submarine sandwich task - ci math · 2014. 7. 29. · submarine sandwich task card materials: green...

Unlessotherwisenoted,thisworkislicensedunderaCreativeCommonsAttribution‐ShareAlike4.0InternationalLicense.ThismaterialisbaseduponworksupportedbytheNationalScienceFoundationunderGrantNo.1316235.Anyopinions,finding,andconclusionsorrecommendationsexpressedinthismaterialarethoseoftheauthor(s)anddonotnecessarilyreflecttheviewsoftheNationalScienceFoundation.Thisandotherterrifictaskscanbefoundathttp://www.cimath.org

ComplexInstructionTaskInformationSheet

SubmarineSandwiches

TaskTitle: SharingSubmarineSandwichesTaskAuthors: Adaptedfrom

Fosnot,C.T.,&Dolk,M.L.A.M.(2002).Youngmathematiciansatwork:Constructingfractions,decimals,andpercents.Portsmouth,NH:Heinemann.

AdaptedbyTeachMathGroup(AmyRothMcDuffie,CoreyDrake,ErinTurner,MaryFoote,TonyaBartell)

Tags:mathorpedagogicalcontent

Math

LearningGoals Objectives(mathematicaland/orpedagogical):

FractionalfairsharingComparingfractionquantities

CommonCoreContentStandardsAddressed:

DevelopingUnderstandingofFractions 3.NF.1 3.NF.3d

ExtendUnderstandingofFractionEquivalenceandOrdering

4.NF.1 4.NF.2 4.NF.3

CommonCoreStandardsforMathematicalPracticeAddressed:

MathematicalPractices:1,2,3,4

SetupInformation SpecificNorms Everyonecontributesandnoonetakesover

Everyonerecords Everyoneexplainsallofthework

SpecificRoles Multipleabilityorientation(SeetheSmarterTogether!bookformoreinformation.)

Inordertobesuccessfulatthistask,yourgroupisgoingtoneedto:

makeequalparts partitionshapes communicateideas comparefractionalquantities connectmathematicsproblemtoexperiences


sharingthingsoutsideofschool usemultiplerepresentations listentothereasoningofothers craftmathematicalarguments modelrealworldcontextswithmathematics persevereinproblemsolving

Nooneofusisgoodatallofthesethings,butweareeachgoodatsomeofthem.Togetheryourgrouphastheabilitiesyouneedtobesuccessful.

Materialstoprepare

Sheetsofplaingreenpaper Markers pencils

Makecopies: Submarinesandwichtemplates(severalforeachgroup) Taskcard(2pergroup)(copyPart1onaseparatepage

fromParts2‐5) Problemsforpairs(copypageonepergroupandcutin

half)

TaskEnactment Launch Wholeclassdiscussionofexperienceswhenstudentshave

sharedsomethingwithothers.Thepurposeofthisdiscussionistodrawoutpotentialmathematicalfundsofknowledge,orpracticesthatstudentsinengageinathomeorintheircommunitiesrelatedtosharingthingsequally.Inadditiontosharingfood,suchaspizza,brownies,andsandwiches,youcouldalsotouchonotherkindsofsharingbutultimatelyfunnelthediscussiontowardsharingfooditemthatcanbecutintopieces.

Closure Asagroupchoosetwosolutionstoanyoneproblemandbereadytoexplain(tothewholeclass)howyouknowwhichshowsthegreateramountofsubmarinesandwichperperson.Whatareourconcernswhenwesharefairly?

minimumnumberofcuts? eachpersongetsequalcut

Anyspecificdirections?

Handoutpart1togroupsof4students.Asgroupsfinishandcanexplaintheirsolutions,handoutdirectionstoparts2‐6alongwithenvelopeswithadditionalproblems.


Whenrecordingonsheet,studentsmustdrawtheirownrepresentations,notallowpartnerstodrawontheirpaper.

DuringcheckinwithteacherafterPart4,theteachershouldascertainwhetherstudentsaremakingsufficientsenseofthetasktocontinuetoPart5.

Possiblevariations–

howmightthistaskbeadjustedfordifferentcontentorgradelevel?

Easiernumbercombinationsorfewerproblems.IfyouaredoingthiswithPSTs,aftertheproblemsolvingsession,showthevideofromFosnot&Dolk,YoungMathematiciansatWork.

Moreinformation

abouttaskdesign(Justincaseyou

haven’talreadyhadenoughdetails)

Whyspecifythatstudentsshouldwriteongreenpaper?Fortworeasons:First,iftheteacheriswalkingaroundcheckingtoseewheregroupsare,andsheseesstudentsworkingwiththegreenpaperrepresentation,sheknowsimmediatelywheretheyareinthetask.Second,sinceposterpaperiswhite,iftherepresentationthattheyuseisaonadifferentcoloredpaper,itwillstandoutmore.(Thisisparticularlytrueiftheydecidetocutthingsoutofthegreenpaperandgluethemontheposterpaper–whiteonwhitedoesn’tworkwell.)Thisisnotabigdealofcourse,butthereissomereasoningbehindit.Ofcourseblue,orange,red,purpleoranyothercolorwouldworkjustaswell.Sothegreenpartwasjustrandom.Whyprovidesandwichcutouts?Thereasonforprovidingthesandwichcutoutswastwo‐fold.One,itisavisualreferent(thatlooksrealisticenoughtotriggersomeunderstanding)forchildrenwhomaynotknowrightawaywhatsubmarinesandwichesare.Ifchildrenthinkjustofanindividualsandwich,andnotthatsandwichescanbetheselongishthingsthatcanbepartitionedintomorethan2or3pieces,thatcanbeproblematicinthesetasks.Soforchildrenwhomaynothavetheculturalknowledgeofwhatasubsandwichis,wethoughtarealisticlookingvisualwouldbeuseful.Theymightseethepictureandrecognizesubsassomethingtheyhaveinfactseenbefore,oratleasthaveanimageinmindofwhattheyare.Second,thecutoutssupportpaperfoldingstrategies,somethingthatisharderwithothertoolslikelinkingcubes,drawings,etc.Sohavingcutoutsavailableinadditionaltoothertoolsjustopensthespaceforpossiblestrategies.Theideawasnottopushchildrentousethecutouts,justtoofferitasapossibletool.


