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UCL SCRATCHMATHS CURRICULUM
MODULE 6:Coordinates and
Geometry
TEACHER MATERIALS
DevelopedbytheScratchMathsteamattheUCLKnowledgeLab,London,England
Imagecredits(pg.3):Bottomleft:Image:©2007Nuno Pinheiro &DavidVignoni &DavidMiller&JohannOllivierLapeyre &KennethWimer &RiccardoIaconelli / KDE / LGPL3
Investigation1EmergingShapes
Investigation2CoordinateShapes
Investigation3Transformations
3
MODULE 6:COORDINATES AND GEOMETRY
INTRODUCTION TO MODULE 6
Module6explorescoordinatesacrossallfourquadrantsandrequirespupilstousetheirknowledgeofvariabletoexplorescale.Pupilsdeveloptheirknowledgeofcoordinatesthroughdifferentcontextsincludingtransformations(reflectionandtranslation)andmathematicalshapeswhichemergebyexploitingtherandomblock.ThismodulecouldpotentiallybelinkedwithseveraldifferentareasoftheKeyStage2curriculumbeyondmathematicsandcomputingsuchasgeographyandEnglish.
GEOGRAPHY:LOCATIONAL KNOWLEDGE
Withinthefirstinvestigationpupilshavetheopportunitytoexperimentwithcoordinatesinordertocreateflagpatternswhichcouldbelinkedwithspecificcountriesthatpupilsarelearningaboutwithinthegeographycurriculum.
ENGLISH:SPELLINGWithinthesecondinvestigationpupilscode anddecodewordsusingletterspositionedatdifferent positionsonthecoordinatesgrid.ThiscouldbelinkedtospellingparticularwordsspecifiedwithintheEnglishcurriculumsuchasthosewithsilentlettersortrickyhomophones.
COMPUTING MATHEMATICS
► Repetition► Variable► Definitions► Debugging► Decomposition► Selection► LogicalReasoning
► Coordinates► Randomness► Reflection► Translation► Scale Factor► Division&rounding► Regularandirregular
polygons
KEY VOCABULARY AND CONCEPTS COVERED BY MODULE 6
Aisle/IsleCereal/SerialDraft/Draught
4
MAP OF MODULE 6
Investigation3Transformations
Investigation1EmergingShapes
Investigation2CoordinateShapes
Thered dashedlineindicatesthecoreactivitieswhichareimportanttocompletebeforemovingontothenextactivities.
ForactivitieswhichrequirepupilstocontinuewithaprojectfromapreviouslessonyoucanalternativelyusethesuggestedINTprojectforthosepupilswhodonothaveaprojecttocontinuewithorifyouwishallpupilstobeginfromthesamepoint.
RestlessFleeeee
Starterproject:6-FleeeeeDots
UnpluggedandHands-on:EnvisageandExplore
IntroducingScale
Continuewith:6-FleeeeeDots
DottyPatterns
Continuewith:6-FleeeeeDots
Activity1 Activity2 Activity3 Activity4
LettersandCoordinates
Starterproject:6-GridLetters
BusyFleeeeeandCleverPoints
Starterproject:6-Coordinates
TrickyTriangles
Continuewith:6-Coordinatesorstartwith:6-Coordinates
INT1
QuirkyQuadrilaterals
Continuewith:6-Coordinatesorstartwith:6-Coordinates
INT2
MimicMeeeee
Starterproject:6-MimicMeeeee
Shadows,Translations&Reflections
Continuewith:6-MinicMeeeeeorstartwith:
6-MimicMeeeeeINT
ThroughtheLookingGlass
Starterproject:6-LookingGlass
5
CONNECTIONS TO KS2 COMPUTING CURRICULUM
CURRICULUM OBJECTIVES LINK WITH SCRATCHMATHS
Design,writeanddebugprogramsthataccomplishspecificgoals
Solveproblemsbydecomposingthemintosmallerparts
Useselectionandrepetitioninprograms
Workwithvariables
Usinglogicalreasoningtoexplainhowsomesimplealgorithmsworkandtodetectandcorrecterrorsinalgorithmsandprograms
► Duringthismodulepupilsarerequiredtobuildprogramsthatcreateemergentshapesfromrandomdots,placeandconnectpointsonacoordinategridandalsothatmimicthebehaviour ofanotherspritethroughtranslationandreflection.
► Pupilsarerequiredtousedecompositioninordertounderstandthemathematicswithindifferentoperationsandexpressionstheyareusingintheirscripts,aswellaswhenbuildingthemimickingbehaviour,tohelpdeveloptheirunderstandingofhowthetwospritesarelinked.
► Pupilsarerequiredtouseselectionintheirscriptsthroughusingdifferentkeyboardcommandstomovetheirspriteandstampdifferentletters.
► Pupilsusetwoformsofrepetitionindrawingtheiremergentshapesmadeupofarepeatednumberofrandomdots,tobeabletocontinuouslymimicthebehaviour ofanotherspriteandalsoinanextensiontoanimatetheirspriteindifferentways.
► Pupilsusevariableswhenworkingwithdifferentcoordinategridintervalsandalsotoenablespritestosnaptospecificgridpoints.
► Pupilsarerequiredtouselogicalreasoningwhenenvisagingthemissingvaluesinscriptstocreatedifferentemergingshapes.
► Withinanextensionactivitypupilsarealsoaskedtoexamineandexplainthedifferencesbetweenseveraldifferentalgorithmsfordrawingemergingflagpatterns.
LINKS TO PRIMARY NATIONAL CURRICULUM
6
MODULE 6: INVESTIGATION 1Emerging Shapes
Thisinvestigationdevelopsreadingandsettingcoordinatesbyexploringandbuildingscriptswhichproduceemergentshapes.Thestartoftheinvestigationusesabackdrop(withaxisintervalsmarked)andascriptwhichutilisesa1-1mappingbetweencoordinatesandpixels.Astheinvestigationdevelopspupilsengagewithscale,convertingstandardpixelcoordinates togridcoordinates (differentintervalsonthexandyaxis).
Wehavedeliberatelyselectedanewsprite– theFleeeee(with5Esinhonourofourpedagogicalstrategy!)– insteadofreusingtheBeetletomakeitclearthatwearefocusingoncoordinatesandmovingdifferently byusingtheblocksgotox:…y:…andreporterblocksxposition andyposition.Pupilsengagewithpatternsincoordinates,forexamplemultiplesof20whencreatingadotpattern.
uActivity6.1.1– RestlessFleeeeeuActivity6.1.2– UnpluggedandHands-on:EnvisageandExplainuActivity6.1.3– IntroducingScaleuActivity6.1.4– [Extension]DottyPatterns
Scratchprojects 6-FleeeeeDots6-FleeeeeDotsFINAL6-FleeeeeDotsExtensionFINAL
CURRICULUM OBJECTIVES LINK WITH SCRATCHMATHS
MathematicsIdentify, describeandrepresentthepositionofashapefollowingareflectionortranslation.Describemovementsbetweenpositionsastranslationsofagivenunittotheleft/rightandup/down.Solveproblemsinvolvingsimilarshapeswherethescalefactorisknownorcanbefound.
Describepositionsonthefullcoordinatesgrid.
(KS3)Workwithexperimentsthatinvolverandomness.
► Pupilsarerequiredtoenvisage andbuildscriptswhichcreateareflectedemergentshapeintheyaxisandtheninthexaxis.
