Directions for Using Worksheets on Thinking about 3D Shape based.docx
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DirectionsforUsingWorksheetsonThinkingabout3DShapebased
DirectionsforUsingWorksheetsonThinkingabout3DShape（basedonOwens’unpublished3Dtest）
Equipment
Rectangularprisms（e.g.,Cuisenairerods,boxesorLegopieces（3shapesincludingthinone）,cone,cylinder,cube,opencubeswhichcanbeopenedout,asquareofpaper
Introduction
∙Saytheseworksheetsareaboutthinkingin3Dspaceandabout3Dshapesorsolids.
∙Showatleast5different-sizedrectangularprismssuchascuisinairerod,boxfordisks,athinandthickerLegoblocks.Whenevershowingobjectsor3Dshapesturnthemslowlyaroundandover.AskWhatdoyoucallthese?
（expectrectangularprismsbutiftheysaycuboidorsquareprismsaythatwewillincludethemallasrectangularprisms.Allthesidesarerectanglesandtheysitflatonthetablewiththetopparallel）.
∙Showaclosedcubeandanopencube.Askforthenamesandwhythedifferenceinname.Askforthenumberofsides（6and5respectively）.
Showatriangularpyramidandasquarepyramid.AskWhatdoyoucallthese?
（expectpyramidandpromptforthetwokinds）.Showthedifferenceinthebasesandthatthepyramidscometoapointwithtriangularsidefaces.Asktheclasstorepeatthenameandtosaywhytheycallitbythatname.
∙Showacone,acylinder.Askforthenames.
WorksheetA:
Aretheshapesthesame?
RecognisingRotated3DShapes
SayThediagramsorpicturesonthesepagesareof3DShapesorsolids.Lookatthefrontpage.Whatisthefirstpicture?
（cone）Second?
（cylinder）.Readtheinstructions.Studentdoestheexamplefirstwithhelpandthencompletesthequestions
WorksheetB:
Canyouseethe3Dshape?
-EmbeddingandDisembedding3DShapes
Jointogether3cuisinairerodstoformarectangularprism.Askwhat3Dshapehasbeenmade?
（rectangularprism）.Howmanyblocksofthesamesizewereneeded?
（3）
SayThissectionisaboutputtingblockstogetherandseeingwhichonesmightfittogethertomakerectangularprisms.
WorksheetC:
CanYouSeeitAnotherWay?
-FoldingandUnfolding3DShapes
Showtheblockstogetherandsketchthefrontviewontheboard.
Takeapieceofpaperandfolditandtearoutashapeinthemiddleoftheopensides.Askastudenttocopywhatitmightlooklikewhenopenedout.
Takethepyramidsandcubespartiallyapartcarefullyandnotethetrianglesandsquares.
WorksheetA:
Aretheythesame?
Example
Lookatthe3DshapeunderSmiley.Ifyouturnitaround
orovercanitlookliketheshapeshownbelow.
CircleYesorNo.
1.YesNo2.YesNo
Lookatthe3DshapeunderSmiley.Ifyouturnitaround
orovercanitlookliketheshapeshownbelow.
CircleYesorNo.
1.YesNo2.YesNo
3.YesNo4.YesNo
5.YesNo6.YesNo
Threeblockshavefallenonthefloor.Oneblockhasacircleface,onehasatriangleface,andonehasarectangleface.Wearelookingdownonthem.Whichoneisunderneathonthebottom?
Circletheshape.
7.
ThreesticksaremarkedwithWhichoneisunderneathonthebottom.
Circletheshapeofitsmark.
8.9.
WorksheetB:
CanyouSeethe3Dshape?
Example
UnderSmileyisafinishedpicture.Thepicturebelow
isnotcomplete.
Putinthelinestocompleteitlikethefinishedone.
UnderSmileyisafinishedpicture.Thepicturebelowis
notcomplete.
Putinthelinestocompleteitlikethefinishedone.
ExampleUnderSmileyisabuildingofblocks.Isthe3Dshape
belowoneoftheblocks?
CircleYesorNo.
YesNoYesNo
UnderSmileyisabuildingof3blocks.Isthe3Dshape
oneoftheblocks?
CircleYesorNo.
1.YesNo2.YesNo3.YesNo
4.YesNo5.YesNo
Example
A3Dshapecanbejoinedtothe3DshapeunderSmiley.
Cantheshapebelowbejoinedtoittomakearectangularprism?
CircleYesorNo.
YesNoYesNo
UnderSmileyaretwoblocks.Cantheybejoinedtomake
theshapebelow.
CircleYesorNo.
YesNoYesNo
YesNoYesNo
Example
A3Dshapecanbejoinedtothe3DshapeunderSmiley.
Canthisshapebejoinedtomakearectangularprism?
CircleYesorNo.
YesNoYesNo
A3Dshapecanbejoinedtothe3DshapeunderSmiley.
Cantheshapesmakearectangularprism?
CircleYesorNo.
1.YesNo2.YesNo
3.YesNo4.YesNo
5.YesNo6.YesNo
Example
LookattheblockunderSmiley.Ifyouhadsomemore
likethiscouldyoumakethesolid3Dshapebelow.
CircleYesorNo.
IfYes,writehowmanyblocksyouneed.
Yes_____NoYes____No
1.Yes____No2.Yes____No
3.Yes____No4.Yes____No
5.Yes_____No6.Yes____No
WorksheetC:
CanYouSeeitAnotherWay?
Example
YoucanlookfromAstraightdownontotheobjectunder
Smiley.YoucanlookatthesidesfromeitherBorC.
