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

Fruity Math

(with a Few

Veggies )

By

Dr. Pam Littletonlittleton@tarleton.edu

Dr. Beth Riggseriggs@tarleton.edu

Rose Ann Jacksonrjackson@tarleton.edu

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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@mathwire.com

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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 tkawas@mathwire.com

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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 tkawas@mathwire.com

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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 ssimek@watermelon.org.

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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