► Pupilsarerequiredtoenvisageandbuildscriptswhichcreateanemergentshapethathasbeentranslatedleft,right,upand/ordownbyaspecifiedamount.
► Pupilsarerequiredtousedifferentgridintervalsandadjustthescaleoftheiremergentshapescriptsappropriately(usingvariables)tomatchthedifferentgrids.
► Pupilsarerequiredtoengagewiththefullcoordinategridtospecifythepositionandsizeoftheiremergentshapes.
► Pupilsemployrandomnesstocreatetheiremergentshapesusingrandomlypositioneddotswithinasetarea.
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtocreateemergentshapeswithinadefinedareausingcoordinates.Envisagehowtorecreateemergentshapesbyidentifyingmaximumandminimumcoordinates
7
MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.1Restless Fleeeee
❶ Pupilsexploretheproject,itsbackdrop,theFleeeee sprite,itssetupscript andthedefinitionsofthedot andpickrandompencolourandshadeblocks.
❷[Extension] PupilsexplorethecostumesofFleeeee andtheblocksblink,nod,walk andrunandthewayhowtheyaredefined.[Donotrunwalk and run inparallelastheanimationswouldinterferewitheachother.]
❸ Pupilsenvisage,discussandrunthegotox:…y:…scriptinthescriptsarea.Whathappensiftheyrunthis‘jumpingscript’againandagain?Theyaddtherepeat blockarounditandthewhenspace keypressed hatblockandexperimentwithdifferentnumbersofrepetitions,e.g.10or100or500…
Ask questionstoconnecttheemergentshapewiththegotox:y:block.Whatisthelength/widthoftherectangle?Howcanthisbecalculatedfromthegotox:y:block?
❹ Intheclassroompresentationthereareseveralpicturesofemergingrectanglesandcorrespondingscriptswithoneorseveralmissingcoordinates.Pupilsfillinthemissinginputsofthepickrandom…to… blocksandrunthescript.
❺[Extension] Intheclassroompresentationtherearemorecomplexandinterestingpicturesofemergingshapes.Pupilsbuildscriptstocreatethem.Thisisanexample,similartotheflagofSwitzerland.
Pupilsopenproject6-FleeeeeDots,Saveasacopy (online)orSaveas (offline)andrename.
Theorderingofthenumberswithinthepickrandomblockhasnoimpact,howeveritmightbehelpfultousetheconventionsaswewouldseeonacoordinateaxis.
Envisage thelengthandwidthoftheemergentshapebeforerunningthescript.Whatarethecoordinatesofthetoprightcornerorthebottomleftcorner?Howdoyouknow?
8
INVESTIGATION 1Activity 6.1.1
WestartedusingspriteswithmultiplecostumesinModule1(Activity1.2.3)forstampingalternatingflowerpatterns.InActivity1.3.3weusedaspritewithsixdifferentcostumesandstartedusingtheswitchcostumetoname usingthespecificnames ofthecostumes.
CONNECTIONS TO Y5SCRATCHMATHS
❷
InModule3weexploitedmultiplecostumesfordifferentpurposes:inactivities3.1.2and3.1.3toexpressdifferentbehavioursofNanoandTera andin3.1.4tomakePicomoveandlookasifhewaswalking.
Thereweemployedtwoimportantideas:
► Ifweusednextcostume andthecurrentcostumeofaspritewasitslastoneitautomaticallyswitchedtothefirstcostume(weusedthisfeatureinModule4aswell).
► Insidethewalkingforever loopwewereusingtheifonedge,bounce blocktomakesurethatthespritebouncedwheneveritrunintoanedge.
CostumesoftheFleeeee spriteareslightlydifferent:therearefiveofthemandtheymaybeusedforseveraldifferentanimations:thefirstfour,whendisplayedintheforeverloop1– 2– 3– 4– 1…willmakeFleeeee lookasifitiswalking.Thereforewecannotusesimplenextcostumeloophere,aswehaveto‘skip’costumenumber5.
Theblink andnod definitionsaresimpleastheyonlyswitchapairofcostumesafixednumberoftimeswithnomovement.Ournewblockrun switchesbetweencostumes2and4butmakesFleeeeemoveaswell.
9
INVESTIGATION 1Activity 6.1.1
Bothdot andsetrandompencolourandshade arenewblockspreparedforpupilssothattheycanquicklystartexploringfurtheractivitieswiththeFleeeee sprite.Pupilshavecreatedthesameorsimilarblocksthemselvesinearlierinvestigations.
Theotherfournewblocks– blink,nod,walk andrun areexploredandusedonlyinstep2[Extension]ofthisactivity.
ADDITIONAL SUPPORT
❶
❷ AllofthesenewblocksaredifferentanimationsbasedonthefactthattheFleeeeespritehasfivesimilarbutnotidenticalcostumes.TheanimationsandtheirdefinitionsarecommentedinmoredetailintheConnectionstoY5ScratchMaths onthepreviouspage.Theyarenotrequiredtobeusedinthisinvestigation.However,ifpupilswantto,theymayhavesomerandomanimationseffectshappeninginparallel.Forexample,theymaywanttheFleeeee tohaveandrunthefollowingorsimilarextrascripts:
10
INVESTIGATION 1Activity 6.1.1
Thevaluesintheredcirclesarethemissingnumbersfromtheclassroompresentation.
ADDITIONAL SUPPORT CONTINUED
❸
❹
11
INVESTIGATION 1Activity 6.1.1ADDITIONAL SUPPORT CONTINUED
❺ Notethatwhencreatingthefollowingpicturesofdifferentemergingshapes:►Morethanonerepeat randomjumpingloopisappliedinthesameareaofthestage,
withdifferentpencolours.► Itisdesirabletoincreasethenumberofjumpstoseveralhundredsorseveral
thousands.Tosavetimewhilerunningsuchscript,youmaydecidetogototheEditmenuandselectTurbomode.Alternatively,youmayturntheTurbomodeon(oroff)byShift+clickingthegreenflag.Pleasenote- inotheractivitiesitisdesirabletoobserveeachstepdoneinthestagesodonotforgettoswitchTurbomodeoffwhennotneeded.
Canyouthinkofanyotherflagsyoucouldcreateinasimilarway?
12
INVESTIGATION 1Activity 6.1.1EXTENSION SUPPORT
Whatarethedifferencesbetweenthethreealgorithms(thefirstoneisfromthepreviouspage)?
Whyaretherereddotsinthe‘white’areainthesecondsolution?
Whydidwehavetomovesetpencolor to…blocksinsidethecontrolstructureforever?
Comparetheprevioussolutionsof(5)withtwofollowingstrategies(algorithms).Trytounderstandthedetailsthatmakethosethreealgorithmssimilarandyetconsiderablydifferent.
Couldyouthinkofthefourthstrategy,aversionofthethirdscript,whichwoulduserepeatblocksinsteadofforever?
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Envisagehowtocreateemergentshapesindifferentquadrantsofthecoordinategrid.bridgE tofullcoordinategrid,reflectionsandtranslations.
13
MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.2Unplugged and Hands-on: Envisage and Explore
Encouragepupilstoexplaintheconnectionbetweenthenumbersusedinthegotox:y:blockandthenumbersusedafterthetransformation.[e.g.areflectionintheyaxishastheeffectoftransformingthex-coordinateintoitsopposite]
Thisactivityconsistsofthreeworksheets.Printanddistributethem.
