coordinates and geometry - ucl.ac.uk suggested int project for those pupils who do not have a...

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

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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

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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


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

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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?

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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.

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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:

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Thevaluesintheredcirclesarethemissingnumbersfromtheclassroompresentation.

ADDITIONAL SUPPORT CONTINUED

❸

❹

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INVESTIGATION 1Activity 6.1.1ADDITIONAL SUPPORT CONTINUED

❺ Notethatwhencreatingthefollowingpicturesofdifferentemergingshapes:►Morethanonerepeat randomjumpingloopisappliedinthesameareaofthestage,

withdifferentpencolours.► Itisdesirabletoincreasethenumberofjumpstoseveralhundredsorseveral

thousands.Tosavetimewhilerunningsuchscript,youmaydecidetogototheEditmenuandselectTurbomode.Alternatively,youmayturntheTurbomodeon(oroff)byShift+clickingthegreenflag.Pleasenote- inotheractivitiesitisdesirabletoobserveeachstepdoneinthestagesodonotforgettoswitchTurbomodeoffwhennotneeded.

Canyouthinkofanyotherflagsyoucouldcreateinasimilarway?

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INVESTIGATION 1Activity 6.1.1EXTENSION SUPPORT

Whatarethedifferencesbetweenthethreealgorithms(thefirstoneisfromthepreviouspage)?

Whyaretherereddotsinthe‘white’areainthesecondsolution?

Whydidwehavetomovesetpencolor to…blocksinsidethecontrolstructureforever?

Comparetheprevioussolutionsof(5)withtwofollowingstrategies(algorithms).Trytounderstandthedetailsthatmakethosethreealgorithmssimilarandyetconsiderablydifferent.

Couldyouthinkofthefourthstrategy,aversionofthethirdscript,whichwoulduserepeatblocksinsteadofforever?

LEARNING OBJECTIVES


Envisagehowtocreateemergentshapesindifferentquadrantsofthecoordinategrid.bridgE tofullcoordinategrid,reflectionsandtranslations.

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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

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MODULE 6 ● INVESTIGATION 1 ● ACTIVITY 6.1.2Unplugged and Hands-on: Envisage and Explore

WORKSHEETS SOLUTIONS

❷

❸ Ifthetaskise.g.Right100Down50(asisthefirsttask),thereisalsoanalternativeapproachtodrawbothoriginalandtranslatedrectanglesinparallel,seebelow:

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Fillinthemissingcoordinatessothatthescriptproducestheem

ergingrectangleinthepicture.ThenbuildthesecondscriptinScratch(sim

ilartothefirstone)toproducethesameshapebutreflectedintheyaxis.

WHATTO

DO

INVESTIG

ATIO

N1

Activity 6.1.2

NAM

E

❶

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ergingrectangleinthepicture.ThenbuildthesecondscriptinScratch(sim

ilartothefirstone)toproducethesameshapereflectedinthexaxis.

WHATTO

DO

INVESTIG

ATIO

N1

Activity 6.1.2

NAM

E

❷

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ergingshapeinthepicture.Thenbuildthesecondscripttoproducethesam

eshapetranslatedright,left,upordown–

basedontheinstruction.W

HATTODO

INVESTIG

ATIO

N1

Activity 6.1.2

NAM

E

❸

LEARNING OBJECTIVES


Explorehowtocreateemergingshapesofdifferentscalefactors.Explainhowtochangethescaleofthecoordinatesgrid.

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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.

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Fortheinitialsmallsquareuseinputsforthepickrandom…blockslike-15to15or-20to20…,sothatevenaftermultiplyingby10iy willfit(asxcoordinates)intothestage:

ADDITIONAL SUPPORT

❶

❷

Whenyoumakeanewvariableandbuildablocktosetitsvalue(to10oranyothervalue),donotforgettoruntheset block.Otherwisethevalueofthevariablewillbe0,itsinitialvaluepre-setbyScratch.