A,
lookingdown
Fromwhichpositiondoyouseetheviewshown?
CircleA,BorC.
C
B
ABCNoABCNoABCNo
Fromwhichpositionareyoulookingattheobject?
CircleAfromthetop,
Bfrominfront,
Cfromtheside,
orifyoudon’tknow,circleNo.
A
B
C
ABCNoABCNoABCNo
A
C
B
ABCNoABCNoABCNo
A
B
C
ABCNoABCNoABCNo
Example
Asquarepieceofpaperisfoldedinhalftakingthetoptothebottom.
Aholeispunchedinandthenitisopenedupagain.Willitlookliketheoneshown?
CircleYesorNo.
YesNoYesNo
Asquarepieceofpaperisfoldedinhalftakingthetoptothebottom.
Aholeispunchedinitoracornercutoffandthenitisopenedupagain.
Willitlookliketheoneshown?
CircleYesorNo.
YesNoYesNo
YesNoYesNo
Example
TheshapeunderSmileyisfoldedup.Canitformthe3Dshape?
CircleYesorNo.
YesNoYesNo
Theshapeisfoldedup.Canitformthe3Dpyramid?
CircleYesorNo.
YesNoYesNoYesNo
Cantherectangularpaperbefoldedtomakethehollow3Dshapeshown?
CircleYesorNo.
Ifso,drawinthewhereyouwouldfoldthepaper,ifanyhardfoldisneeded.
YesNo
YesNo
YesNo
Canthetriangularpaperbefoldedtomakethehollow3Dshapeshown?
CircleYesorNo.
Ifso,drawinthewhereyouwouldfoldthepaper,ifanyfoldisneeded.
YesNo
YesNo
YesNo
S2Lesson1-Pop-upCards
Description
Studentsmakesimplepop-upcardsinaninvestigativemode.
Purpose
Studentsexperiencehow3Dcanbegeneratedandmodifiedbyfoldingbackwardsorforwards.Thecutsprovidesymmetricalchanges.
Outcomes
SGS2.1Makes,compares,describesandnamesthree-dimensionalobjectsincludingpyramids,andrepresentsthemindrawings
Knowledgeandskills
Studentslearnabout
WorkingMathematically
Studentslearnto
∙identifyingthree-dimensionalobjectsintheenvironmentandfromdrawings,photographsordescriptions
∙describethree-dimensionalobjectsusingeverydaylanguageandmathematicalterminology（Communicating）
∙explorewhatcanbecreatedfromfoldingandcuttingtomakethree-dimensionalobjects
Keyideas
Createnetsfromeverydaypackaging
Expectedlearningstrategies
Thestudentusespatternandmovementinher/hismentalimageryandisdevelopingconceptualrelationships.Thestudent:
∙Predictschangesmentallymodifyingshapesandtheirattributesusingmotionorpatternanalysis
∙Discussespatternsandmovementsassociatedwithcombinationsofshapesandrelationshipsbetweenshapes.
Materials
Paperorcardboardperstudentandscissors.Colouredpencils.Examplesofboughtandhomemadepop-upcards.
S2Lesson1-Pop-upCards
Activities
TeachingPointsandQuestions
Introduction
∙Showthestudentsomepurchasedpop-upcardsandyourownhome-madeones.
∙Takeacardandfoldit.Askstudentstopredictwhatmighthappenifyoumakeacutataslopeonthefold.
∙Tryitandopenupthecard.Askstudenthowyoumightmakethefoldpokeinwards.
∙Tryitandfoldithard.Re-closethecardandslowlyreopen.
∙Askstudentswhatitlookslikeandthendrawaface,sayofabirdiftheysayitlookslikeabeak.
Theseactivitiescanbecomeartproblemsolvingactivities.
Pop-upscanbemadebyslopingcutsonfold,bytwoperpendicularcuts,bydiagonalfoldsatthetopwhensidesarecutaway.
Theycanbedecoratedbygluingonpiecesorjustcolouringintomakeapicture.
Whatwillhappenifwemakeacutatthispoint?
Whathappensifwefolditinwards?
Howcanwemakethesecutsstickout?
Symmetryisakeyfeatureofthiswork.
Pushintocard
Activity（individual）
Studentsmayfindthebeakeasiesttodoandtheycaneasilydraweyesaroundit.
Discussthesymmetryofthefoldsthatgoinwardsoroutwards.
Glueaheartorsimilarcut-outonthefrontoftherectangularfoldedcut.
Iftheyaremakingcards,studentscandecidewhatisanappropriatemessagetowriteinside.
Conclusion（wholeclass）
Somestudentsdisplaytheircardsandshowhowtheyopenup.
Whichlinesaresymmetricalaboutthefold?
Couldyoupredictwhatmighthappenifyoumadeanothercut（orfold）paralleltothisone?
Studentsshareideasandhelpeachothertodeveloptheircards.
S2Lesson2–ShadowShapes
Description
Studentsinvestigatetheshadowsmadebyavarietyof3dimensionalobjects
Purpose
Studentsneedtoexperienceandimaginewhatashapewilllooklikefromadifferentperspective.Theydisembedtheface-onviewandrealisesomepartsarethenhiddenfromview.
Outcomes
SGS2.1Makes,compares,describesandnamesthree-dimensionalobjectsincludingpyramids,andrepresentsthemindrawings.
Knowledgeandskills
Studentslearnabout
WorkingMathematically
Studentslearnto
∙comparinganddescribingfeaturesofprism,pyramids,cylinders,conesandspheres
∙sketchingthree-dimensionalobjectsf
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