Pupilsareaskedto(a)fillinmissingcoordinatestoproducetheshapeinthepicture,then(b)addanotherscriptwhichwillproduceidenticalshapebutreflectedortranslated– accordingtotheinstructionsin❶ reflectedintheyaxis,in❷ reflectedinthexaxis,andin❸translated.
WORKSHEETS SOLUTIONS
❶
14
MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.2Unplugged and Hands-on: Envisage and Explore
WORKSHEETS SOLUTIONS
❷
❸ Ifthetaskise.g.Right100Down50(asisthefirsttask),thereisalsoanalternativeapproachtodrawbothoriginalandtranslatedrectanglesinparallel,seebelow:
15
Fillinthemissingcoordinatessothatthescriptproducestheem
ergingrectangleinthepicture.ThenbuildthesecondscriptinScratch(sim
ilartothefirstone)toproducethesameshapebutreflectedintheyaxis.
WHATTO
DO
INVESTIG
ATIO
N1
Activity 6.1.2
NAM
E
❶
16
Fillinthemissingcoordinatessothatthescriptproducestheem
ergingrectangleinthepicture.ThenbuildthesecondscriptinScratch(sim
ilartothefirstone)toproducethesameshapereflectedinthexaxis.
WHATTO
DO
INVESTIG
ATIO
N1
Activity 6.1.2
NAM
E
❷
17
Fillinthemissingcoordinatessothatthescriptproducestheem
ergingshapeinthepicture.Thenbuildthesecondscripttoproducethesam
eshapetranslatedright,left,upordown–
basedontheinstruction.W
HATTODO
INVESTIG
ATIO
N1
Activity 6.1.2
NAM
E
❸
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtocreateemergingshapesofdifferentscalefactors.Explainhowtochangethescaleofthecoordinatesgrid.
18
MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.3Introducing Scale
❶ Pupilsbuildthescripttoproduceasmall emergingsquarecentredat0,0 (seeright).Theythenpulloutthepickrandom…blockfromthey:…holeofthegoto… andrunthescriptagain.[They:… holewillresettothedefaultvalueof10.] Theychangethey:…valuetootherconstantvaluesandexplore.[Oneofthevaluestheytryshouldbe0.Exploreanddiscuss]
❷ Pupilspulloutthepickrandom-25to25 fromthex:… holeaswell,butkeepitisolatedandexplorewhichvaluesitproduceswhenclicked.Theybuildacompositereporterblock– formultiplyingthesamerandomvalueby10…
…andexplorewhichvaluesitproduceswhenclicked.Theyexploreitwithdifferentmultipliers:2,5,100….Whendiscussed,theymakeavariableScale anduseitinsteadthemultiplierwithdifferentvalues.
❸ Pupilsinsertthewholecompositeblockbackintothex:… holeandrunthescript.Theyduplicateitintothey:… holeaswellandrunthescript.Theyincreasethepensizeinthesetupscript (to8or10orevenmore–uptotheScale valueitself)andexperimentwithdifferentsmallnumbers forpickrandom… blocks.
❹ PupilssetScale to25andrunthescript,thenswitchbackdroptogrid25 withoutclearingthestage.Discussthedualwayofreferringtothepoints(dots)here:standardCartesiancoordinatesandournew‘grid25coordinates’ (identicaltothegridpointsofTheGridWorldinModule5).RenameyourvariableScale togrid,whichisnowmoreintuitive.
❺ Pupilsbuildscriptsthatproduceemergingrectanglessimilartothoseintheclassroompresentation.
Discuss:Whatroledoesthismultiplierplayhere?Whatifwereplaceitby1,or5,or20?[Itisascalefactorfornumbersrandomlypickedfromthespecifiedinterval]
Discuss: IfwesetScale to10,whichvaluesyoucanuseinbothpickrandom…blockssothattheemergingshapefitswithinthestage?WhatifwesetScale to20?
Pupilscontinueintheirproject6-FleeeeeDots.Thefinalversionofthisprojectattheendofactivity6.1.3willbe 6-FleeeeeDotsFINAL.
19
INVESTIGATION 1Activity 6.1.3
Fortheinitialsmallsquareuseinputsforthepickrandom…blockslike-15to15or-20to20…,sothatevenaftermultiplyingby10iy willfit(asxcoordinates)intothestage:
ADDITIONAL SUPPORT
❶
❷
Whenyoumakeanewvariableandbuildablocktosetitsvalue(to10oranyothervalue),donotforgettoruntheset block.Otherwisethevalueofthevariablewillbe0,itsinitialvaluepre-setbyScratch.
Note- whenareporterblockispulledoutfromablock,thevaluerestoredasaninputinthatblockistypically10.
❸
20
INVESTIGATION 1Activity 6.1.3ADDITIONAL SUPPORT CONTINUED
❹
Trytheone(withthepensizesetto50)ontherightaswell.
Notealsothatthebiggerthedotsget,thesmallerrepeat numbersufficestocoverthewhole(oralmostthewhole)emergingrectangle.
Notehowstraightforwarditistoseetheconnectionbetweenthepickrandom…to…inputvaluesandthegridcoordinates,whenusingtheScale setto25andgrid25 backdrop.
NotealsothatsetScale to…andsetpensizetoScale blocksmaybemovedtothesetupscript.
Experimentwithdifferentpensizes.Notethatifthegridsizeis10,apensizeof10workswellassetpensizeto… setstheperimeterofthedotdrawnbythedot block.Thepictureonthepreviouspageillustratesjumpingwiththepensizeof5,belowleftis8andtherightis10.Therefore,insteadofsetpensizeto5 orsetpensizeto8wewillusemoreageneralcommandsetpensizetoScale:
21
INVESTIGATION 1Activity 6.1.3ADDITIONAL SUPPORT CONTINUED
Pupilskeepthegrid variableas25andtrytocreatesomeoftheseemergingrectanglesandshapes,orsimilar(continuedonnextpage).Theymayalsosetgrid to10,switchthebackdroptogrid10andtrysomeothershapes.Discuss:whichofthesesshapeshavewhatkindofsymmetries?
❺
Torenameavariable,gototheData group,rightclick(offline)orShift+click(onlineandoffline)thevariableblock,selectrenamevariableandinthedialogue
boxchangeitsname.Allblockswiththeoldnameinyourprojectwillbeautomaticallymodified.Inasimilarway,youcanrenameyourownblocksoranybroadcastmessage.
Sincewearenowusinggrid25 backdrop(andlateralsogrid10)anddrawingbigdots– thesamesizeasthegrid,itmightbymoreintuitivetorenameourvariableScale togrid – aswedidinModule5- Investigation3,whichisstraightforwardinScratch.
22
INVESTIGATION 1Activity 6.1.3ADDITIONAL SUPPORT CONTINUED
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtosimplifythejumpingscripttobeasingleline.Explainhowtosettheleftandrightmostpositionsthatthespritewilljumpto.
MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.4[Extension] Dotty Patterns
LetFleeeee nowjumponlywithinoneline.❶ Pupilstrytorestrictthepickrandom… valuesfor
they:…positiontobethesamenumber,e.g.pickrandom-3to-3– thejumpingbehaviournowhappenswithinoneline.Forthiswemaysimplifythewholerepeat byreplacingthegoto… blockbysetxto…anduse
beforerepeat onlyonceforthewholejumping.Pupilsbuildthissimplifiedjumpingbehaviour,makingtheirownblockfortherepeat partofit–namedforexampleonelinejumping.
