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 http://www.tarleton.edu/team/  “Fruity” Math (with a Few Veggies )  By  Dr. Pam Littleton [email protected]  Dr. Beth Riggs [email protected] Rose Ann Jackson [email protected]

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  • 8/10/2019 Fruity Math With a Few Veggies Handout

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    http://www.tarleton.edu/team/

    Fruity Math

    (with a Few

    Veggies )

    By

    Dr. Pam [email protected]

    Dr. Beth [email protected]

    Rose Ann [email protected]

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    Shape

    C

    O

    M

    P

    R

    I

    S

    O

    N

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    Asteachers,itisimportantthatwehelpourstudentsdevelopastrong

    conceptualunderstandingofweightandmass. Herearesomeideasforusto

    thinkaboutasweaddressthesetopics.

    When

    are

    our

    students

    expected

    to

    know

    the

    difference

    between

    weight

    and

    mass?

    ThedifferencebetweenweightandmassisspecifiedintheTEKSfor4th

    grade.

    (See4.11E.) Theactualknowledgeandskillsstatementandstudentexpectation

    isstatedasfollows:

    (4.11) Measurement. Thestudentappliesmeasurementconcepts. Thestudent

    isexpectedtoestimateandmeasuretosolveproblemsinvolvinglength(including

    perimeter)andarea. Thestudentusesmeasurementtoolstomeasure

    capacity/volumeandweight/mass.

    Thestudentisexpectedto:

    (E) explainthedifferencebetweenweightandmass.

    Whyarethetermssometimesseparatedasweightandmassbutother

    other

    times

    the

    term

    is

    weight/mass?

    Upuntil4th

    grade,themathematicsTEKSdonotmakeadistinctionbetween

    weightand

    mass

    since

    all

    of

    our

    measurements

    are

    being

    taken

    in

    the

    same

    locationontheEarth! Eventhoughweasteachersknowthatweightandmass

    aredistinctattributes,theattributesarebundledtogetherasweight/massinthe

    TEKSforKindergartenthrough3rd

    grade. Beginningin4th

    grade,thedistinction

    betweentheseattributesbecomesofficialinthemathematicsTEKS.

    Weight

    and

    ass

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    If

    I

    am

    teaching

    Kindergarten,

    1st,

    2nd,

    or

    3rd

    grade,

    why

    should

    I

    even

    worry

    aboutthedistinctionbetweenweightandmass? Mystudentswontbe

    expectedtoexplainthedifferenceuntil4th

    grade!

    Vocabularyand

    early

    conceptual

    development

    related

    to

    measurement

    of

    weight

    andmassisHUGE! EventhoughtheTEKSbundletheattributesofweightand

    massasweight/massinK3,teachersinthesegradelevelsmustpayclose

    attentiontovocabularydevelopment,tools,andsoforthsothatthestudents

    wonthavetounlearnanythingwhentheygetto4th

    grade. Forexample,

    gramsisaunitusedtomeasuremass,notweight! Teachersshouldsay

    somethinglike,LetsdeterminethemassofthisorangeingramsnotLets

    weightheorangeingrams.

    SowhataresomeareasofvocabularyandearlyconceptualdevelopmentthatI

    should

    be

    aware

    of

    as

    a

    teacher?

    Someofthemostimportantareastopayattentiontoarethefollowing: Units,

    tools,andtheactualdistinctionbetweenweightandmass. Theseideasare

    summarizedonthefollowingchart.

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    Weight M

    Units

    MetricSystem: Typicalunitforweightisthe

    Newton.

    Customary

    System: Typicalunitsforweightarethe

    ounceandthepound.

    MetricSystem: Typica

    milligram,gram,andk

    Customary

    System: A

    thedram,andthegrai

    commonthoughbecau

    cumbersome. Theuni

    veryoften.

    Note: Somestudentsareunderthemisconceptionthatmassismetricwh

    however,thislineofthinkingisnotcorrect. Massisanattribute,andthere

    customaryunitsthatcanbeusedtomeasuremass. Similarly,weightisana

    metricunitsandcustomaryunitsthatcanbeusedtomeasureweight. Grant

    common

    than

    others,

    but

    just

    because

    we

    dont

    use

    a

    unit

    frequently

    doesn

    Tools

    SpringScale

    PlatformScale

    Scale

    PanBalance

    Balance

    DistinctionAmeasureofthegravitationalforceexertedonan

    object.Weightdependsonlocation. Forexample,

    anobjectwillhavelessweightontheMoonthanit

    willhaveonEarthsincetheforceofgravityislesson

    theMoon.

    Theamountofmatter

    constant,regardlessof

    Note:Even

    though

    weight

    and

    mass

    are

    distinct

    attributes,

    they

    are

    proportio

    themassofanotherobjectwillweightwiceasmuchtoo(aslongasbothobje

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    What

    is

    expected

    and

    appropriate

    with

    regard

    to

    weight/mass

    at

    the

    Kindergartenlevel?

    AttheKindergartenlevel,thestudentsaremakingdirectcomparisonsbetween

    twoobjectsforweight/mass. (SeeK.10D.) Asteachers,weshouldaskquestions

    thatwillelicitthecomparativelanguageasmentionedinpartDoftheTEKS.

    Whichobjectfeelsheavier?Whichobjectfeelslighter?

    What

    is

    expected

    and

    appropriate

    with

    regards

    to

    weight/mass

    at

    the

    1st

    grade

    level?

    Atthe1stgradelevel,thestudentsstillaremakingdirectcomparisonsfor

    weight/mass. Thenumberofobjectsisnowtwoormoreinsteadofjusttwo

    objectsat

    atime

    as

    in

    Kindergarten,

    and

    the

    students

    put

    the

    objects

    in

    order

    accordingtoweight/mass. (See1.7F.)

