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EXPLORING MATHEMATICAL RELATIONSHIPSMODULE 5:INVESTIGATION 2
MathematicallySimilarRectangles
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ACTIVITY 5.2.1
SequenceofSquares
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
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Openproject5-AlteringPolygons- ifonline Saveasacopyandaddyourname- ifoffline Saveasandaddyourname
Usetheexistingsquare blockinashortscripttodrawasquareofthesidelengthof20.
Usingthesamescripttodrawsquareswithsidelengths40,60,80,100…
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
(ifyoudonotclearthestageafterdrawingeachsquare)
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Draginthechangesidelengthby...blockandkeepitisolated.Exploreit,useit.Explorethesidelengthmonitorinthestage.
u Whatisthedifferencebetweentheblockschangesidelengthby…andsetsidelengthto…?
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
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Clearthescreenandbuildascripttodrawthewholepatternofgrowingsquaresinoneclick.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
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u Haveyouusedtherepeat blocktomakeyourscriptshort?
u Howmanysquaresarethereinyourpattern?
u Whatisthesidelengthofthefirstsquare?Thesecondsquare?
u Whatisthefinalsidelengthdrawn?Whatisthevalueofthesidelength variableattheend?Explainthedifference.
Discussthescriptsbelow,envisagetheoutputofeachscript.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
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u Whatistheinitialvalueofthesidelength variableineachscript?Whatisitsfinalvalueafterfinishingtherepeat loop?
Buildascripttodrawarowofidenticalsquaresnexttoeachother.
Buildascripttodrawarowofincreasingsquares,thefirstonehavingthesidelengthof20andeachoneincreasingby10.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
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[Extension]Modifyyourpreviousscriptsothesquareshaveagapof10betweenthem.
[Extension]Modifyyourscriptsothateachsquarehasarandomsidelengthbetween30and60.
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
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[Extension]Herearethreealternativesolutionswhichalldrawtheoutputbelow.Discuss:whichoneiseasiertoread?
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
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[Extension]Tryandrecreatesomeofthepatternsbelowbybuildingonwhatyouhavedonesofar.Thinkofyourown.
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
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ACTIVITY 5.2.2
AlteringRectangles
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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Continueinyour5-AlteringPolygonsproject.
Buildascripttodrawarectanglewithaheightof100andbaseof30.
Makeanewblockcalledrectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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Makeanewvariablecalledheight anduseitinthemoveblockwithintherectangle definition.
Drawdifferentrectanglesbysettingthevalueofheight andrunningtheblockrectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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Usetheblockchangeheight by…insiderepeat todrawvariouspatternsofgrowingrectangles.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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Makeanewvariablecalledbaseandchangeyourrectangledefinitionsothatitusesboththevariablesheight andbase.
ExperimentwiththeBeetlepointingindifferentdirectionsanddrawingthesamerectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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u Whatisthesame andwhatisdifferent aboutyourrectangles?
Readthescriptsbelowandenvisagetheoutcomes.Matchthescriptwiththesetofrectanglesitwouldcreate.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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Explorethelineconnectingtheupperrightcornersoftherectangles.Someofthemwecall“magic”.
u Whatdoyounoticeaboutthe“magic”line?
u Arethefirstandlastrectanglesineachsequencethesame?
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
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[Extension]Trytocreatethepatternsbeloworsimilarusingyourrectangle block:
MODULE 5:INVESTIGATION 2Activity5.2.2– [Extension]AlteringRectangles
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ACTIVITY 5.2.3
ExploringMathematicalSimilarity
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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Continueinyourproject5-AlteringPolygons.
Buildascriptthatsetsthevariablesheight to60andbase to30.Drawarectangleusingthesevalues.
MaketheBeetle usethesay…blocktocalculateandsaythevalueofheightdividedbybase.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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u Intheexampleabovewhatdoesthenumber2represent?
Buildanotherscriptwhichdrawsarectangle,says… thevalueofheight / baseandthenchangesthevaluesofheight andbase.
Runthescriptseveraltimesandobservethesequenceofrectanglesandvalues.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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CompletethetablesA toD onyourworksheetbydoingthefollowingsteps:
n Buildthetwoscripts.n Clickontheset blockstosettheheight and base values.n Clickthesecondscriptandthennotedownthevalue
displayedinthetable– repeatthisprocesssevenmoretimes.
Ensure youhavecorrectlysettheheight andbase valuesbeforeclickingonthesecondscript.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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CompletethetablesE toH onyourworksheetbydoingthefollowingsteps:
n Buildthetwoscripts.n Choosetheinitialvaluesandthevaluestochange…by…
andtypetheseintotheemptyholes(alsonotedownonyourworksheet).
n Clickontheset blockstosettheheight and base values.n Clickthesecondscriptandthennotedownthevalue
displayedinthetable– repeatthisprocesssevenmoretimes.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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u Canyoubuildascriptsothatyoursequenceofrectangleshasa“magic”line?Explainhowyoudidthistoanotherpupil.
u Whenthereisa“magic”linewhatwilltheBeetlesay?
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
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EXTENSION ACTIVITY 5.2.4
Unplugged:RectangleJumble
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
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Aschoolhasaswimmingpoolthatis60x15metres.Discusswhichoftheseplanscouldbeascaledrawingofthepool.
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
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Sorttheserectanglesintothreegroups:n rectangleswithheight2timesthebase(2to1)n rectangleswithheight3timesthebase(3to1)n rectangleswithheight4timesthebase(4to1)
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
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Foreachofthescriptsonthetoprowfindascriptonthebottomrowthatwilldrawaproportionalrectangle.
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
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MyInvestigation2 checklist:
Ibuiltascriptwhichdrawsasquareusingavariableforthesidelength.Ibuiltascriptthatdrawsapatternofincreasingsquaresusingthechangebyblock.Ibuiltascripttodrawarectangleusingvariablesfortheheightandbase.Ibuiltascriptthatdrawsapatternofincreasingrectanglesusingthechangebyblock.Icreatedapatternofproportionallysimilarrectanglesandexplainedthe“magic”line.Ienvisagedwhichrectangleswereproportionallysimilartoeachother(fromimagesaswellasscripts).
MODULE 5:INVESTIGATION 2
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avariablesblockwhichwillchangethecurrentvalueofavariablesbyaspecifiedamount.
MODULE 5INVESTIGATION 2:KeyVocabulary
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