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Math Grade 8

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  • 7/31/2019 Math Grade 8

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    Grade8Mathematics 1 CommonCoreSampleQuestions

    New York State

    Testing Program

    MathematicsCommon Core Sample Questions

    Grade

    The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and nonprofitorganizations or institutions to reproduce these materials for their own use, but not for sale, provided copyright notices are retained as they appear inthis publication. This permission does not apply to mass distribution of these materials, electronically or otherwise.

  • 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.

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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.

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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.

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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.

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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.

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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

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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.