    ImdetectingatrendinKindergartenand1st

    gradewiththedirect

    comparisons!

    What

    should

    direct

    comparison

    of

    weight/mass

    look

    likeintheKindergartenand1st

    gradeclassrooms?

    Studentsshouldplacetheitemsintheirhandsfirst(oneitemineachhand)and

    makeaprediction

    concerning

    which

    object

    feels

    heavier,

    lighter,

    or

    ifthe

    items

    feelaboutthesame(aboutequaltoeachotherinweight/mass). Thisexperience

    leadsnicelyintousingapanbalance!

    Aftermakingaprediction,studentscanuseapanbalancetodirectlycomparethe

    weight/massoftheitems. Thepanthatgoesdownholdstheobjectthathas

    moremass. Thatobjectfeelsheavierwhenyoudirectlycomparetheminyour

    hands. AtthedirectcomparisonlevelforKindergartenand1stgrade,thestudents

    arenotquantifyingtheweight/masswithanykindofunit.

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    What

    is

    expected

    and

    appropriate

    with

    regards

    to

    weight/mass

    at

    the

    2nd

    gradelevel?

    In2nd

    grade,thedirectcomparisonofobjectswithregardtoweight/mass

    remains. Thecomparativelanguageremainsaswell. Thedifferenceisthatin2nd

    grade,thestudentsarenowexpectedtoextendtheirworkwithweight/massby

    selectingandusinganonstandardunittodeterminetheweight/massofagiven

    object. Studentsshouldalsobegintorecognizeandusemodelsthatapproximate

    standardunitsforweight/mass. (See2.9D.)

    So

    what

    might

    weight/mass

    activities

    look

    like

    in

    the

    2nd

    grade

    classroom?

    Asan

    example,

    you

    might

    have

    your

    students

    use

    apan

    balance

    to

    determine

    howmanybeansittakestobalanceanobject. Thestudentsarebasicallyfinding

    theamountofbeansthathavetheequivalentweight/massasthegivenobject.

    Studentsneedpracticemeasuringtheweight/massofobjectsandreportinghow

    manyunitsastheyquantifytheweight/massoftheobject. Inaddition,the

    knowledgeandskillsstatementmentionsthatthestudentsshouldrecognizeand

    usemodelsthatapproximatestandardunits. Forexample,youmightsaytoyour

    studentsthatacentimetercubehasamassofabout1gram. Thenyoucouldask

    thestudents

    how

    many

    centimeter

    cubes

    it

    would

    take

    to

    balance

    the

    object

    in

    question. Otheritemsthatcouldbeusedtoapproximatestandardunitsfor

    weight/massincludethefollowing:

    Centimetercubes(about1gram)

    Nickel(about5grams)

    Largepaperclip(about1gram)

    Milklid(about2grams)

    Beans

    (about

    1

    gram

    but

    not

    consistent)

    Bagsofsugar,flour,etc

    (availablein1pound,4pounds,5

    pounds,etc)

    Fishingequipmentlikesinkers

    (variousouncescheckthelabel)

    Cheese(availablein1pound

    blocks)

    Small

    jars

    of

    cooking

    spices

    (variousouncescheckthelabel)

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    What

    is

    expected

    and

    appropriate

    with

    regards

    to

    weight/mass

    at

    the

    3rd

    gradelevel?

    DirectcomparisonsandcomparativelanguageremainintheTEKSthrough3rd

    grade. Thedifferencenowisthatstudentsareusingstandardunitsfor

    weight/mass,withanemphasisstillonconcretemodels. (See3.11D.)

    Whatmightactivitiesforweight/masslooklikeinthe3rd

    grade

    classroom?

    Thestudentsmightuseapanbalanceandgramstackersorpiecesfromabrass

    masssettodeterminethemassoftheobject. Itisalsoimportantforthe

    studentstocontinuetobuildanddevelopmentalbenchmarksforstandardunits

    ofweight/mass.

    The

    benchmarks

    will

    be

    more

    effective

    for

    the

    students

    ifthey

    includeeverydayobjectswithwhichthestudentsarefamiliar. Thestudentscould

    collectitemsfromhomeorfromaroundtheschooltobringtoclassas

    benchmarksaredeveloped. Activitiessuchasthesewillhelpstudentstoidentify

    concretemodelsthatapproximatestandardunitsofweight/mass.

    4th

    grade

    is

    where

    the

    distinction

    between

    weight

    and

    mass

    is

    acknowledgedintheTEKS.ArethereotherthingsIshouldthinkabout

    for

    4th

    grade?

    TheTEKSdonotmentiondirectcomparisonforweight/massatthe4th

    grade

    level. Theomissionofthedirectcomparisonsimpliesthatmasteryofthisconcept

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    isexpectedbytheendof3rd

    grade. Inaddition,4th

    gradestudentswillbe

    expectedtoestimateandusemeasurementtoolsforweight/massusingstandard

    unitsinthemetricandcustomarysystems. Studentsmostlikelywillbefamiliar

    withthepanbalance(toolusedtomeasuremass). Studentscanuseaplatform

    scaleor

    aspring

    scale

    to

    measure

    weight.

    Simple

    conversions

    between

    different

    unitsofweightwithinthecustomarymeasurementsystemarealsoaddressedin

    4th

    grade. (See4.11ABE.)

    What

    might

    weight

    and

    mass

    activities

    look

    like

    in

    the

    4th

    grade

    classroom?

