TIPM3 二級和三級課件

TIPM3

Grades2and3February15MonicaHartmanAgendaHomeworkandLessonSharingGeometricMeasurement–relatingareatomultiplicationandadditionGeometry–reasonwithshapesandattributesFractions.PerimeterandAreaProblemGeometry2.G.Partitionarectangleintorowsandcolumnsofsamesizesquaresandcounttofindthetotalnumberofthem.GeometricMeasurement3.MD.5Recognizeareaasattributeofplanefiguresandunderstandconceptofareameasurement3.MD.6Measureareabycountingunitsquares3.MD.7Relateareatotheoperationsofmultiplicationanddivision3.MD.8SolverealworldandmathematicalproblemsinvolvingperimetersofpolygonsStackingtheFactsUsingtheareamodeltoprovidemeaningformultiplicationFollowthedirectionsoftheinstructorasyouusethematerialsforthisactivity/Geometry2.G.3Partitioncirclesandrectanglesintotwo,three,orfourequalshares,describethesharesusinghalves,thirds,halfof,athirdof,etc.,anddescribethewholeastwohalves,threethirds,fourfourths.Recognizethatequalsharesofidenticalwholesneednothavethesameshape.Geometry3.G.2Partitionshapesintopartswithequalareas.Expresstheareaofeachpartasaunitfractionofthewhole.ChartthePartsLearningGoal:Topartitionshapesintotwo,three,andfourequalshares.Eachpersonatthetablewillchooseoneoftheshapesfromthebluesheetofsixshapes.Youneedfourofthechosenshape.Leaveoneshapealone;foldtheothershapestomaketwo,three,orfourequalparts.Cutonthefold.Gluetheoriginalshapeinthetopleftcornerofasheetofconstructionpaper.Gluethethreecut-upshapesbacktogetherundertheoriginalshape.GeoboardFractionsMakealargesquareontheGeoboard.Showhowyoucandividethatsquareintotwoequalparts.Howmanywayscanyoudividethesquareintoequalparts?Areallthepartscongruent?RecordtwodifferentwaysonyourGeoboardpaperWhatistheareaandperimeterofyourshapes?Labelthem.GeoboardFractionsMakealargerectangleontheGeoboard.Showhowyoucandividethattriangleintotwoequalparts.Howmanywayscanyoudividetherectangleintoequalparts?Areallthepartscongruent?RecordtwodifferentwaysonyourGeoboardpaper.Whatistheareaandperimeterofyourshapes?Labelthem.PuzzleMakersMakethepuzzlesfoundintheenvelopesonyourtable.TradeyourpuzzlewithyourpartnersatthetableTraceyourshapeonapieceofpaper,thencutoutyourshape.Makeapuzzlebycuttingtheshapeintotwo,three,orfourequalpieces.Labelyourpieceswiththefractionname.Giveyourpuzzleandthepaperwiththetracedshapetoyourpartnerstomake.LunchTheRelationshipBetweenPerimeterandAreaImagineoneofyourstudentscomestoclassveryexcited.Shetellsyouthatshefiguredoutatheorythatyounevertoldtheclass.Sheexplainsthatshehasdiscoveredthatastheperimeterofarectangleincreases,theareaalsoincreases.Sheshowsyouthispicturetoprovewhatsheisdoing.4cm4cm8cm4cmPerimeter=16cmArea=16squarecentimetersPerimeter=24cmArea=32squarecentimetersHowwouldyourespondtothisstudent?ThreePossibleResponses1.Divertthestudentfrompursuingideasoutsidethescheduledcurriculum.2.Beresponsibleforevaluatingthetruthofthestudent’sclaim.Engagethestudentinexploringthetruthoftheclaim.ChineseTeachersApproach1.Justifyingthestudents’claimascorrect(16/72).FirstLevelofUnderstanding:Disprovingtheclaim(50of72)SecondLevelofunderstanding:IdentifyingthepossibilitiesThirdLevelofUnderstanding:ClarifyingtheconditionsbyexploringthenumericalrelationshipsbetweenperimeterandareaandelaboratingonthepossibilitiesExplainingtheconditions(Proofbyusingthedistributiveproperty.*Ma,Liping(1999).KnowingandTeachingElementaryMathematicsTeachingWithCurriculumFocalPointsApplicationsofComposingandDecomposingPolygons(page60–topofpage63)TheDistributiveProperty(3.OA.5)StrengtheningFluencyThroughConnections(65–67)DemonstratetheDistributivePropertywitharectanglemadefromthegridpaper.PlanningTogether