❷ TomakeFleeeeemovetotheupper‘line’(andpossiblyrunonelinejumpingthereagain)pupilsbuildandexplore…
Pupilsbuildascriptusingonelinejumpinginsiderepeat - makingFleeeee jumponelinehighereachtime.Theymayusedifferentrandompencoloursfordotsineachline.
❸ Pupilsexploretheonelinejumping definition:whatsetstheleftmostpositionwithinalinewhereFleeeeemayjump?Theyturnthatvalueintoavariable,namede.g.Left.TheyuseLeft inthedefinitionandexploredifferentinitialvaluesofLeft.
❹ PupilsinsertchangeLeft by1blockinsidetherepeatandexploredifferentinitialvaluesandresultingpatterns.TheymayalsotrychangingLeft intherepeat loopby2,by-1etc.
❺ Sofarinourexamplestherightmostpositionwithineachlinewas1.PupilstryitasLeft +5 orLeft +2.
❻ Therightmostpositionmaybespecifiedbyanothervariableandchangeitselfintherepeat loopaswell.
Notethat-3 inthesetyto…blockontheleftrepresentsthegridcoordinate ofalldotsinthatlineofthegrid,while-3× grid istheirCartesianyco-ordinate.
Pupilscontinueintheirproject6-FleeeeeDots.ThefinalversionofthisprojectattheendofActivity6.1.4willbe 6-FleeeeeDotsExtensionFINAL.
23
24
INVESTIGATION 1Ext. Activity 6.1.4
Thesearethestepsofthetransitionfrompreviousjumpingintothenewonelinejumping - pickrandom… fory: canbeturnedinto(b) andusedseparatelyin(c) beforetherepeat block,whichwillnowusesetxto…andcanbeturnedintoanewblock:
ADDITIONAL SUPPORT
❶
❷
WhydoesFleeeee alwaysendsuponelineabovethelastlinedrawn?[becausethelastlineintherepeatistochangeybygrid]
25
INVESTIGATION 1Ext. Activity 6.1.4ADDITIONAL SUPPORT CONTINUED
❸
❹
Duetothefactthatpickrandom-4to1 producesthesamesetofvaluesaspickrandom1to-4,wecansetLeft toavaluewhichisinfacttotherightofthesecondinput,seetheexampleabove.
26
INVESTIGATION 1Ext. Activity 6.1.4ADDITIONAL SUPPORT CONTINUED
27
INVESTIGATION 1Ext. Activity 6.1.4ADDITIONAL SUPPORT CONTINUED
❻
❺
LINKS TO PRIMARY NATIONAL CURRICULUM
28
MODULE 6: INVESTIGATION 2Coordinate Shapes
Thisinvestigationdevelopstheuseofcoordinatesinthecontextofverticesofshapeswhichhavegeometricproperties.Theactivitiesencouragethereadingandwritingofcoordinatenotationthroughtheuseoftheletterofthealphabetonagrid.Scalingisrevisitedtotransformpixelcoordinatestogridcoordinates.Connectionscanbemadetothegeometricpropertiesofshapesbycreatingproblemsandencouragingpupilstoexchangetheirowncreationsusingthe6-CoordinatesFINALprojectwhichisbuiltduringtheinvestigation.
uActivity6.2.1– LettersandCo-ordinates
uActivity6.2.2– BusyFleeeee AndCleverPoints
uActivity6.2.3– TrickyTriangles
uActivity6.2.4– QuirkyQuadrilaterals
Scratchprojects 6-GridLetters 6-Coordinates6-GridLettersFINAL 6-CoordinatesINT1
6-CoordinatesINT26-CoordinatesFINAL
CURRICULUM OBJECTIVES LINK WITH SCRATCHMATHS
MathematicsDescribepositionsonthefullcoordinatesgrid.Interpretremaindersaswholenumberremainders,fractions,orbyrounding,asappropriateforthecontext.Solveproblemsinvolvingsimilarshapeswherethescalefactorisknownorcanbefound.Compareandclassifygeometric shapes,includingquadrilateralsandtriangles,basedontheirpropertiesandsizes.Plotspecifiedpointsanddrawsidestocompleteagivenpolygon.
► Pupilsarerequiredtocodeanddecodemessagesusingthe positionsoflettersonthecoordinatesgrid.
► [Extension]Pupilsencountertheneedtoroundtheresultofdivisionoperationsinordertogetspritestosnaptothenearestgridpoint.
► Pupilsarerequiredtousethegridvariable(inasimilarwaytothepreviousinvestigation)toadapttheirprojecttodifferentgridintervals.
► Pupilscreateandexchangecoordinateproblemswhosesolutionsrequirecoordinateandpropertiesofshapeknowledge.
Explorehowtocreateacoordinatecodingscheme.Exchangemessages/taskswithapartnertodecodeusingthecoordinatecodingscheme.
29
MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.1Letters and Coordinates
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Pupilsnavigatetheredpointspritebyarrowsandscatterthelettersinthegrid.
❶ Pupilsexploretheproject,theredpointsprite,itssetupscript anditscostumes.
❷ SimilartoActivity5.3.2wewanttocontrolthepositionoftheredpoint spritebyfourarrowkeys.Pupilsbuildfourscripts:e.g.whenuparrowkeypressed,thespritewillpointindirection0(up) andmoveforwardbygrid steps.Similarly,theotherthreearrowkeyswillmakeitpointinthecorrespondingdirectionandmove tothenextgridpoint.
❸ Pupilschoosealetter(e.g.thefirstletteroftheirname)andbuildascript:ifthatletterispressed,theredpointwillswitchitscostumetothatletter(i.e.thecostumewiththatname),stamp theletterandswitchbacktoitsredpointcostume.
❹ Theybuild(byduplicating)severalsimilarscriptsforsomemorelettersandinpairsplaytheactivitiesonthefollowingpage.
Discuss:Whatarethenamesofthecostumes?Arethereanyvariablesintheproject?
Discuss:Whatisthevalueofthegrid variable?Howcanwefindout?Howdoesitcorrespondwiththebackdrop?[Clickthegrid variableblockinthepalette,ordragoutontothestage,itwillreport25.Eachsquareonthebackdropcorrespondsto25pixels.Wecancheckthisbydraggingtheredpointspritetocornersofthegridonthebackdrop.]
Usethefollowinglistofcoordinatestoreadtheword:
RememberhowthecostumesoftheonesspriteinModule4werenamed?Theywere1,2,3…Nowtheyareredpoint,thenA,B,C…
Pupilsopenproject6-GridLetters,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.2.1willbe 6-GridLettersFINAL.
(1,1)
(-2,3)
(1,1)
(-3,-1) (-2,2)
(1,1)
L O N D O N
30
ACTIVITY INSTRUCTIONS CONTINUED
Coordinatechallenge– fromnRich activity5038(https://nrich.maths.org/5038)
Individually
Canpupilspositionthetenlettersintheircorrectplacesaccordingtotheeightcluesbelow?