    Studentsshouldhavemanyopportunitiestoreinforcetheirmentalbenchmarks

    forstandard

    units

    for

    weight

    and

    mass

    that

    they

    have

    been

    developing

    since

    3rd

    gradeastheyestimatetheweightorthemassofanobject. Thestudentsmay

    wanttousedirectcomparisonshere(eventhoughdirectcomparisonsarenot

    specificallymentionedintheTEKS). Holdingareferentforastandardunitinone

    handandholdingtheobjecttobemeasuredintheotherhandcanassistthe

    studentsinmakingagoodestimateforweightormass. Aftermakingthe

    estimate,thestudentswillneedhandsonpracticeusingbalancesandscalesto

    confirmtheirpredictions. Rememberthatbalancesmeasuremass,whilescales

    measureweight! FortheconversionsintheTEKS,thestudentsneedpractice

    reportingweightsusingdifferentunits. Forexample,aftermeasuringtheweight

    ofanobjectinpounds,havethestudentsreporttheweightinouncesaswell.

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    What

    is

    expected

    and

    appropriate

    at

    the

    5th

    and

    6th

    grade

    levels

    for

    weight/massconcepts?

    In5th

    grade,weight/massismentionedintheknowledgeandskillsstatement,but

    notspecificallymentionedinthestudentexpectations. However,student

    expectation(A)statesthatstudentsperformsimpleconversionswithinthesame

    system,implyingthatstudentscontinuetoreinforcetheirknowledgeofsimple

    conversionsforweight/massthatbeganin4th

    grade. (See5.10A.)

    In6th

    grade,studentsarecontinuingtoestimatemeasurements,selectanduse

    appropriateunitsandtools,andconvertmeasureswithinthesamemeasurement

    system. (See6.8ABD.)

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    Itisntuntil8th

    gradethatweformallyteachsurfacearea;however,aseducatorswecanlaythe

    foundation

    for

    that

    concept

    at

    a

    very

    early

    age.

    I

    like

    to

    use

    stickers

    as

    a

    non

    standard

    way

    to

    begintheconceptofteachingsurfacearea;certainlylaterontheywilllearnthatsurfaceareais

    measuredinsquareunitsratherthanstickers.Ihavethestudentsestimatehowmanystickers

    itwilltaketocovertheoutsideofwhateverfruitorvegetablethatweareusing.Iamreallyjust

    tryingtogetthestudentstounderstandthattheoutsideofa3dimensionalfigureisits

    surfacearea. Theywillformallybeginlearningaboutvolumein4th

    grade. However,manyof

    ourstudentsgetsoconfusedwithalltheformulasandwhentouseeachone,butwhenthey

    havedonemanyoftheseactivitiesataearlyage,thereismuchlessconfusiononthedifference

    betweensurfaceareaandvolume.

    Suggestionsfor

    Classroom

    Use:

    First,wewillpredicthowmanystickerswillcovertheoutsideofouritem.Iamnotrealpicky

    abouthowclosetheirstickersare Ijusttellthemtotryandcoveralltheskinasbestasthey

    cananditisokaytooverlapstickers.

    Secondly,wecovertheiteminstickers.Ihavefounditeasieriftheynumberthemastheygo

    ratherthancountthemafterplacingthemontheobject.

    Third,wecheckourpredictions/estimations.Howclosewasourestimate?

    Fourth,wecomparewithothergroupsintheroomanddiscusswhyournumbersmightbe

    differentorwhytheyarealmostthesame. Ofcoursetheycouldbedifferentbecauseoneitem

    islargerorsmallerthantheotheroronegroupputtheirstickersclosertogetherthananother

    group.

    Besureandhavethestudentsrecordallofthisinformationonarecordingsheet.

    Surface

    rea

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    Itisntuntil6th

    gradethatweformallyteachcircumference;however,aseducatorswecanlaythe

    foundationforthatconceptataveryearlyagejustaswehavedonewithpreviousconceptsinthis

    unit.

    Students

    just

    love

    the

    word

    Circumference;

    it

    is

    like

    a

    million

    dollar

    word

    to

    them.

    As

    math

    teachersweneedtobediligentinusingthecorrectmathvocabularywithourstudents.Somepeople

    believeweshouldwaituntiltheconceptisformallyintroducedtogivethemthecorrectvocabulary.

    I,however,disagreewiththisprinciplebecauseittakestoolongtounteachthewrongvocabulary.

    Whynotteachitcorrectlythefirsttime? Rememberinthisactivitywearejusttryingtogetthe

    studentstounderstandthatcircumferenceisthedistancearoundsomething.

    SuggestionsforClassroomUse:

    First,wewillpredict/estimatethecircumferenceofouritem.Asateacheryoumustdecidewhether

    to

    use

    the

    English

    or

    Metric

    scale

    of

    measurement.

    I

    typically

    use

    both.

    I

    dont

    teach

    conversion,

    but

    I

    wantthemtohaveagoodbaselinewithbothmeasurementsystems.

    Secondly,weeitheruseatapemeasureorapieceofstring/ribbontomeasurethecircumferenceof

    theitem.Ifwehaveusedastring/ribbon,wewillneedtothenmeasurethatlengthwitharuler. Itis

    hardtowrapthestring/ribbonaroundtheitemandholdtheitem. Ihavefoundthatthisactivity

    worksbestinpairs.

    Third,wewillcheckourpredictions/estimations.Howclosewereourestimates?Astheyear

    progresses,yourstudentsestimationswillmostlikelygetcloserandclosertotheiractual

    measurements.

    Fourth,wecomparewithothergroupsintheroomanddiscusswhyournumbersmightbedifferent

    or

    why

    they

    are

    almost

    the

    same.

    Of

    course

    they

    could

    be

    different

    if

    the

    items

    are

    a

    different

    size

    or

    ifweareusingadifferentmeasurementscale.

