5
8
AR
AB
PartB: 4PartC: 2.5
AlignedCCLS: 8.G.4,8.EE.6,and8.EE.7bCommentary:ThisquestionalignstoCCLS8.G.4,8.EE.6,and8.EE.7bbecauseitassesses
theconstructionandapplicationofasimilarityratio,thecreationofalinearequation,
andsolvingalinearequationwithonevariable.
7/31/2019 Math Grade 8
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7/31/2019 Math Grade 8
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Grade8Mathematics 10 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:CR
Inthecoordinateplanebelow, ABCissimilarto AEF.7
Whatisthevalueof ?x
Key:x=4AlignedCCLS:8.EE.6Commentary:ThisquestionalignstoCCLS8.EE.6becauseitassessesthestudents
understandingthatslopeisthesamealongalinebetweenanytwodistinctpoints.
Rationale:Thestudentcancompute06
211
tofindtheslopeof .2
3AC Next,the
student
finds
the
slope,
,
6
0
28
x xFA
and
then
the
student
will
set
ratios
equal
x
6
2
3
tofindx=4.
7/31/2019 Math Grade 8
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Grade8Mathematics 11 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:MC
xx2
17
3
12)12(
3
2
8
Whichstepwouldnotbeapossiblefirststepforsolvingthisequation
algebraically?
A multiplyingeverytermintheequationbysix
B subtracting3
12 from7
C subtracting x
2
1from2x
D multiplying 1 by3
2
Key:C
AlignedCCLS:8.EE.7bCommentary: This question aligns to CCLS 8.EE.7b because it assesses the students
ability to use the distributive property and to combine like terms when solving anequation.
Rationale:OptionCiscorrect.Giventhat2xismultiplyingafactorof3
2,distributionor
someotheralgebraicbeginning thatwouldbenecessarybeforesubtracting x2
1 from
2x.OptionsA,B,andDallrepresentreasonablestartingpoints.
7/31/2019 Math Grade 8
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Grade8Mathematics 12 CommonCoreSampleQuestions
Domain:ExpressionsandEquations
Item:CR
Davidcurrentlyhasasquaregarden.Hewantstoredesignhisgardenandmake
itintoarectanglewithalengththatis3feetshorterthantwiceitswidth.He
decidesthat
the
perimeter
should
be
60
feet.
9
Determinethedimensions,infeet,ofhisnewgarden.
Showyourwork.
Key:11feetwideand19feetlong
AlignedCCLS:8.EE.7bCommentary:ThisquestionalignstoCCLS8.EE.7bbecauseitassessesthestudents
abilitytofindtheperimeterofarectanglebyexpandingexpressionsusingthe
distributivepropertyandcollectingterms.
Rationale:Width=11andlength=19producesarectanglewithaperimeterof60.Thelengthis3feetshorterthantwicethewidth.
Letw=width
2w3=length
2(w+2w3)=60
2w+4w6=60
6w=66
w=11
2w3=19
Otherprocessesmayalsoresultinthecorrectanswer.
7/31/2019 Math Grade 8
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Grade8Mathematics 13 CommonCoreSampleQuestions
Domain:Functions
Item:CR
Thethreedifferentlinearfunctionsbelowarerepresentedinthreedifferent
ways,asshown.10
Whichfunctionhasthegreatestrateofchange?Doesanypairoffunctionshavethe
samerateofchange?Justifyyouranswer.
Key:Thelinearfunctionin Ihasthegreatestrateofchangeofthethreegivenfunctions.ThelinearfunctionsinIIandIIIeachhavearateofchangeof
2
3.
AlignedCCLS:8.F.2Commentary:ThisquestionalignstoCCLS8.F.2becauseitassessesastudentsabilitytorecognizeandcomparepropertiesof functionsrepresented indifferentways:tableof
values,graphically,andalgebraically.
Rationale:ITherateofchangeis2.
IIandIIITherateofchangeforeachis2
3.
7/31/2019 Math Grade 8
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Grade8Mathematics 14 CommonCoreSampleQuestions
Domain:Functions
Item:MC
Ofthefourlinearfunctionsrepresentedbelow,whichhasthegreatestrateof
change?11
Key:DAlignedCCLS:8.F.2Commentary:ThisquestionalignstoCCLS8.F.2becauseitassessesastudentsabilityto
compareratesofchangesforfunctionsrepresentedindifferentways.
Rationale:OptionD iscorrectbecause the rateofchange is ;2
5 inOptionA it is2, in
OptionBitis,3
4andinOptionCitis
.3
7
7/31/2019 Math Grade 8
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Grade8Mathematics 15 CommonCoreSampleQuestions
Grade 8MathematicsCommon Core Sample QuestionsThese materials are copyrighted. Reproducing any part of these materials by anyone other than New York State school personnel is illegal.