Clues:
1. Thelettersat(1,1),(1,2)and(1,3)areallsymmetricalaboutaverticalline.
2. Theletterat(4,2)isnotsymmetricalinanyway.
3. Thelettersat(1,1),(2,1)and(3,1)aresymmetricalaboutahorizontalline.
4. Thelettersat(0,2),(2,0)haverotationalsymmetry.
5. Theletterat(3,1)consistsofjuststraightlines.
6. Thelettersat(3,3)and(2,0)consistofjustcurvedlines.
7. Thelettersat(3,3),(3,2)and(3,1)areconsecutiveinthealphabet.
8. Thelettersat(0,2)and(1,2)areatthetwoendsofthealphabet.
Codebreaking
Inpairs
1. Pupil1and2stampthealphabetlettersintothefourquadrants.
2. Pupil1writesasecretquestionusingcoordinatenotationfortheiralphabetgrid.
3. Pupil2decodesthequestionandrespondsusingcoordinatenotationfortheiralphabetgrid.
Coordinatebingo
Individually,ledbytheteacher
1. Pupilsstamp15coordinatesusingtheletterOonthe-4to4axesonly(tospeedupthegame– e.g.seepictureonright)
2. Teacher(akatheBingoCaller)callsoutcoordinateslikebingonumbers.
3. PupilsstamptheletterXovertheOiftheirchosencoordinatesarecalledout.
4. Thefirstpupiltocrossoffall15oftheirchoicesisthewinnerandshouldshoutout“Bingo!”.
INVESTIGATION 2Activity 6.2.1
A B C D E P S X Y Z
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INVESTIGATION 2Activity 6.2.1
Thisisthesetupscriptoftheredpoint sprite.Notethatthefirstblockcouldhavebeendeletedastheinitialvalueofthegrid variableissavedintheproject.However,thescriptiseasiertoreadandunderstandwiththis.
ADDITIONAL SUPPORT
❶
❷
❸ Herearetheexamplescriptsfortwoletters– TandO(notethattheyarealmostidenticalandanyotherscriptcanbecreatedbyduplicatingandslightlymodifying).Theredpointspritesitsinagridpoint,see(a).ThenwepressT– thespritewillswitchitscostumetoletterTwithasmalldarkbluedot,stampit,thenswitchbacktoitsredpointcostume,see(b).Wethenpresse.g.therightarrowkey,see(c),thenpressO,see(d),thenpressdownarrow,see(e).
Withthispicture,thewordTOcanbealternativelyrepresentedas(2,2),(3,2).Intheotherwayround,thelistofcoordinates(2,2),(3,2),(3,2)canbereadasTOO.
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtodrawalinethatconnectstwopointsonthecoordinatesgrid.Explainhowtoreconnectthepointswhenthepositionofonespriteischanged.
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.2Busy Fleeeee and Clever Points
Discuss:WhataretheinitialScratchcoordinatesofeachsprite?Whataretheirgridcoordinates?Howdothesecorrespond?
❶ Pupilsexploretheproject,itsspritesandtheirscripts.ThepointAhasonlyonecostumeandcanbemovedwithinthegridbythearrowkeys.ThepointBspritehasonlyitssetupscript.Theyhavedifferentcolourstostressthattheywillbehavedifferently.
❷ ExploreonesmalldifferencebetweenpointsA andB:inthedevelopingmode(whichweusethemost)bothspritescanbedraggedbymouse;pointAcanbemovedbythearrowkeysaswell.However,inthefullscreenmode(alsoknownastheplayer,clickthebuttonnexttotheprojectname)pointAcannotbedragged,whilepointB can(seethesettingsinthesprite’sinformationwindow andnotethedifference).
❸ AlthoughitmaylooklikeFleeeee hasnotgotmuchtodointhisproject,thisisnotthecase:Whenasked,itwillconnectpointsA andB byalineandjumpbacktoits‘home’positioninthecorner.PupilsbuildascriptforFleeeee todothat,debugit,thenturnitintoadefinitionofanewblockconnect.
❹ PupilsbuildawhenspacekeypressedscriptforFleeeee thatwillconnect thepoints.Theyuseit,movepointA byarrowsandconnectagain.Pupilsaddtheclear blockabovetheconnect (clear thestagebeforeconnectingbyanewline).Theyexploretheoptionwithreplacingwhenspace keypressed bywhengreenflagclicked forever …(connect thepointsagainandagain).
❺[Extension] Pupilsusetheblink andnod blocks(provided)andbuildtheforever animationsforFleeeee:fromtimetotimeitwillblink oritwillnod.
❻[AdvancedExtension]WhenpointB isbeingdragged,wemayormaynotpositionitexactlyintooneofthegridpoints.Nowpupilsbuildaforever scriptwhichwillmakepointB‘snap’tothenearestgridpoint.
ThesamebehaviourmaythenbecopiedtopointA– whichcanbebothdraggedormovedbyarrowsinthedevelopingmode.
Pupilsopenproject6-Coordinates,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.2.2willbe 6-CoordinatesINT1.
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INVESTIGATION 2Activity 6.2.2ADDITIONAL SUPPORT
❶
❷Fullscreenmode(orplayermode)on/off.
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INVESTIGATION 2Activity 6.2.2
Forconnectingspritesbyalinewewillusethegoto sprite blockfor‘jumping’.NotethatFleeeee turnsitspendown onlyafteritsfirstjump.Then– withitspendown–jumpstothesecondpoint,turnsitspenupandjumpsback‘home’.ItallhappenssoquicklythatitlooksasifFleeeee didnotmoveatall.
ADDITIONAL SUPPORT CONTINUED
❸
❹ In(a)belowFleeeee connectsthepointsAandBwheneverwepressthespacekey.Asthereisnoclear block,thepreviouslinesstayonthestageaswell.In(b)thepreviouslineisfirstclearedaway.In(c)thelinebetweenAandBis‘updated’againandagainsoitlookslikearubberbandattachedtothesetwopoints.
❺ Eachofthefollowingforever scriptswaits arandomnumberofseconds(inoursolution,between1and10)andrunstheanimation.
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INVESTIGATION 2Activity 6.2.2ADDITIONAL SUPPORT CONTINUED
❻ FromActivity6.1.3wealreadyknowthatforanygridpoint representedintheScratchcoordinatesbyxposition andyposition wecaneasilyfindthegridcoordinatesbydividingbothnumbersbythegridsize:
However,ifB wouldnotsitexactlyinagridpoint,like(85,60),thesenumberswouldnotbeintegers:
Toturnthesenumbersintointegerscorrespondingtogridpoints,wehavetoroundthem:
So,ifB sitsat(85,60),theclosestgridpointis(3,2)– seethepicturetopright.ThuswewantB tosnaptothatpoint.Tomakethesnap blockmorereadable,letusgiveclearnamestothesetwovalues– xgrid andygrid,thegridcoordinatesofB.
TomakepointB ‘snap’tothatgridpointwemustmultiplyxgrid andygrid bythegridsize–toturnthosegridcoordinatesbackintostandardScratchcoordinates:
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Exploreand explainthecoordinatesoftheverticesofdifferenttypesoftrianglesExchangeproblemswhichinvolvetrianglesandcoordinates.
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.3Tricky Triangles
❶ PupilsexplorethecostumesofthepointBsprite.
❷ PupilsduplicatethepointB sprite,switchitscostumetocostumenamedC andrenamethenewspritetopointC – sothatitwillbecomeourthirdpoint.Theychangetheinitialgridcoordinatesinthisnewsprite’ssetupscript.
❸ Pupilsextenttheconnect scriptoftheFleeeeesothatitconnectsallthreepoints,thusdrawingatriangle.
❹[Optional] Pupilsswitchbackdroptogrid10andmodifythescriptssothatallspritesreactcorrespondingly.
SuggestedTasks
InterestingIsoscelesWholeclasswithteacher
Youcanusetheprojecttoask openquestionstothewholeclasswhichencouragepupilstodeveloptheirenvisagingandgeometricalreasoningskills.
Forexample:setBandCtobetheverticesofahorizontaledgeofatriangle.