Note- whenareporterblockispulledoutfromablock,thevaluerestoredasaninputinthatblockistypically10.

❸

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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:

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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.

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LEARNING OBJECTIVES


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.

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INVESTIGATION 1Ext. Activity 6.1.4

Thesearethestepsofthetransitionfrompreviousjumpingintothenewonelinejumping - pickrandom… fory: canbeturnedinto(b) andusedseparatelyin(c) beforetherepeat block,whichwillnowusesetxto…andcanbeturnedintoanewblock:

ADDITIONAL SUPPORT

❶

❷

WhydoesFleeeee alwaysendsuponelineabovethelastlinedrawn?[becausethelastlineintherepeatistochangeybygrid]

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INVESTIGATION 1Ext. Activity 6.1.4ADDITIONAL SUPPORT CONTINUED

❸

❹

Duetothefactthatpickrandom-4to1 producesthesamesetofvaluesaspickrandom1to-4,wecansetLeft toavaluewhichisinfacttotherightofthesecondinput,seetheexampleabove.

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27


❻

❺


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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


MathematicsDescribepositionsonthefullcoordinatesgrid.Interpretremaindersaswholenumberremainders,fractions,orbyrounding,asappropriateforthecontext.Solveproblemsinvolvingsimilarshapeswherethescalefactorisknownorcanbefound.Compareandclassifygeometric shapes,includingquadrilateralsandtriangles,basedontheirpropertiesandsizes.Plotspecifiedpointsanddrawsidestocompleteagivenpolygon.

► Pupilsarerequiredtocodeanddecodemessagesusingthe positionsoflettersonthecoordinatesgrid.

► [Extension]Pupilsencountertheneedtoroundtheresultofdivisionoperationsinordertogetspritestosnaptothenearestgridpoint.

► Pupilsarerequiredtousethegridvariable(inasimilarwaytothepreviousinvestigation)toadapttheirprojecttodifferentgridintervals.

► Pupilscreateandexchangecoordinateproblemswhosesolutionsrequirecoordinateandpropertiesofshapeknowledge.

Explorehowtocreateacoordinatecodingscheme.Exchangemessages/taskswithapartnertodecodeusingthecoordinatecodingscheme.

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MODULE 6 ● INVESTIGATION 2 ● ACTIVITY 6.2.1Letters and Coordinates

LEARNING OBJECTIVES


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

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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!”.


A B C D E P S X Y Z

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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


Explorehowtodrawalinethatconnectstwopointsonthecoordinatesgrid.Explainhowtoreconnectthepointswhenthepositionofonespriteischanged.

32

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.

33

INVESTIGATION 2Activity 6.2.2ADDITIONAL SUPPORT

❶

❷Fullscreenmode(orplayermode)on/off.

34


Forconnectingspritesbyalinewewillusethegoto sprite blockfor‘jumping’.NotethatFleeeee turnsitspendown onlyafteritsfirstjump.Then– withitspendown–jumpstothesecondpoint,turnsitspenupandjumpsback‘home’.ItallhappenssoquicklythatitlooksasifFleeeee didnotmoveatall.


❸

❹ In(a)belowFleeeee connectsthepointsAandBwheneverwepressthespacekey.Asthereisnoclear block,thepreviouslinesstayonthestageaswell.In(b)thepreviouslineisfirstclearedaway.In(c)thelinebetweenAandBis‘updated’againandagainsoitlookslikearubberbandattachedtothesetwopoints.

❺ Eachofthefollowingforever scriptswaits arandomnumberofseconds(inoursolution,between1and10)andrunstheanimation.

35


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


Exploreand explainthecoordinatesoftheverticesofdifferenttypesoftrianglesExchangeproblemswhichinvolvetrianglesandcoordinates.

36

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

37


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


38


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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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


Exploreand explainthecoordinatesoftheverticesofdifferenttypesofquadrilaterals.Exchangeproblemswhichinvolvequadrilateralsandcoordinates.