    Again,besureandhavethestudentsrecordallofthisinformationonarecordingsheet.

    ircumference

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    Forolderstudents,thisisagreattimetointroducepi(). Aftertheyhavedeterminedtheircircumference,havethestudentsfindthediameteroftheirobject.(Forsomeobjects,thisiseasier

    thanothers.

    For

    instance,

    you

    can

    cut

    an

    orange

    or

    apple

    across

    and

    measure

    the

    diameter

    more

    easily.) Afterstudentshavefoundboththecircumferenceanddiameter,havethemdividethe

    circumferencebythediameter.Dependingonhowwelltheyhavemeasured,theresultofthe

    divisionshouldbeclosetopi()3.14..Thatiswhenyoucanexperimentwithmanyotherobjectsandseeifeachtimeyoudividethecircumferencebythediameteryouwillget . Studentsareusuallyveryimpressedwiththisandwanttotrynumerousobjectstotestthehypothesis.

    Anotherreallyfunthingtoshowstudentsistohavethemcutapieceofribbonorpapertapethatis

    thesamelengthasthecircumferenceoftheobject.Thenhavethemmeasuretheribbonacrossthe

    diameter itshouldgoacrossthediameter3timeswithalittleleftover(againrepresentingthe

    3.14).Nowtakethatlittlebitthatisleftover(.14)anduseitasaguidetocreasetheribboninto

    parts.

    Ifyoumeasuredeverythingcorrectlyyouwillendup22parts. Thefirst21partsrepresentthethree

    diameters andtheleftoverpart(.14)willbe;thereforethecircumferencestripnowshows

    3.14 . Thisisawonderfulwaytoshowthat canbeapproximatedby

    .

    ircumference II

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    Animportantconceptinunderstandingtherelationshipbetweenvolumeand

    capacityisthatanobjectsubmergedinwaterwilldisplaceavolumeofwater

    equaltothevolumeoftheobjectthatwassubmerged.

    Somestudentsareunderthemisconceptionthatanobjectdoesnthavevolume

    unlessavolumeformulaexistsforthemtouse! Byusingcommonfruitsor

    vegetables(manyofwhichareirregularlyshapedobjectsforwhichnovolume

    formulaexists),studentscanstrengthentheirunderstandingofvolumebyusing

    therelationshipbetweenthevolumeofacentimetercube(1cubiccentimeter)

    andtheamountofwaterdisplacedwhenthecubeissubmergedinwater(1

    milliliter). Anotheroutcomefromthisactivityisthatstudentswilldevelopand

    refinetheirfamiliaritywiththemilliliteroneofthecommonlyencountered

    standardunits

    for

    capacity

    in

    the

    metric

    system.

    ThisactivityaddressestheTEKSbyhelpingtobuildaconceptualunderstandingof

    volume.Astrongconceptualunderstandingofvolumeservesaspreparationfor

    thedevelopmentanduseofvolumeformulas(ofrectangularprisms)inthe

    5thgradeTEKS,andthedevelopmentanduseofvolumeformulasforother3D

    figuresinmiddleschool.

    Suggestions

    for

    Classroom

    Use:

    Giveeach

    group

    of

    students

    agraduated

    cylinder

    that

    is

    calibrated

    in

    milliliters. Asmallcylinder(around25millilitersor50milliliters)works

    well.

    Havethempoursomewaterintothecylinder,fillingitfromonethirdto

    twothirdsfull.

    Volume

    and

    apacity

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    Explainhowtoreadthemarkingsonthegraduatedcylinder. Thestudents

    shouldreadthecylinderateyelevel. Thewaterwillformameniscusit

    willbehigheratthesidesofthecylinderthanitisinthecenterofthe

    cylinder. Thestudentsshouldreadthemarkingonthecylinderthatislevel

    withthe

    bottom

    of

    the

    meniscus.

    If

    the

    reading

    from

    the

    graduated

    cylinderfallsbetweentwomillilitermarkings,studentsshouldusethe

    eyedroppertoaddasmallamountofwatertothecylindertoraisethe

    waterleveltoamillilitermarking.

    Havestudentsreadandrecordtheinitialwaterlevelinthecylinder.

    Askstudentstopredictwhatwillhappenwhentheydrop1centimeter

    cubeintothewater. Then,havethemdropthecentimetercubeintothe

    watertotesttheirprediction.

    Allowthestudentstoexperimentlongenoughtocometothefollowing

    conclusion:1milliliter

    of

    water

    is

    displaced

    by

    each

    centimeter

    cube.

    Each

    centimetercubehasavolumeof1cubiccentimeter. So,amilliliterof

    watertakesupthesameamountofspaceasacubiccentimeter.

    Giveeachgroupofstudentsanorange(oranothertypeoffruitorveggieas

    longasitdoesntfloatinwater). Inaddition,makesuretheobjectwillfit

    intothegraduatedcylinder. Studentsmayneedtogetalargergraduated

    cylindertoaccommodatetheirpieceoffruit.

    Havethestudentsmakeapredictionforthevolumeofthepieceoffruit

    (usingcubiccentimeters). Remindthemthatthevolumeoftheirobjectwill

    beequal

    to

    the

    amount

    of

    water

    displaced

    when

    the

    object

    is

    submerged

    in

    water(measuredinmillilitersinthegraduatedcylinder).

    Finally,havethestudentsmeasurethevolumeoftheirpieceoffruitusing

    thegraduatedcylinder.

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    Estimation is hard for students at all grade levels. Usually as teachers, we just

    do not have a lot of time to spend on it, but having something that students

    estimate on a regular basis will help develop their estimation skills. I have themestimate jars or bottles full of things each morning, as well as have them always

    estimate the number of seeds in any fruit or vegetable that we might have on

    hand. The more of these experiments we do, the better the students get at

    predicting and estimating.