Ask whatarethecoordinatesofAtocreateanisoscelestriangle?
Isthereanothersolution,another?
Canyouexplainyouranswer?
Pupilscontinueintheirownversionofproject6-Coordinates,oropenthe6-CoordinatesINT1,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.2.4is6-CoordinatesINT2.
ACTIVITY INSTRUCTIONS
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.3Tricky Triangles
TypesoftrianglesInpairs
MoveA,B,Ctocreateanexampleofdifferenttypesoftriangles.
Saveapictureofthestageforeachexample.(Rightclickthestage).Exchangeyourexampleswithanotherpupil,compareyourimages.Whatisthesame,whatisdifferent?
Onesolution
Encouragepupilstoexplain whydiagonaledgesareequalinlength.Pupilsmightneedtobepromptedtocounthowmanysquaresupandacrossdescribethediagonaledge.E.g.intheisoscelesexampleabove,wecanseethattheedgeABis3squaresacrossand4up,thisisthesameasedgeBCwhichis3squaresacrossand4down.
Note:Itisimpossibletocreateanequilateraltriangleusingwholenumbercoordinates,theproofofthisisdegreelevelmathematics!Canyouturnthetriangleintothreedifferentisoscelestriangles?
Right-angledtriangle Right-angledisoscelestriangle
Scalenetriangle
Isoscelestriangle
ACTIVITY INSTRUCTIONS
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.3Tricky Triangles
AGoesUp,AComesDownIndividually
SetuptheinvestigationbydraggingpointBto(2,3),Cto(2,-2)andAto(-2,-2).Askpupilsthequestionsbelow.
Q1.Whattypeoftrianglehaveyoumade?
Q2.Usingonlytheupanddownarrows(e.g.thex-coordinateisalways-2).
canyou:
• makeadifferentright-angletriangle?
Extension
Canyou:
• turnthetriangleintothree differentisoscelestriangles?
• explainhowyouknowthetrianglesareisosceles?
A1.Aright-angledtriangle
Theexplanationisbaseduponthespecialtrianglewhichhassideswhichmeasure3,4and5.PythagorasisbeyondKS2butpupilscanjustifybymeasuringonsquarecmpaperandisaninterestingphenomenon!
Acanbeatpositions(-2,0),(-2,-5)and(-2,6)
Aisat(-2,3)
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INVESTIGATION 2Activity 6.2.3
PointB hasfivecostumesformorepointstobeaddedlater.(Youmaywanttochangethepositionofthelettersinthecostumesandbackdropseditor.However,keepthecentreofeachcostumeinthecentreofthebluecircle.)
ADDITIONAL SUPPORT
❶
❷
❸
Notethat:
► YoumayeitherinsertswitchcostumetoC intothepointC sprite’ssetupscript orjustrunitoncethendeleteit.
► WhenduplicatingpointB,allscriptsareduplicatedaswell.Thus,ifyouhavebuiltthesnappingbehaviourforpointB,newspritepointC willhaveitaswell.
WhileinthepreviousactivityFleeeee connectedonlytwopoints–byaline,nowithastomakethe‘roundtour’frompointAtopointB,topointC andbacktopointA,thengetbacktoits“home”position.
NewspritepointC inthispicturehasgridcoordinates(2,-2).
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Exploreand explainthecoordinatesoftheverticesofdifferenttypesofquadrilaterals.Exchangeproblemswhichinvolvequadrilateralsandcoordinates.
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.4Quirky Quadrilaterals
❶ PupilsduplicatethepointC sprite,switchitscostumetoD andrenamethenewspritetopointD.Theychangetheinitialgridcoordinatesinthenewsprite’ssetupscript.
❷ Pupilsextendtheconnect scriptoftheFleeeee sothatitconnectsallfourpointstodrawaquadrilateral.
❸[Extension] Pupilsswitchbackdroptogrid10 andmodifythescriptssothatallspritesreactcorrespondingly.
Pupilscontinueintheirownversionofproject6-Coordinates,oropenthe6-CoordinatesINT2,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.2.4is6-CoordinatesFINAL.
SuggestedTasks
CoordinateChallengeWholeclasswithteacher
Youcanusetheprojecttoask openandclosedquestionstothewholeclasswhichencouragepupilstodeveloptheirenvisagingandgeometricalreasoningskills,asinthepreviousactivity.TherearemanyexamplesofthistypeofquestioninpreviousKS2testingmaterialsfreelyavailableonline.
Example 1
SetBandCtobetheverticesofanedgeofaparallelogram(paralleltothex-axis),andDtoanothervertexasintheimage.
Ask whatarethecoordinatesofAtocreateaparallelogram?
Canyouexplainyouranswer?Howdoyouknowthesidesareparallel?
Example2
Asquarewithvertices(ABCD)hascoordinatesA(2,3)andB(4,-1).WhatarethecoordinatesofCandD?
(2,3)
(4,-1)
ACTIVITY INSTRUCTIONS
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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.4Quirky Quadrilaterals
TypesofQuadrilateralsInpairs
MoveA,B,C,Dtocreateanexampleofeachofthedifferenttypesofquadrilaterals.
Saveapictureofthestageforeachexample.(Rightclickthestage).Exchangeyourexampleswithanotherpupil,compareyourimages.What’sthesame,whatisdifferent?
Onesolution
Thesearenotallsoobvious,encourageandchallenge!
Squares
TrapeziumKite
Rectangle
Rhombus
Parallelogram
Arrowheadconcavequadrilateral
Convexquadrilateral
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INVESTIGATION 2Activity 6.2.4ADDITIONAL SUPPORT
❶
❷
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Thisinvestigationdevelopspupils’understandingoftheeffectofreflectionandtranslationoncoordinatepointsinaverytactileandpracticalway.Pupilsexplorewhathappenstoasprite’spositionastheycontrolthemovementofonespriteandanotherspritemimicsitsbehaviourbyfollowingarule.Forexampleinthepicturebelow,astheFleeee sprite(pink)isdraggedaroundthestage,theMeeeee sprite(orange)willmimictheFleeee sprite’spositionreflected intheyaxis.
Pupilsshouldcontinuetoexploreandexplaintheeffectofdifferenttransformationsontheposition(thecoordinates)ofanobjectaftertransformation.
uActivity6.3.1– MimicMeeeeeuActivity6.3.2– Shadows,TranslationsandReflectionsuActivity6.3.3– ThroughtheLookingGlass
MODULE 6: INVESTIGATION 3Transformations
LINKS TO PRIMARY NATIONAL CURRICULUM
Scratchprojects 6-MimicMeeeee 6-MimicMeeeeeINT 6- MimicMeeeeeFINAL
CURRICULUM OBJECTIVES LINK WITH SCRATCHMATHS
MathematicsDescribepositionsonthefullcoordinatesgrid.Solveproblemsinvolvingsimilarshapeswherethescalefactorisknownorcanbefound.Identify, describeandrepresentthepositionofashapefollowingareflectionortranslation.Describemovementsbetweenpositionsastranslationsofagivenunittotheleft/rightandup/down.Compareandclassifygeometricshapes.Plotspecificpointsanddrawsides tocompleteagivenpolygon.
► Pupilsarerequiredtodrawandthentranslate/reflectpatternsandshapesinallfourquadrants.
► [Extension]Pupilshave theopportunitywithinanextensionactivitytoexploredifferentscalefactorsintheirtranslateddrawings.
► Pupilsarerequiredtoexploretranslationsofpatternsandshapesthroughusingasecondspritethatmimicsthebehaviour ofthefirst.
