Computer Science in Algebra

Computer Sciencein Algebra

Instructor Handbook

2015-2016

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VideoGamesandCoordinatePlanesLessontime:30-60Minutes

LESSONOVERVIEWStudentsdiscussthecomponentsoftheirfavoritevideogamesanddiscoverthattheycanbereducedtoaseriesofcoordinates.TheythenexplorecoordinatesinCartesianspace,identifyingthecoordinatesforthecharactersinagameatvariouspointsintime.Oncetheyarecomfortablewithcoordinates,theybrainstormtheirowngamesandcreatesamplecoordinatelistsfordifferentpointsintimeintheirowngame.

LESSONOBJECTIVESStudentswill:

Createadatamodelthatdescribesasimplevideogame.Describethemovementsofvideogamecharactersbytheirchangeincoordinates.

ANCHORSTANDARDCommonCoreMathStandards6.NS.8:Solvereal-worldandmathematicalproblemsbygraphingpointsinallfourquadrantsofthecoordinateplane.Includeuseofcoordinatesandabsolutevaluetofinddistancesbetweenpointswiththesamefirstcoordinateorthesamesecondcoordinate.

Additionalstandardsalignmentcanbefoundattheendofthislesson

TEACHINGSUMMARYGettingStarted

1)Vocabulary2)LearningaLanguage

Activity:VideoGamesandtheCoordinatePlane3)ReverseEngineeraDemo4)CoordinatePlanes

Wrap-up5)BrainstormingaGame

TEACHINGGUIDE 1

MATERIALS,RESOURCES,ANDPREPFortheStudent

ReverseEngineeringTable(inthestudentworkbook)VideogameDesignTemplate(inthestudentworkbook)

FortheTeacherLessonslidedeckExampleGamePrintedcutoutsoftheNinja,Dragon,andUnicorn

GETTINGSTARTED1)VocabularyThislessonhasthreenewandimportantwords:Apply-useagivenfunctiononsomeinputsReverseEngineer-toextractknowledgeordesigninformationfromanexistingproductSprite-agraphiccharacteronthescreen.Sometimescalledabitmaporanimage.

2)LearningaLanguageWelcometoCode.orgCSinAlgebra!Inthiscourseyou’llbelearninganewprogramminglanguage-awaytotellcomputersexactlywhatyouwantthemtodo.JustlikeEnglish,SpanishorFrench,aprogramminglanguagehasitsownvocabularyandgrammarthatyou’llhavetolearn.Fortunately,thelanguageyou’llbeusingherehasalotincommonwiththesimplemaththatyoualreadyknow!Connectthismaterialwiththingsstudentsalreadyknow:

Whatmakesalanguage?Doesanyonespeakasecond(orthird)language?Doyouspeakadifferentlanguagethanyourparents/grandparents?Aretherelanguagesthatsharefeatures,suchasacommonroot(Romance,Germanic)orasimilaralphabet(Latin,Cyrillic,Arabic,Kanji)?Aretherelanguagesthataredesignedforspecificpurposesorwithincertainconstraints(signlanguage,Esperanto)?Mathisalanguage,justlikeEnglish,Spanish,oranyotherlanguage!

Weusenouns,like"bread","tomato","mustard"and"cheese"todescribephysicalobjects.Mathhasvalues,likethenumbers1,2or3,todescribequantities.Wealsouseverbslike"toast","slice","spread"and"melt"todescribeoperationsonthesenouns.Mathematicshasfunctionslikeadditionandsubtraction,whichareoperationsperformedonnumbers.Justasyoucan"slicepieceofbread",apersoncanalso"addfourandfive".

Amathematicalexpressionislikeasentence:it’saninstructionfordoingsomething.Theexpression4+5tellsustoadd4and5.Toevaluateanexpression,wefollowtheinstructionsintheexpression.Theexpression4+5evaluatesto9.

ACTIVITIES:3)ReverseEngineeraDemoLet’sbeginbyexploringasimplevideogame,andthenfiguringouthowitworks.Openthislinktoplaythegame,andspendaminuteortwoexploringit.Youcanusethearrowkeystomovetheupanddown-trytocatchtheunicornandavoidthedragon!Thisgameismadeupofcharacters,eachofwhichhasitsownbehavior.Theunicornmovesfromthelefttotheright,whilethedragonmovesintheoppositedirection.Theninjaonlymoveswhenyouhitthearrowkeys,andcanmoveupanddown.Wecanfigureouthowthegameworksbyfirstunderstandinghoweachcharacterworks.