    Suggestions for Classroom Use:

    First, always have the students predict the number of seeds in the object. (You

    will be surprised by the number of students that do not know that there is onlyone seed/pit in a peach, for instance.)

    Second, cut the object open and inspect and count the number of seeds in the

    object. (Sometimes it is helpful to suggest that the students group their seeds in

    10s or 100s depending on the object.)

    Third, be sure they record the actual number of seeds on some type of

    recording sheet.

    Fourth, compare each table or groups findings with the entire class. This is a

    good time to teach some common measures of central tendency (mean,

    median, and mode) and range.

    Fifth, creating a graph (line, bar, pictograph, stem and leaf, etc.) of the class

    data is a fun way to compare and contrast their classroom information.

    Seed rediction

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    STACKING ORANGES

    Grades K-8

    Why Do It: To help participants enhance their logical-thinking skills as they first seek hand-

    on and then abstract solution patterns for an everyday problem.

    Material Needed: A bag of 35 oranges (or balls all of the same size) and 4 pieces of 2 X 2

    X 18 lumber for the base framework (or use heavy books).

    Procedure:

    1. Tell the participants that for their new math job they will need to stack oranges, like

    grocery stores sometimes do. Ask how the orange stacks stay piled up; why dont theyfall down? Discuss the concept that the stacks are usually in the shape of either

    square or triangle based pyramids. Then allow the students to begin helping with the

    orange-stacking experiment.

    2. As they are sometimes easier to conceptualize, the participants might begin piling and

    analyzing patterns when the oranges are stacked as square-based pyramids. Have them

    predict and then build the succeeding levels. The top (Level 1) will have, of course, only

    1 orange. How many oranges will be required for the next level down (Level 2)? What

    about Level 3; discuss possibilities and then build it. How about Level 4? Since therearent enough additional oranges to build a still larger base level (Level 5), how might

    we figure the number that would be needed?

    3. It may be sufficient for young students to predict, build, and develop logical concepts

    for dealing with Levels 1 4. Older students, however, should likely get into the

    business of logically analyzing the orange-stacking progression. Thus, from the top

    down, Level 1 = 1 orange; Level 2 = 4 oranges; Level 3 = 9 oranges; Level 4 = 16 oranges;

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    Level 5 will require 25 oranges. How many oranges will be needed for Level 6, Level 8,

    Level 10, or Level 20? Write a statement or a formula that we can use to tell how many

    oranges will be needed at any designated level.

    4. When ready, students might also be challenged with stacking oranges as triangular-

    based pyramids. With 35 oranges the participants will be able to predict, build, and

    analyze Levels 1 - 5 . Then, how many oranges will be needed for Level 6, Level 8, etc.?

    As before, write a statement or a formula that we can use to tell how many oranges

    will be needed at any designated level.

    Extensions:

    1. When finished with the orange-stacking experiments, the participants may, after

    washing their hands, be allowed to eat the oranges. (Note: Be certain that no one is

    allergic to oranges.)

    2. The findings from both the square and triangular orange-stacking experiments

    might be set forth as bar graphs and then analyzed, compared and contrasted.

    3. Advanced students might be challenged to try orange stacks with bases of other

    shapes. What if the base was a rectangle using 8 oranges as the length and have a

    5-orange width, etc. In another situation if 7 oranges formed a hexagon base, how

    many oranges would need to be in the level above it; how many would be needed to

    form a new base under it, etc.?

    Solutions:

    1. At first , participants will often notice that Level 2 has 3 more oranges than

    Level 1, Level 3 has 5 more oranges than Level 2Level 4 has 7 more oranges,

    etc. This realization will allow them to figure out the number of oranges needed

    at any level, but the required computation will be cumbersome!

    2. A more efficient method occurs when the participants realize that all of the

    Levels are square numbers. That is, Level 1 = 12= 1 orange,; Level 2 = 22= 4

    oranges; Level 3 = 32= 9, etc.

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    Cool Facts from Sunkist for Kids

    1.

    Youd have to eat 7 cups of corn flakes to get the same amount of fiber as

    one medium orange.

    2.

    Navel oranges are named that because of the belly-button formation

    opposite the stem end.

    Hint: The bigger the navel in an orange, the sweeter the orange.

    3.

    When is an orange green? When it is a Valencia!

    4.

    After chocolate and vanilla, orange is the worlds favorite flavor.

    5.

    Christopher Columbus brought the first orange seeds and seedlings to the

    New World on his second voyage in 1493.

    Sunkist offers games, experiments, and recipes at their website for teachers

    and students.

    www.sunkist.com/kids/facts/oranges.asp

    OrangeJuiceCake

    Ingredients:

    13.5packageinstantvanillapudding

    118.25ouncepackageyellowcakemix

    4eggs

    cupvegetableoil

    1cupcoldwater

    cupofbutter

    cupwhitesugar

    cuporangejuice

    Directions:

    1. Preheatovento350degrees.GreasealargeBundtpan.

    2. Combinethecakemix,puddingmix,water,oil,andeggstogether.Mixwithanelectricmixeron

    mediumspeedfor2minutes.PourbatterintoBundtpan.

    3. Bakefor30minutes,oruntilknifeinsertedincakecomesoutclean.

    4. Combinethebutter,sugar,andorangejuiceinasaucepan.Boilthismixtureforabout2minutes.

    Whitestillwarm,pokeholesinthetopofthecakewithafork.Pourorangejuicemixtureovercake.

    Whenthecakeissaturatedplaceitonaplant,andjusttopwithconfectionerssugar.

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    Pumpkin Math

    1.

    Does the size of the pumpkin make any difference in

    the number of seeds inside the pumpkin?