Thesandwichcutoutsareoval,makingithardforstudentstocreatetrulyequalshares.Isthataproblem?Whatmattersinpartitioningiswhatthechildistryingtodo—whenchildrentrytosplitthingsinto3equalpartstomakethirds,thepiecesarerarelyequaleveniftheystartwitharectanglemodel(evenfoldingexactthirdsiskindofimpossible),andtheintentioniswhatmatters.Aslongaschildrenknowwhattheymeantodoandknowwhatthepiecesrepresent,thatisallthatmatters.Thefactthatthethirdsareexactlyequalintermsofareabecauseonehasroundededgesisnottheissue.Childrencanrecognizethatbutstillkeeptrackofthefactthattheyarepartitioningsomethinginto3rdsand3rdsareequalparts.Thissameissuecomesupwithchildren’sdrawings.Withcutoutsthatstartouttobethesamesize,andwhenclassesofkidshaverepeatedexperienceswithequalsharingtasks,thiscomesupasatopicofgroupdiscussionprettyquickly.Childrenmovepastitfairlyeasily.Iftheyarerelyingonlyonvisualcomparisonmethodstocomparefractions,itcancreateproblemsbecause4thcanlookdifferentthan3rdsforexample,etc.Sothathastobeaddressed,butwewantchildrenusingotherkindsofreasoningtocomparefractions,beyondjustwhichonelooksbigger.


SuggestedRoles(AdaptedfromAmyMcDonald)

Facilitator

Gets the team off to quick start Makes sure everyone understands the

information on the task card. Organizes the team so they can complete

the task Keeps track of time Substitutes for absent roles

“Who knows how to start?” “I can’t get it yet… can someone

help?” “We need to keep moving so we

can…” “Let’s find a way to work this out.”

Resource Manager

Makes sure the team is using all resources

well, especially people. Calls the teacher over for a team question Collects supplies for the team Cares for and returns supplies Organizes clean up

“I think we need more information here.”

“I’ll call the teacher over” “We need to clean up. Can you…

while I…?” “Do we all have the same question?”

Recorder / Reporter

Gives update statements on team’s progress

Makes sure each member of the team records the data

Organizes and introduces report “We need to keep moving so we

can…” “I’ll introduce the report, then…” “Did everyone get that in your

notes?”

Reflection Leader

Helps the group reflect on their work during the task and at the end.

Asks questions about the group’s activity: “What strategies have we used?” “What worked?” “What isn’t working/didn’t work?”


SubmarineSandwichTaskCard

Materials: Greenpaper Submarinesandwichtemplates Markers,pencilsNORMS:

Everyonecontributesandnoonetakesover Everyonerecords Everyoneexplainsallofthework

Directions:Part1)Asagroup,solvethefollowingproblem.6peopleshare4submarinesandwichessothateachpersongetsthesameamount.Howmuchofonesandwichdoeseachpersonget?• Onagreensheetofpaper,representtwodifferentwaystosharethesandwiches.

o Showhowyousplitthesandwicheso Showhowmuchsandwichonepersongetso Usewords,pictures,andnumbers

• Eachpersonshouldshareoneexperienceinwhichtheysharedfoodwithothers.

• Whenyouaredone,eachpersonraisesahandtosignaltheteacher.


Part2)Eachpairshouldsolvetheirtwoproblems.Thinkaboutthestrategiesyoujustused.Part3)Onagreensheetofpaper,eachpersonshouldrepresentasolutionforoneoftheproblems

o Showhowyousplitthesandwicheso Showhowmuchsandwichonepersongetso Usewords,pictures,andnumbers

Part4)Asagroupoffour,taketurnspresentingyoursolutionstothegroup.(Eachpersonmustshareonesolution.)Asagroup,determineifeachsolutionmakessense.Askquestionstoclarifyideas.Helpthepresentermakechangesifnecessary.Whenthegroupagreesthatallsolutionsmakesense,CHECKWITHTHETEACHER.Part5)Asagroup,arrangethefivesolutions(onthegreensheetsofpaper)sothattheamountofsubmarinesandwichthateachpersongetsisorderedfromleasttogreatest.Part6)Selectsolutionsfortwodifferentproblemsandbereadytoexplainhowyouknowwhichshowsthegreateramountofsubmarinesandwichperperson.


ProblemsforPair#1

5peopleshare3submarinesandwichessothattheyeachgetthesameamount.Howmuchofasubmarinesandwichdoesonepersonget?

4peopleshare3submarinesandwichessothattheyeachgetthesameamount.Howmuchofasubmarinesandwichdoesonepersonget?‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

ProblemsforPair#2




Theseimagesarefromhttp://sweetclipart.com/sub‐sandwich‐clip‐art‐12.TheyarelicensedasAttribution‐NonCommercial‐ShareAlike3.0Unported.


Theseimagesarefromhttp://sweetclipart.com/sub‐sandwich‐colorable‐line‐art‐364.TheyarelicensedasAttribution‐NonCommercial‐ShareAlike3.0Unported.

submarine sandwich task - ci math · 2014. 7. 29. · submarine sandwich task card materials: green...

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