Directions:1)Dividestudentsintogroupsof2-4.2)Provideeachstudentwithacopyofthereverse-engineeringtable.3)Asstudentsdemothegame,askthemtofillinthe"Thinginthegame..."columnwitheveryobjecttheyseeinthegame.4)Discusswiththewholegroupwhichthingstheycameupwith.Characters?Background?Score?5)Next,foreachofthethingsinthegame,fillinthecolumndescribingwhatchanges.Size?Movement?Value?6)Askstudentstosharebackwiththewholegroup.Notehowstudentsdescribedchanges-howdetailedwerethey?Whatwordsdidtheyusetodescribemovement?

4)CoordinatePlanesComputersusenumberstorepresentacharacter’spositiononscreen,usingnumberlinesasrulerstomeasurethedistancefromthebottom-leftcornerofthescreen.Forourvideogame,wewillplacethenumberlinesothatthescreenrunsfrom0(ontheleft)to400(ontheright).WecantaketheimageoftheDragon,stickitanywhereontheline,andmeasurethedistancebacktothelefthandedge.AnyoneelsewhoknowsaboutournumberlinewillbeabletoduplicatetheexactpositionoftheDragon,knowingonlythenumber.WhatisthecoordinateoftheDragonontherighthandsideofthescreen?Thecenter?WhatcoordinatewouldplacetheDragonbeyondthelefthandedgeofthescreen?

Byaddingasecondnumberline,wecanlocateacharacteranywhereonthescreenineitherdimension.Thefirstlineiscalledthex-axis,whichrunsfromlefttoright.Thesecondline,whichrunsupanddown,iscalledthey-axis.A2-dimensionalcoordinateconsistsofboththex-andy-locationsontheaxes.SupposewewantedtolocatetheNinja’spositiononthescreen.Wecanfindthex-coordinatebydroppingalinedownfromtheNinjaandreadthepositiononthenumberline.They-coordinateisfoundbyrunningalinetothey-axis.Acoordinaterepresentsasinglepoint,andanimageis(bydefinition)manypoints.Somestudentswillaskwhetheracharacter’scoordinatereferstothecenterofthe

image,oroneofthecorners.Inthisparticularprogram,thecenterservesasthecoordinate-butotherprogramsmayuseanotherlocation.Theimportantpointindiscussionwithstudentsisthatthereisflexibilityhere,aslongastheconventionisusedconsistently.Whenwewritedownthesecoordinates,wealwaysputthexbeforethey(justlikeinthealphabet!).Mostofthetime,you’llseecoordinateswrittenlikethis:(200,50)meaningthatthex-coordinateis200andthey-coordinateis50.Dependingonhowacharactermoves,theirpositionmightchangeonlyalongthex-axis,onlyalongthey-axis,orboth.Lookbacktothetableyoumade.CantheNinjamoveupanddowninthegame?Canhemoveleftandright?Sowhat’schanging:hisx-coordinate,hisy-coordinate,orboth?Whatabouttheclouds?Dotheymoveupanddown?Leftandright?Both?

LESSONTIP Thekeypointforstudentshereisprecisionandobjectivity.Therearemanypossiblecorrectanswers,butstudentsshouldunderstandwhyanysolutionshouldbeaccurateandunambiguous.Thisrequiresstudentstoproposesolutionsthatshareacommon"zero"(thestartingpointoftheirnumberline)anddirection(literally,thedirectionfromwhichacharacter’spositionismeasured).

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OPTIONALACTIVITY:Dependingontimingandthebackgroundofyourstudents,havingonestudentplaceacharacteronalargegraphandanotherstudentstatingthecoordinatesisexcellentpractice.Studentsoftenneedextrapracticerememberingwhichcoordinatecomesfirst.Coordinatesdonothavetobeexactbuttheyshouldbeinthecorrectorder.Extendingthistoallfourquadrantstoincludenegativenumbersisalsoexcellentpractice.Fillintherestofthereverse-engineeringtable,identifyingwhatischangingforeachofyourcharacters.

WRAP-UP5)BrainstormingforaGameUsethegameplanningtemplatetomakeyourowngame.JustlikewemadealistofeverythingintheNinjagame,we’regoingtostartwithalistofeverythinginyourgame.Tostart,yourgamewillhavefourthingsinit:

ABackground,suchasaforest,acity,space,etc.APlayer,whocanmovewhentheuserhitsakey.ATarget,whichfliesfromtherighttotheleft,andgivestheplayerpointsforhittingit.ADanger,whichfliesfromtherighttotheleft,whichtheplayermustavoid.

LESSONTIP Thestructureofyourstudents'gameswillverycloselyresemblethedemothey'vejustplayed.ManystudentswillwanttoreachforthestarsanddesignthenextHalo.Remindthemthatmajorgameslikethattakemassiveteamsmanyyearstobuild.Someofthemostfunandenduringgamesarebuiltonverysimplemechanics(thinkPacman,Tetris,orevenFlappyBird).