► PupilsarerequiredtorevisitactivitiesfromY5involvingdrawingpolygonpictures(suchashousesmadefromsquaresandtriangles),buttoextendthesetoalsoincorporateareflectedversionofthedrawing.
Explorehowtomakeonespritemimicthebehaviour ofanothersprite.Explainhowthismimickingbehaviour works.
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MODULE 6 ● INVESTIGATION 3 ● ACTIVITY 6.3.1Mimic Meeeee
DragFleeeee aroundthestage.Discuss:WhatishappeningwithMeeeee?WhydoesFleeeee notleavealinewhenwedragit?
NowwhenweclickgreenflagandstartdraggingFleeeee,itseemstobedrawingaline.
Discuss:Why?Whoinfactdrawstheline?WhereisMeeeee?
❶ Pupilsexploretheproject,itssprites,theircostumesandscripts.WhileMeeeee hasonlyasimplesetupscript,Fleeeee alsohastwoanimationblocksnod andblink andtwoforever scriptstousethem– pupilsarefamiliarwiththesefromInvestigation1.
❷Fleeeee isa‘hero’forMeeeee– itwantstobejustlikeFleeeee,itwantstoobserveFleeeee andlearnfromit.PupilswillhelpMeeeee bybuildingawhengreenflagclickedscript,whichwillmakeMeeeeeforever lookatFleeeee,using:
❸ Pupilsmodifythis‘spying’scriptofMeeeee:itwillalwayssay thecurrentxpositionofFleeeee,using:
❹ PupilsmakeMeeeee imitateFleeeee byanotherscriptwhichwillforever switchitscostumetothecurrent costume# ofFleeeee.
❺ Pupilsreplacesay inthescriptbysetxto…blocksothatwhentheydragFleeeee,Meeeee willmimicitsactualxposition.
❻ Pupilsreplacesetxto…andxpositionofFleeeee bysetyto…andypositionof Fleeeee.
❼ PupilschangetheinitialpositionofFleeeee tobe0,0,setMeeeee’s pendown andusegotox:…y:…forxandypositionsofFleeeee insteadofmimickingjustoneofxpositionorypositionof Fleeeee.[Removethepointtowards blockandobservetheeffect.]
PupilsdragFleeeee aroundthestage,andMeeeeewillmimicitspositionanddrawwithitspen.
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONSPupilsopenproject6-MimicMeeeee,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.3.1willbe 6-MimicMeeeeeINT.
Therearetwobackdropsintheproject– grid50 oraxes.Choosewhicheverworksbestforyourpupilsfortheseactivities.
DragFleeeee afteraddingthesetxtoblock.Whatdoyounotice?[Meeeee’s ycoordinatedoesn’tchange.]
Replacethesetxblockwith sety.WhatdoyounoticewhenyoudragFleeeee [Meeeee’s xcoordinatedoesn’tchange.]
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INVESTIGATION 3Activity 6.3.1
Setupscripts ofbothspritesarebelow.Fleeeee alsohastwodefinitionsofblink andnod(notshownhere)andtwoadditionalforever loopstoperiodicallyruntheanimations.
ADDITIONAL SUPPORT
❶
❷ Hereweareusingasimplepointtowards…Motion block,whichhasasmalldropdownmenuinit.WeselectthenameofFleeeee andaddwhengreenflagclicked hatblockwithforever,sothatMeeeee pointstowardsFleeeee whereveritmoves– orisbeingdragged.Toseetheresult,dragFleeeee aroundthestage.
Comparethetwopossiblesolutions,seebelow.Makesurepupilsunderstandwhythesolutionontherightwouldnotworkcorrectly[ItisbecauseMeeeee wouldpoint– i.e.looktowardsFleeeee onlyoncewhenthegreenflagispressed,insteadofturningandpointingtowardsFleeeee whereveritmovesorisdragged.]
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INVESTIGATION 3Activity 6.3.1
For“spying”i.e.learningaboutsomesettingsofanotherspriteweuseahighlygeneralandpowerfulreporterblockfromtheSensing group.ItisoneofveryfewScratchblockswhichhastwodropdownmenus– bothontheleftsideandontherightside.Wehavealreadyuseditinextensionactivity4.3.4.
ADDITIONAL SUPPORT CONTINUED
❸
❹
NotethatifyouopenedtherightdropdownmenuwithFleeeee beingselectedinthespritesarea,thelistofoptionswouldcontainStageandallothersprites(Meeeee inourcurrentsituation)
Encouragepupilstoexploreandexplainwhy(asinpreviousstep)thisscriptwouldnotworkproperlywithouttheforever block.Todemonstratethis,theydragFleeeee aroundthestage.
Discusstogetherthelistofsettingsfromtheleftdropdownmenu– toexploresomeotheritemshereaswell.Oneofthemwillbeusedinthenextstep.
Notethatifwerunthis“spying”script,itwilllookasifMeeeee knewhowtoblink andnod –butinfactitdoesnot,itonlymimicsthecostumesofFleeeee allthetime.
AnalternativesolutionistokeepthepointtowardsFleeeee blockandaddthesay…blockinsidethesameforever,seeright.
YoumaywanttodeletebothofthesepointtowardsFleeeee andsay… scriptslaterintheactivityasthesay…bubblecouldbecomedistracting.
TotestthismimicbehaviourofMeeeee,dragFleeeee alongthestage.Whydoesitnotleavealine– evenifweturnitspendown?Itisbecausedraggingaspriteisadirectmanipulationoperation,notcomputational– programmedoperationlikemakingitmove…steps.
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INVESTIGATION 3Activity 6.3.1ADDITIONAL SUPPORT CONTINUED
❻
❼
❺
Analternativesolution(andforthisparticulartaskevensimpler)wouldbetousethegotoFleeeeeMove block,seebelow.However,inthefollowingactivitieswewillneedthesolutionwithgotox:…y:…blockaswewillinsertdifferentexpressionsinit.
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtomakeonespritetranslatethedrawingbehaviour ofanothersprite.Explainhowtorestrictthemovementofaspritetoasinglequadrantofthegrid.
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MODULE 6 ● INVESTIGATION 3 ● ACTIVITY 6.3.2Shadows, Translations and Reflections
Ask:WhenFleeeee hasitspendown whyareallthelinesred?[ThebluelinesofFleeeee areimmediatelycoveredbyredlinesofMeeeee.]
Sofar,wehavebeendraggingFleeeee aroundthestage.Inthisactivitywewillbuildascriptforittoglide.Meeeee willstillmimicFleeeee,howeverthemimickingeffectwillbeconsiderablyimprovedwhenclicked.
❶ Pupilsbuildanisolatedglide blockforFleeeee – toflyatrandomwithinthewholestageoronthesamesideoftheyaxis.TheyclickthegreenflagsothatMeeeee ismimickingFleeeee.Theyaddarepeat10aroundtheglide andalsoawhenthisspriteclickedhatblock.
❷ Pupilsreplacepenup inthesetupscript ofFleeeeewithpendown.Note:Meeeee stilldrawsredlines.Toseebothredandbluelines,pupilsmodifythemimickingscriptofMeeeee bymovingtheitsposition10pixelshorizontallye.g.
❸ PupilsuseanOperatorblocktochangetheypositionof Fleeeee andexploreusingsmallvaluesoftranslation(e.g.between– 10to+10).UsedifferentpensizesandpencoloursofFleeeee andMeeeee tocreatea“linewithashadow”effect.