    2.Do the number of rib lines relate to the number of

    seeds inside?

    3.Do the number of rib lines relate to the size of the

    pumpkin?

    4.Estimate the weight of the pumpkin, then weigh it.

    How close was your estimate?

    5.

    Estimate the circumference (the total distance around

    it) of your pumpkin, then measure it. How close was

    your estimate?

    6.Estimate the surface area of your pumpkin in

    stickers. How close was your estimate?

    7.Estimate the number or seeds in the pumpkin, then

    dig them all out and count them. Hint: group them in

    10s or 100s. How close was your estimate.

    8.

    Which estimate did you predict the best? Why?

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    Jack o Lantern Glyph

    Materials needed:

    PencilCrayons, pencil colors, and/or markers

    Assembly instructions:

    Rib Lines

    Draw a line for each year you are oldEye Shape

    Circles - if there are 2 people in your family

    riangles - if there are 3 people in your familySquares - if there are 4 people in your familyPentagons - if there are 5 people in yourfamilyHexagon - for 6 or more people in your family

    Eye Color

    Black - if you like bugs and snakesYellow - if you do not like bugs and snakesGreen - if you like bugs but not snakesBlue - if you like snakes but not bugs

    Nose Shape

    Rectangular - if you have a petHeart shaped - if you do not have a pet

    Mouth Shape

    Smile- if you will wear a friendly costumeFrown - if you will wear a scary costumeSmile with teeth - if you will not wear acostume

    Stem Color Yellow - if you like suckers the bestBrown - if you like chocolate candy the testGreen - if you like all kinds of candyBlack - if you don't like candy at all

    Eyebrow Shape Smooth - if you are a girlJagged - if you are a boy

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    9

    8

    7

    6

    5

    4

    3

    2

    1

    A B C D E F G H I

    Jack-0-Lantern

    Name: Date:

    Jack-o-Lantern 1 tkawas[email protected]

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    Jack-0-Lantern

    O = orange YB = brownW = whiteB W

    YO

    Y = yellowO = orange

    OW

    W = whiteO = orange

    YO

    Y = yellowO = orange

    = yellow

    C7

    D7

    E7

    F7

    G7

    B7

    B6

    C6

    D6

    O

    O

    O

    O

    WO

    WO

    O

    O

    E6

    F6

    G6

    B5

    C5

    D5

    E5

    F5

    G5

    YO

    Y

    O

    B4C4

    D4E4

    F4G4

    B3

    C3

    D3

    E3

    F3

    G3

    O

    O

    YO

    YO

    Y

    Y

    C2

    D2

    E2

    F2

    B2

    G2

    D8

    E8

    O

    O

    O

    O

    0W

    OW

    B W

    W B

    O

    Y

    O

    OY

    O

    O

    O

    O

    O

    O

    O

    O

    Jack-o-Lantern 2 [email protected]

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    9

    8

    7

    6

    5

    4

    3

    2

    1

    A B C D E F G H I

    Jack-0-Lantern

    Name: Answer Key

    Jack-o-Lantern 3 [email protected]

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    Toasted Pumpkin Seeds Recipe

    INGREDIENTS

    One medium sized pumpkin

    Salt

    Olive oil

    METHOD

    1Preheat oven to 400F. Cut open the pumpkin and use a strong metal spoon to scoop out the

    insides. Separate the seeds from the stringy core. Rinse the seeds.

    2In a small saucepan, add the seeds to water, about 2 cups of water to every half cup of seeds. Add

    a half tablespoon of salt for every cup of water (more if you like your seeds saltier). Bring to a boil.

    Let simmer for 10 minutes. Remove from heat and drain.

    3Spread about a tablespoon of olive oil over the bottom of a roasting pan. Spread the seeds out over

    the roasting pan, all in one layer. Bake on the top rack until the seeds begin to brown, 10-20 minutes.

    When browned to your satisfaction, remove from the oven and let the pan cool on a rack. Let the

    seeds cool all the way down before eating. Either crack to remove the inner seed (a lot of work and in

    my opinion, unnecessary) or eat whole.

    Yummy Pumpkin Seeds

    Ingredients

    1 1/2 cups raw whole pumpkin seeds

    2 teaspoons butter, melted

    1 pinch salt

    Directions

    1. Preheat oven to 300 degrees F (150 degrees C).

    2. Toss seeds in a bowl with the melted butter and salt. Spread the seeds in a

    single layer on a baking sheet and bake for about 45 minutes or until golden

    brown; stir occasionally.

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    EASY PUMPKIN PIEINGREDIENTS:

    cup sugar1 teaspoons pumpkin pie spice teaspoon salt1 can (15 oz) pumpkin (not pumpkin pie mix)1 cups evaporated milk or half and half2 eggs, beaten

    1 Pillsbury Pet-Ritz frozen deep-dish pie crust

    DIRECTIONS:

    Heat oven to 425F. In large bowl, mix filling ingredients. Pour into pie crust. Bake 15 minutes. Reduce oven temperature to 350F; bake 40 to 50 minutes

    longer or until knife inserted near center comes out clean. Cool 2 hours. Serve orrefrigerate until serving time. Store in refrigerator.

    ROASTED PUMPKIN SEEDS

    Pumpkin seeds2 tbsp. butter1/2-1 tsp. Worcestershire sauce to taste1/2 tsp. garlic powder or to taste1/2 tsp. onion powder or to tasteLittle saltTake seeds out of pumpkin. Wash seeds thoroughly. Lay onparchment paper to dry (overnight is best).

    In a saucepan, melt butter. Take off heat, mix in all other ingredients.

    Stir together with seeds until all seeds are well covered. Lay out singlelayer on a cookie sheet. Bake at 250F for 2 hours.