2CSinAlgebra|Lesson2

EvaluationBlocksandArithmeticExpressionsLessontime:30-60Minutes

LESSONOVERVIEWStudentswillbeginusingEvaluationBlockstoexploretheconceptofmathasalanguage,andmorespecifically,aprogramminglanguage.BycomposingarithmeticexpressionswithEvaluationBlocks,studentswillbeabletovisualizehowexpressionsfollowtheorderofoperations.

Convertarithmeticexpressionstoandfromcode.UseEvaluationBlockstoreflecttheproperorderofoperationsforanexpression.

ANCHORSTANDARDCommonCoreMathStandardsA.SSE.1:Interpretexpressionsthatrepresentaquantityintermsofitscontext.

1)Vocabulary2)Introduction

Activity:EvaluationBlocks3)OnlinePuzzles

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREPFortheStudent

EvaluationBlocksWorksheet(inthestudentworkbook)FortheTeacher

Lessonslidedeck 5

GETTINGSTARTED1)VocabularyThislessonhasfivenewandimportantwords:EvaluationBlock-ablockofcodethatrepresentsthestructureofanexpressionEvaluate-performthecomputationinanexpression,producingananswerExpression-acomputationwrittenintherulesofsomelanguage(suchasarithmetic,code,oranEvaluationBlock)Function-amathematicalobjectthattakesinsomeinputsandproducesanoutputValue-aspecificpieceofdata,like5or"hello"

2)IntroductionAmathematicalexpressionislikeasentence:it’saninstructionfordoingsomething.Theexpression4+5tellsustoadd4and5.Toevaluateanexpression,wefollowtheinstructionsintheexpression.Theexpression4+5evaluatesto9.Sometimes,weneedmultipleexpressionstoaccomplishatask.Ifyouweretowriteinstructionsformakingasandwich,itcouldmatterverymuchwhichcamefirst:meltingthecheese,slicingthebread,spreadingthemustard,etc.Theorderoffunctionsmattersinmathematics,too.Ifsomeonesays"fourminustwoplusone,"theycouldmeanseveralthings:

Subtracttwofromfour,thenaddone:(4-2)+1Addtwoandone,andsubtracttheresultfromfour:4-(2+1)

Dependingonwhichwayyoureadtheexpression,youmighthaveverydifferentresults!Thisisaproblem,becauseweoftenusemathtosharecalculationsbetweenpeople.Forexample,youandyourcellphonecompanyshouldagreeupfrontonhowmuchyouwillpayforsendingtextmessagesandmakingcalls.Differentresultsmightmeanthatyourbilllookswrong.Weavoidproblemsbyagreeingontheorderinwhichtousethedifferentoperationsinanexpression.Therearetwowaystodothis:

1. Wecanallagreeonanordertouse2. Wecanadddetailtoexpressionsthatindicatetheorder

Mathematiciansdidn’talwaysagreeontheorderofoperations,butnowwehaveacommonsetofrulesforhowtoevaluateexpressions.Whenevaluatinganexpression,webeginbyapplyingtheoperationswrittenatthetopofthepyramid(multiplicationanddivision).Onlyafterwehavecompletedallofthoseoperationscanwemovedowntothelowerlevel.Ifbothoperationsarepresent(asin4-2+1),wereadtheexpressionfromlefttoright,applyingtheoperationsintheorderinwhichtheyappear.EvaluationBlocksprovideavisualwaytoindicatetheorderofoperationsinanexpression.AllEvaluationBlocksfollowthreerules:

Rule1:Eachblockmusthaveonefunction,whichisdisplayedatthetopoftheblock.Rule2:Thevaluesforthatfunctionareplacedbelow,inorderfromlefttoright.Rule3:Ifablockcontainsanotherblockasavalue,thatinnerblockmustbeevaluatedbeforetheouterblock.

Beforestudentsgetstartedonthecomputers,youcanhavethemworkthroughtheevaluationblocksworksheetinthestudentworkbook.

ACTIVITY:EVALUATIONBLOCKS3)OnlinePuzzlesTheprogramminglanguageyouaregoingtolearnusesEvaluationBlockstovisuallyrepresentmathematicalfunctions.EachblockofcodeiseitheraFunction,oraValue-headtoCSinAlgebraStage2inCodeStudiotogetstartedprogramming.

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StringsandImagesLessontime:30-60Minutes

LESSONOVERVIEWTocomputemorethanjustnumbers,studentswillneedtolearnabouttwonewdatatypes,Strings(anystringofalphanumericcharacters)andImages.Usingthesenewdatatypes,we'llcomposeprogramsthatproduceandmanipulateimages.

WriteandevaluateexpressionsforgeneratingStringsandImages.