❹ PupilsrestrictFleeeee’s randomglidingwithintheupperleftquadrantandmakeMeeeee drawidenticalglide doodlestranslated(a)Right200,(b)Down150,(c)Right50Down50 orsimilar.
❺ Pupilsreplacetheoperatorswithmultiplyxoryposition(orboth)ofFleeeee by-1– creatingreflecteddoodlesinthexoryaxisorboth.
❻[Extension] Pupilsmultiplyxoryposition(orboth)by0.5or-0.5andexploretheoutcomedoodle.
Pupilscontinueintheirownversionofproject6-MimicMeeeee,oropenthe6-MimicMeeeeeINT,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.3.2is6-MimicMeeeeeFINAL.
Useeithergrid50 backdroporaxes,whicheverworksbestforyourpupils.
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INVESTIGATION 3Activity 6.3.2
Pupilsmayexperimentwithdifferenttimesintheglide block.
ADDITIONAL SUPPORT
❶
❷
❸ Addingpositivenumbertoxpositionof FleeeeemeanstranslatingMeeeee’s drawingtotherightorhorizontally.Subtractinganumberfromypositionof FleeeeemeanstranslatingMeeeee’s drawingdownwardsorvertically.
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INVESTIGATION 3Activity 6.3.2ADDITIONAL SUPPORT
❹ HerewerestrictedtheglidingareaofFleeeee totheupperleftquadrantonly.
Analternative(butmorechallenging)solutionwouldbetohavepenup inthesetupscriptofMeeeee andmodifyitsmimickingscriptinthefollowingway:
Here,forthetranslationRight200,wemodifiedtheinitialpositionofMeeeee toalsobeatranslatedinitialpositionofFleeeee.Otherwise,therewouldbealinefromMeeeee connectingitsinitialposition0,0 tothefirsttranslatedpointat200,0.
ThistranslationisRight50Down50.
ThistranslationisDown150.
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INVESTIGATION 3Activity 6.3.2ADDITIONAL SUPPORT
❺
❻ Ifwemultiplyxand/orypositionofFleeeee by0.5,theresultingdoodlewillbehalfthesize(areduction).Exploremultiplyingby-0.5.Exploremultiplyingxbyonenumberandybyadifferentnumber,e.g.1and-0.5or-0.5and-0.5
LEARNING OBJECTIVES
MATHEMATICS CONNECTIONSACTIVITY INSTRUCTIONS
Explorehowtocreatereflectedpolygondrawings.Explainthedifferencesbetweencreatingatranslatedandreflecteddrawing.
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MODULE 6 ● INVESTIGATION 3 ● ACTIVITY 6.3.3Through the Looking Glass
❶ Pupilsopentheproject,clickthegreenflagandexplorehowMeeeee imitatesFleeeee.
❷ PupilsclickthetwoblockscriptforFleeeee withamove… andaturn…block.Theyclickitseveraltimes– itseemstoworkwellforprogrammingFleeeee andMeeeee imitating.Butthereisanissue:trytobuildascriptforFleeeee todrawarectanglee.g.50by100andnoticethefollowing:
(Seeadditionalsupportforexplanation).Todebugthisprobleminsteadofmove…steps pupilsuseanewmoveblockwe’vedefinedasstroll…steps (tobehaveasa‘slow’move).
❸ Pupilsmakevariablesidelength anduseitwiththestroll… blocktheydefinetheirownsquare.Theyusesquare tocreatemorecomplexpictures(seeadditionalsupportandpupilpresentation).
❹[Extension] PupilsmodifythemimickingscriptofMeeeee to(a)insteadofreflectinginthexaxis,itwillmultiplyxpositionof Fleeeeeby0.5,(b)reflectthedrawingofFleeeee intheyaxis.
❺[Extension]Pupilsdefinedifferentpolygonsusingsidelength instroll… andusethemtocreatecomplexdrawings.
❻[Extension]Usingsquare andtriangle,pupilsdefinetheirownhouse androwofhousesofrandomsizes,withMeeeee drawingitsreflectionintheyaxis.
Pupilsopenproject6-LookingGlass,Saveasacopy (online)orSaveas (offline)andrename.ThefinalversionofthisprojectattheendofActivity6.3.3willbe 6-LookingGlassFinal.
Inactivity6.3.1wedraggedFleeeee,andMeeeeemimickeditsxandypositions,aswellasitscostume#.Inactivity6.3.2wemadeFleeeee glide alongthestage.NowwearegoingtoprogramFleeeee aswedidearlierwithBeetle.Meeeee willimitateallmovementsofFleeeeeasifinalookingglass(mirror).
Ask:whyisthefirstlinered?
Discuss: whomovedfirstandwhosecond?
Buildregularpolygons,squares,triangles,hexagons,octagonstoutilizetheknowledgefromearliermodules.
Askhowdowecalculatetheangletoturn?[360/numberofsides.Rememberthespriteturnsthroughtheexteriorangle.Aspritewillturnthrough360° asittracestheoutlineofanyclosedshape.]
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INVESTIGATION 3Activity 6.3.3ADDITIONAL SUPPORT
❶
Pupilsarealreadyfamiliarwithallofthesescriptsfromthepreviousprojects.IsolatedshortscriptsherecaninspirethemtotestMeeeee andthewayitimitatesFleeeee.Pupilsclickthescriptrepeatedly.
Donotforgettoclickthegreenflagfirst– tomakeallsetupscriptsandforever scriptsrun.
ThesetupscriptsforMeeeee putsthependownafterjumpingtoitsinitialposition.Inthefirstforever scriptthereisasophisticatedblockformakingMeeeee pointasif‘inthemirror’,see(a).TheeffectwillbeforMeeeee tofaceintheoppositedirectionofFleeeee.
Thesameoperatorblockworkswellforreflectionsintheyaxiswhenmimickingstarts,see(b).
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INVESTIGATION 3Activity 6.3.3ADDITIONAL SUPPORT CONTINUED
❷ WhilescriptslikethetwobelowleftbelowworkwellforbothFleeeee andimitatingMeeeee,scriptsontherightdonot.Asequenceofmove andturnblocksinsideonerepeat runssoquicklythatthemimickingscriptofMeeeee‘misses’theintermediatesteps.Forexample,whendrawingrectangles,Meeeeejumpsdirectlytotheoppositecorneroftherectangle.
Ifweputawait0.1secs blockaftermove andturn,everythingwouldworkwell.
However,thesafest solutionistomakeFleeeeemove“slower”.Wedonotwantpupilstoinsertawait blockaftereachmove,sowedefineanewversionofthemove blockwiththeshortwaitbuiltin.AlthoughsuchadefinitionexceedsthecomputationalskillsofY6pupils,weconsiderittobeanappropriateopen‘window’tosecondarycomputing– ourownnewblockswithinputsillustrateoneofmanycomputingconceptstolearninKS3computing.
Pupilswillusestroll…steps inexactlythesamewayasmove…steps block.
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INVESTIGATION 3Activity 6.3.3ADDITIONAL SUPPORT CONTINUED
❸
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INVESTIGATION 3Activity 6.3.3ADDITIONAL SUPPORT CONTINUED
❹
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INVESTIGATION 3Activity 6.3.3ADDITIONAL SUPPORT CONTINUED
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Meeeee reflectsthedrawingofFleeeee intheyaxis.
InthisoneMeeeeemultipliesxpositionofFleeeee by0.5.
Switchbackdroptotheintheday orinthenight.