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    Watermelon Math

    Estimate how much the watermelon weighs.

    Will the watermelon sink or float?

    Guess how many seeds are in a watermelon.

    Estimate circumference of a watermelon.

    Watermelon Math Center

    Make 10 green rinds and write a number word on them.

    Make 10 red watermelon parts and place seeds on them.

    Students match the rind to the watermelon.

    Here is a baggie center I made. The student matched the rind to the correct watermelon.

    Watermelon Fractions

    Make fractions using paper watermelons (halves, quarters, thirds...)

    Watermelon Dice Game

    For each game: Cutout a large watermelon from cardstock. Cut out 40 watermelon seeds.

    To play: students play in twos. Each student gets 20 watermelon seeds and one die. Students

    take turns rolling the die. First to get all their seeds on the watermelon wins

    Watermelon Seed Math Game

    Prepare a set of watermelon cards with numbers 1-9. Place cards face down. Student draws

    two cards and adds them together to find the sum.

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    Watermelon Glyph

    How old are you - Place seeds on to match age.

    Watermelon is your favorite fruit - seeds are round.

    Watermelon is not your favorite fruit - seeds are square.

    I am a boy - yellow rind

    I am a girl - green rind

    Which do you like best?

    I like watermelon flavored Kool-Aid best - pink watermelon

    I like watermelon flavored gum best - red melon

    Math or Reading?

    1 bite mark - I prefer math

    2 bites - I prefer reading

    Watermelon Cookies

    3/4 c. butter or margarine

    3/4 c. sugar

    1 egg

    1/2 t. almond extract

    2 1/4 c. all-purpose flour

    1/4 t. salt

    1/4 t. baking powder

    Red and Green food coloringRaisins ( Used to resemble watermelon seeds)

    In a mixing bowl, cream butter, sugar, egg, and extract until light and fluffy. Combine flout,

    salt, and baking powder; stir into creamed mixture and mix well. Remove 1 cup of dough; set

    aside. At low speed, beat in enough red food coloring to tint dough deep red. Roll into a 3

    1/2-in.-long tube; wrap in plastic wrap and refrigerate until firm, about 2 hours. Divide 1 cup

    of reserved dough into two pieces. To one piece, add enough green food coloring to tint dough

    deep green. Do not tint remaining piece of dough. Wrap each piece separately in plastic wrap;

    chill until firm. On a floured sheet of waxed paper, roll untinted dough into a 8 1/2-in. x 3

    1/2-in. rectangle. Place red dough along short end of rectangle. Roll up and encircle red

    dough with untinted dough; set aside. On floured waxed paper, roll the green dough into a10-in. x 3 1/2-in. rectangle. Place tube of red/untinted dough along the short end of green

    dough. Roll up and encircle tube with green dough; Cover tightly with plastic wrap; refrigerate

    at least 8 hours or overnight. Unwrap dough and cut into 1/8-in. slices, place 1 in. apart on

    ungreased baking sheets. Lightly press raisins and sesame seeds into each slice. Bake at 375

    for 6-8 min. or until cookies are firm, but not brown. While still warm, cut each cookie in

    half or into pie-shaped wedges. Remove to a wire rack to cool.

    Makes 3 dozen

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    ump With ill

    Rockstar Nutritionist Jump with Jill

    Promotes Watermelon

    The "Eat More Watermelon! Jump with JillTour" kicked off National Nutrition Month inMarch. This rock 'n roll nutrition tour sings tothe tasty tune of watermelon throughoutelementary schools nationwide. From

    California to New Jersey, and Nebraska toTexas, the tour will run from March throughSeptember 2011 and is expected to reach over 30,000 kids. The showseducational, movement-inducing tunes are an innovative way to teach kidsthe benefits of enjoying fruit like watermelon over soda or candy.

    Watermelon is naturally sweet and is like eating a multi-vitamin; its highin lycopene, Vitamin C, A, and it has Vitamin B6, says show creator JillJayne, a registered dietitian and musician. Its nutritious, and delicious,

    and fun to eat. There is no food Id rather sing about!"

    Better known as the Rockstar Nutritionist, Jill Jayne has created areputation of healthy rock since 2006. Her unique approach to nutritionaddresses the childhood obesity crisis in a way that todays media-savvykids can digest. Using music, dance, and interactive learning, the showimproves retention of healthy habits by using the same tools used by massmedia marketers to sell junk food. Jill teaches entire schools about healthyeating and staying active. Jills work has been performed for over 100,000

    kids across the United States and has been featured in national mediaoutlets including NPR, PBS, The Washington Post, and industry tradepublications.

    To learn more about the Jump with Jill program, and to see if she's comingto a school near you, visit her website at www.jumpwithjill.comor contactStephanie Simek at [email protected]

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    Watermelon

    Seed Spitting

    Another idea for using watermelons in your mathematics

    classroom is to hold a seed spitting contest with your

    students, and let your kids practice their estimation and

    measurement skills for linear measurement.

    Many towns in Texas have annual festivals where seed spittin

    contests are held. Students could research these festivals (for

    example the Watermelon Thump in Luling, TX, or the Peach

    & Melon Festival in De Leon, TX) and also research various

    techniques for spitting watermelon seeds before the contest is

    held.

    By the way. Did you know that the World Record for

    spitting a watermelon seed is ----- 75 feet, 2 inches This

    record was set at the 81

    st

    De Leon Peach & Melon Festival on

    August 12, 1995, by Jason Schayot. This feat passed the

    previous world record of 68 feet, 9.125 inches set by Lee

    Wheelis at the Luling Watermelon Thump in 1989

    (http://web.mac.com/jptate/De_Leon_Handbook/World_Re

    cord.html).

