mathematically similar rectangles - ucl.ac.uk · drag in the change side length by... block and...
TRANSCRIPT
![Page 1: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/1.jpg)
EXPLORING MATHEMATICAL RELATIONSHIPSMODULE 5:INVESTIGATION 2
MathematicallySimilarRectangles
1
![Page 2: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/2.jpg)
ACTIVITY 5.2.1
SequenceofSquares
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
2
![Page 3: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/3.jpg)
Openproject5-AlteringPolygons- ifonline Saveasacopyandaddyourname- ifoffline Saveasandaddyourname
Usetheexistingsquare blockinashortscripttodrawasquareofthesidelengthof20.
Usingthesamescripttodrawsquareswithsidelengths40,60,80,100…
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
(ifyoudonotclearthestageafterdrawingeachsquare)
3
![Page 4: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/4.jpg)
Draginthechangesidelengthby...blockandkeepitisolated.Exploreit,useit.Explorethesidelengthmonitorinthestage.
u Whatisthedifferencebetweentheblockschangesidelengthby…andsetsidelengthto…?
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
4
![Page 5: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/5.jpg)
Clearthescreenandbuildascripttodrawthewholepatternofgrowingsquaresinoneclick.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
5
u Haveyouusedtherepeat blocktomakeyourscriptshort?
u Howmanysquaresarethereinyourpattern?
u Whatisthesidelengthofthefirstsquare?Thesecondsquare?
u Whatisthefinalsidelengthdrawn?Whatisthevalueofthesidelength variableattheend?Explainthedifference.
![Page 6: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/6.jpg)
Discussthescriptsbelow,envisagetheoutputofeachscript.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
6
u Whatistheinitialvalueofthesidelength variableineachscript?Whatisitsfinalvalueafterfinishingtherepeat loop?
![Page 7: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/7.jpg)
Buildascripttodrawarowofidenticalsquaresnexttoeachother.
Buildascripttodrawarowofincreasingsquares,thefirstonehavingthesidelengthof20andeachoneincreasingby10.
MODULE 5:INVESTIGATION 2Activity5.2.1– SequenceofSquares
7
![Page 8: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/8.jpg)
[Extension]Modifyyourpreviousscriptsothesquareshaveagapof10betweenthem.
[Extension]Modifyyourscriptsothateachsquarehasarandomsidelengthbetween30and60.
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
8
![Page 9: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/9.jpg)
[Extension]Herearethreealternativesolutionswhichalldrawtheoutputbelow.Discuss:whichoneiseasiertoread?
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
9
❶ ❷
❸
![Page 10: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/10.jpg)
[Extension]Tryandrecreatesomeofthepatternsbelowbybuildingonwhatyouhavedonesofar.Thinkofyourown.
MODULE 5:INVESTIGATION 2Activity5.2.1– [Extension]SequenceofSquares
10
![Page 11: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/11.jpg)
ACTIVITY 5.2.2
AlteringRectangles
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
11
![Page 12: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/12.jpg)
Continueinyour5-AlteringPolygonsproject.
Buildascripttodrawarectanglewithaheightof100andbaseof30.
Makeanewblockcalledrectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
12
![Page 13: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/13.jpg)
Makeanewvariablecalledheight anduseitinthemoveblockwithintherectangle definition.
Drawdifferentrectanglesbysettingthevalueofheight andrunningtheblockrectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
13
![Page 14: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/14.jpg)
Usetheblockchangeheight by…insiderepeat todrawvariouspatternsofgrowingrectangles.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
14
![Page 15: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/15.jpg)
Makeanewvariablecalledbaseandchangeyourrectangledefinitionsothatitusesboththevariablesheight andbase.
ExperimentwiththeBeetlepointingindifferentdirectionsanddrawingthesamerectangle.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
15
u Whatisthesame andwhatisdifferent aboutyourrectangles?
![Page 16: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/16.jpg)
Readthescriptsbelowandenvisagetheoutcomes.Matchthescriptwiththesetofrectanglesitwouldcreate.
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
16
![Page 17: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/17.jpg)
Explorethelineconnectingtheupperrightcornersoftherectangles.Someofthemwecall“magic”.
u Whatdoyounoticeaboutthe“magic”line?
u Arethefirstandlastrectanglesineachsequencethesame?
MODULE 5:INVESTIGATION 2Activity5.2.2– AlteringRectangles
17
![Page 18: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/18.jpg)
[Extension]Trytocreatethepatternsbeloworsimilarusingyourrectangle block:
MODULE 5:INVESTIGATION 2Activity5.2.2– [Extension]AlteringRectangles
18
![Page 19: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/19.jpg)
ACTIVITY 5.2.3
ExploringMathematicalSimilarity
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
19
![Page 20: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/20.jpg)
Continueinyourproject5-AlteringPolygons.
Buildascriptthatsetsthevariablesheight to60andbase to30.Drawarectangleusingthesevalues.
MaketheBeetle usethesay…blocktocalculateandsaythevalueofheightdividedbybase.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
20
u Intheexampleabovewhatdoesthenumber2represent?
![Page 21: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/21.jpg)
Buildanotherscriptwhichdrawsarectangle,says… thevalueofheight / baseandthenchangesthevaluesofheight andbase.
Runthescriptseveraltimesandobservethesequenceofrectanglesandvalues.
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
21
![Page 22: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/22.jpg)
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
22
![Page 23: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/23.jpg)
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
23
![Page 24: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/24.jpg)
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
24
u Canyoubuildascriptsothatyoursequenceofrectangleshasa“magic”line?Explainhowyoudidthistoanotherpupil.
u Whenthereisa“magic”linewhatwilltheBeetlesay?
![Page 25: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/25.jpg)
MODULE 5:INVESTIGATION 2Activity5.2.3– ExploringMathematicalSimilarity
25
![Page 26: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/26.jpg)
EXTENSION ACTIVITY 5.2.4
Unplugged:RectangleJumble
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
26
![Page 27: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/27.jpg)
Aschoolhasaswimmingpoolthatis60x15metres.Discusswhichoftheseplanscouldbeascaledrawingofthepool.
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
27
![Page 28: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/28.jpg)
Sorttheserectanglesintothreegroups:n rectangleswithheight2timesthebase(2to1)n rectangleswithheight3timesthebase(3to1)n rectangleswithheight4timesthebase(4to1)
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
28
![Page 29: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/29.jpg)
Foreachofthescriptsonthetoprowfindascriptonthebottomrowthatwilldrawaproportionalrectangle.
MODULE 5:INVESTIGATION 2Ext.Activity5.2.4– Unplugged:RectangleJumble
29
![Page 30: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/30.jpg)
MyInvestigation2 checklist:
Ibuiltascriptwhichdrawsasquareusingavariableforthesidelength.Ibuiltascriptthatdrawsapatternofincreasingsquaresusingthechangebyblock.Ibuiltascripttodrawarectangleusingvariablesfortheheightandbase.Ibuiltascriptthatdrawsapatternofincreasingrectanglesusingthechangebyblock.Icreatedapatternofproportionallysimilarrectanglesandexplainedthe“magic”line.Ienvisagedwhichrectangleswereproportionallysimilartoeachother(fromimagesaswellasscripts).
MODULE 5:INVESTIGATION 2
30
![Page 31: Mathematically Similar Rectangles - ucl.ac.uk · Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage](https://reader030.vdocument.in/reader030/viewer/2022041216/5e0530da14af00442d6db693/html5/thumbnails/31.jpg)
avariablesblockwhichwillchangethecurrentvalueofavariablesbyaspecifiedamount.
MODULE 5INVESTIGATION 2:KeyVocabulary
31