40

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)


41

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

42


❶

❷

43

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


Scratchprojects 6-MimicMeeeee 6-MimicMeeeeeINT 6- MimicMeeeeeFINAL


MathematicsDescribepositionsonthefullcoordinatesgrid.Solveproblemsinvolvingsimilarshapeswherethescalefactorisknownorcanbefound.Identify, describeandrepresentthepositionofashapefollowingareflectionortranslation.Describemovementsbetweenpositionsastranslationsofagivenunittotheleft/rightandup/down.Compareandclassifygeometricshapes.Plotspecificpointsanddrawsides tocompleteagivenpolygon.

► Pupilsarerequiredtodrawandthentranslate/reflectpatternsandshapesinallfourquadrants.

► [Extension]Pupilshave theopportunitywithinanextensionactivitytoexploredifferentscalefactorsintheirtranslateddrawings.

► Pupilsarerequiredtoexploretranslationsofpatternsandshapesthroughusingasecondspritethatmimicsthebehaviour ofthefirst.

► PupilsarerequiredtorevisitactivitiesfromY5involvingdrawingpolygonpictures(suchashousesmadefromsquaresandtriangles),buttoextendthesetoalsoincorporateareflectedversionofthedrawing.

Explorehowtomakeonespritemimicthebehaviour ofanothersprite.Explainhowthismimickingbehaviour works.

44

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.]

45


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.]

46


For“spying”i.e.learningaboutsomesettingsofanotherspriteweuseahighlygeneralandpowerfulreporterblockfromtheSensing group.ItisoneofveryfewScratchblockswhichhastwodropdownmenus– bothontheleftsideandontherightside.Wehavealreadyuseditinextensionactivity4.3.4.


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.

47


❻

❼

❺

Analternativesolution(andforthisparticulartaskevensimpler)wouldbetousethegotoFleeeeeMove block,seebelow.However,inthefollowingactivitieswewillneedthesolutionwithgotox:…y:…blockaswewillinsertdifferentexpressionsinit.

LEARNING OBJECTIVES


Explorehowtomakeonespritetranslatethedrawingbehaviour ofanothersprite.Explainhowtorestrictthemovementofaspritetoasinglequadrantofthegrid.

48

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.

49


Pupilsmayexperimentwithdifferenttimesintheglide block.

ADDITIONAL SUPPORT

❶

❷

❸ Addingpositivenumbertoxpositionof FleeeeemeanstranslatingMeeeee’s drawingtotherightorhorizontally.Subtractinganumberfromypositionof FleeeeemeanstranslatingMeeeee’s drawingdownwardsorvertically.

50


❹ HerewerestrictedtheglidingareaofFleeeee totheupperleftquadrantonly.

Analternative(butmorechallenging)solutionwouldbetohavepenup inthesetupscriptofMeeeee andmodifyitsmimickingscriptinthefollowingway:

Here,forthetranslationRight200,wemodifiedtheinitialpositionofMeeeee toalsobeatranslatedinitialpositionofFleeeee.Otherwise,therewouldbealinefromMeeeee connectingitsinitialposition0,0 tothefirsttranslatedpointat200,0.

ThistranslationisRight50Down50.

ThistranslationisDown150.

51


❺

❻ Ifwemultiplyxand/orypositionofFleeeee by0.5,theresultingdoodlewillbehalfthesize(areduction).Exploremultiplyingby-0.5.Exploremultiplyingxbyonenumberandybyadifferentnumber,e.g.1and-0.5or-0.5and-0.5

LEARNING OBJECTIVES


Explorehowtocreatereflectedpolygondrawings.Explainthedifferencesbetweencreatingatranslatedandreflecteddrawing.

52

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.]

53


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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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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❸

56


❹

57


❺

❻

Meeeee reflectsthedrawingofFleeeee intheyaxis.

InthisoneMeeeeemultipliesxpositionofFleeeee by0.5.

Switchbackdroptotheintheday orinthenight.

coordinates and geometry - ucl.ac.uk suggested int project for those pupils who do not have a...

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