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ID:40353934
大小:783.44 KB
页数:9页
时间:2019-07-31
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1、VolumeofRotatedFiguresTeacherNotesTopicArea:VolumeofSolidsbyShellMethodNCTMStandards:•Usetwo-dimensionalrepresentationsofthree-dimensionalobjectstovisualizeandsolveproblemssuchasthoseinvolvingsurfaceareaandvolume;•UseCartesiancoordinatesandothercoordinatesystems,suchasnavigational,polar,orsph
2、ericalsystems,toanalyzegeometricsituations;ObjectivesGivenaphotofile,studentswillbeabletofitanequationontothepictureandfindtheequationforthelineofbestfit.Usingtheirknowledgeofpolynomialfunctionsandintegralcalculus,thestudentswillfindthevolumeofafigureformedbyrotatingapolynomialaroundaspecifie
3、daxis.GettingStartedHavestudentsworkinpairstodeterminethecoordinatesofpointsusedtofindthelineofbestfitforapolynomialandusethisequationtosolveproblemsinvolvingrotationofsolids.Priortousingthisactivity:•Studentsshouldhaveanunderstandingofhowtofindaregressionline.•Studentsshouldhaveanunderstandi
4、ngofpolynomialfunctions.•Studentsshouldbeabletowriteandsolveanintegralgiventhefunctionwithupperandlowerbounds.Waysstudentscanprovideevidenceoflearning:•Studentswillbeabletousetheirknowledgeofgeometrytodetermineupperandlowerboundsforanintegral.•Studentswillbeabletofindthevolumeofafigureusingth
5、eshellmethod.Commonmistakestobeonthelookoutfor:•Studentsmayhavedifficultydeterminingupperandlowerbounds.•Studentsmayhavedifficultywiththeintegrationofapolynomial.•Studentsmayusethewrongpolynomialfortheintegration.Definitions:•Regression•UpperandLowerBounds•Integral©2010CASIOComputerCo.,LTD.Al
6、lRightReserved.Page-1-VolumeofRotatedFigures“HowTo”Thefollowingwillwalkyouthroughthekeystrokesandmenusrequiredtosuccessfullycompletethevolumeofrotatedfiguresactivity.ToopenabackgroundimageinPicturePlot:1.FromtheMainMenu,highlightthePicturePloticonandpresslorpress(.2.Pressq(OPEN)toopentheCASIO
7、folder.3.Theg3pfoldercontains47backgroundimages.PressNq(OPEN)toopenthefolder.Scrolldownthelistofimagesandhighlightthedesiredimage.Youwillbeusingthe“Pancakes”inthisactivity.Pressq(OPEN).©rimglow-Fotolia.comToplotspointsontheimageandcreatealist
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