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    Fruity

    Fractionsand more

    Challenge your students to find fractions that occur in nature

    or in their world outside of the classroom.

    Your students shouldnt have much trouble finding many

    fractions, but thirds will most likely be difficult for them to

    find. For example, even on highway signs, you dont ever see

    a sign that says that your next exit is 1/3 mile away

    A great example of thirds in the fruit world is the banana.

    When split lengthwise down the center, the banana will always

    split into equal thirds Go ahead try it

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    Other Fruits

    Thereareseveralotherfruitsthatyoucandosimilarexercises/experimentswithsuchasapples,

    lemons,limes,grapefruit,kiwifruitpeaches,nectarines,apricots,cantaloupes,etc.Ofcourse,some

    do

    not

    lend

    themselves

    to

    counting

    seeds

    (kiwi

    fruit,

    peaches,

    nectarines,

    etc.),

    and

    some

    are

    better

    foronethingthananother.Asateacher,youcanpickandchoosewhichthingsyouwanttoteachand

    emphasizeandwhatyoudonotwanttoteach.

    HowcanIobtainthefruit? Manyschoolsgetcommoditiesfromthestate,andthelunchroomladies

    canbecomeyourbestfriend.Manytimestheyarethrilledatgettingridofsomeoftheirexcessfruit.

    Additionally,gettoknowyourlocalproducemanager. Manytimesaproducemanagerwillgiveyou

    freefruitorvegetablesiftheyaregoingtothrowthemout,ortheywillsellthemtoyouatadiscount

    iftheyknowtheyareforschoollearningexperiences.Remembertoalwayssendthemapersonalized

    thankyounotesignedbyallyourstudents.

    Alwayscheckforallergiesthatyourstudentshavebeforebringinganyfruitorvegetableintoyour

    classroom.

    Therearemanyotherfruitsthatcanbepurchasedforclassroomusesuchasstarfruit,dragonfruit,

    Clementine,jackfruit,kumquat,mango,pineapple,Uglifruit,andthelistgoeson. Youshouldalways

    allowthestudentstotastethefruitiftheysodesire. Manystudentshavenevertastedanythingother

    thananapple,banana,orange,andstrawberryandthatisauniqueexperienceinitselfforthemto

    notonlyseebuttotastesomethingnew.

    Bottomline

    HAVE

    FUN

    MAKE

    IT

    FUN

    AND

    IT

    WILL

    BE

    FUN

    FOR

    ALL!

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    Wehaveusedsomefruitandgivenyoumanyideasofhowtouseotherfruitsbutwhatabout

    vegetables?Letlookatsomeideas:

    Radishes:Thesearegoodforfindingcircumference,diameter,mass,weight,andshape

    comparison.

    Carrots:Thesearegreattousefornonstandardlinearmeasurement,weight,mass,andshape

    comparison.

    Cucumbers:Thesearegreattousefornonstandardlinearmeasurementandshapecomparison.

    Celery:Goodtousefornonstandardlinearmeasurement.

    Potatoes:

    You

    can

    do

    everything

    we

    did

    with

    the

    orange

    with

    a

    potato

    except

    for

    prediction

    and

    calculationofseeds.(Potatoesarecheapandeasytoobtain.)

    Greenbeans:Makewonderfulnonstandardlinearmeasurement.

    Squash:Thesearegreatforweight,mass,andnonstandardlinearmeasurement.

    BellPeppers:Iwouldavoidbecausethejuice/liquidinsidehasatendencytoburneyes.

    And a Few Veggies

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    Literature

    Connections

    Amend,B.(2003).YourMommaThinksSquareRootsareVegetables.KansasCity:AndrewsMcMeelPu

    Burns,M.(1997).SpaghettiandMeatballsforAll!AMathematicalStory.NewYork:Scholastic.

    Carpenter,D.H.(2004).ApplestoOregon.NewYork:Scholastic.

    Cook,D.F.(1998).Kids'PumpkinProjects:Planting&HarvestFun.Charlotte,VT:WilliamsonPublishing

    Fleming,M.(2003).OneLittlePumpkin.NewYork:Scholastic.

    Giganti,P.(1992).EachOrangeHad8Slices.NewYork:GreenwillowBooks.

    Goldstone,B.(2006).GreatEstimations.NewYork:Scholastic.

    HartDavis,A.(1998).AmazingMathPuzzles.NewYork:SterlingPublishingCo.,Inc.

    Hatchett,M.

    A.

    (2011).

    Find

    the

    Mathematics...

    in

    the

    Great

    Outdoors

    of

    Texas!

    Texas

    Mathematics

    Tea

    Hopkinson,D.,&Carpenter,N.(2004).ApplestoOregon.NewYork:Scholastic.

    Kroll,S.(1984).TheBiggestPumpkinEver.NewYork:Scholastic.

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    Leeming,J.(2008).FabulousFunwithPuzzles.NewYork:Time,Inc.

    McNamara,M.(2007).HowManySeedsinaPumpkin?NewYork:Schwartz&WadeBooks.

    Murphy,S.J.(1996).GiveMeHalf!NewYork:Scholastic.

    Murphy,S.J.(1998).LemonadeforSale.NewYork:HarperCollins.

    Pallotta,J.(2002).AppleFractions.NewYork:Scholastic.

    Weiskopf,C.(2002).Lemon&Ice&EverythingNice.NewYork:Scholastic.

    White,L.(1996).TooManyPumpkins.NewYork:HolidayHouse.

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    Name _________________________________ Date ________________

    ruity

    Math

    Recording Sheet

    Object to be measured:_______________

    Attribute

    to

    beMeasured

    Our

    Prediction

    Our

    Measurement