ANCHORSTANDARDCommonCoreMathStandards

A.SSE.1:Interpretexpressionsthatrepresentaquantityintermsofitscontext.Additionalstandardsalignmentcanbefoundattheendofthislesson

Activity:StringsandImages3)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)VocabularyThislessonhasfournewandimportantwords:

String-anysequenceofcharactersbetweenquotationmarks(examples:"hello","42","thisisastring!")Image-atypeofdataforpicturesType-referstoageneralkindofdata,likeNumber,String,Image,orBoolean

2)IntroductionInthepreviousstage,studentsonlyworkedwithasingletypeofvalue-Numbers.Inthisnextstagetheywillgeta

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chancetowriteprogramswithnewdatatypestooutputtext(Strings)andpictures(Images).Showstudentsthe'star'function,andaskthemtodiscussthefollowingquestions:

Whatisthenameofthisfunction?Howmanyargumentsarebeinggiventothisfunction?Whatdoyouthinkthisfunctionwilldo?

Studentsarenotexpectedtoknowalltheanswershere-thegoalisforthemtoapplywhattheyknowaboutEvaluationBlockstoanovelexpression,anddiscussforthemselveswhattheythinkitmightmean.Askthemtojustifytheiranswers,andtoexplainwhytheythinktheyarecorrect.Encouragestudentstolookforpatternsamongthesenewblocks(suchascolors,orquotationmarksaroundthewords"solid"and"purple"-whatmightthosepatternsmean?

ACTIVITY:STRINGSANDIMAGES3)OnlinePuzzlesInthisactivityyou'llusethenewdatatypesStringandImagetocomposeartwithBlocksofEvaluation-headtoCSinAlgebraStage3inCodeStudiotogetstartedprogramming.

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Contracts,Domain,andRangeLessontime:30-60Minutes

LESSONOVERVIEWContractsprovideawayforstudentstobetterunderstandanddiscussfunctions.Throughthislesson,studentswilllookatknownfunctionsandcomeupwiththecontractsthatdescribethosefunctions.

Describeafunctionintermsofitsname,domain,andrange.Createcontractsforarithmeticandimage-producingfunctions.

F.IF.1:Understandthatafunctionfromoneset(calledthedomain)toanotherset(calledtherange)assignstoeachelementofthedomainexactlyoneelementoftherange.Iffisafunctionandxisanelementofitsdomain,thenf(x)denotestheoutputoffcorrespondingtotheinputx.Thegraphoffisthegraphoftheequationy=f(x).

TEACHINGSUMMARYWhat'sinaContract

1)Vocabulary2)What'sinaFunction

Activity:Contracts3)ReadingContracts4)WritingContracts

Wrap-up5)KeepUpYourContracts

Describeafunctionintermsofitsname,domain,andrangeCreatecontractsforarithmeticandimage-producingfunctions

ContractLogFortheTeacher

LessonSlideDeck

GETTINGSTARTED1)VocabularyThislessonhasthreenewandimportantwords:

Contract-astatementofthename,domain,andrangeofafunctionDomain-thetypeofdatathatafunctionexpectsRange-thetypeofdatathatafunctionproduces

2)What'sinaFunctionYou’vealreadyseenseveralfunctionsthattakeintwoNumbers,suchas+,and-.Otherfunctionslike"star",takeinaNumberandtwoStrings.Differentfunctionstakeindifferentinputs,andweneedawaytokeeptrackoftherequirementsforeachfunction.

Whatdoesthe'+'functiondo?Whatdoesittakeasinput?Whatdoesitreturnasoutput?

Howaboutthe'triangle'function?Whatdothesedifferentfunctionshaveincommon?

Let'slookatasimplewaytodescribeanyfunction,it'scalleda"contract"WhatisaContract?

AformalagreementAdescriptionofexpectedbehavior

WhatdoContractstellus?WhatafunctionshoulddoWhatinputsafunctionneedsWhatafunctionreturns

Encouragestudentstothinkaboutcontractsintherealworld.Whatpurposedotheyserve?Ifacontractissigned,doweexpectittobefollowed?Contractshavethreedistinctparts:

1. Name2. Domain3. Range

TheNameofafunctionbrieflydescribeswhatthefunctiondoes.TheDomainofafunctionisthedatathatthefunctionexpects.TheRangeofafunctionisthedatathatthefunctionproduces.Bykeepingalistofallthefunctionsinalanguage,andtheirDomains,programmerscaneasilylookuphoweach

functionisused.However,it’salsoimportanttokeeptrackofwhateachfunctionproduces!Forexample,aprogramwouldn’tuse"star"iftheyweretryingtoproduceaNumber,becausestaronlyproducesImages.DomainsandRangeshelpprogrammerswritebettercode,bypreventingsillymistakesandgivingthemselveshintsaboutwhattodonext.Aprogrammerwhowantstouse"star"canlookuptheDomainandimmediatelyknowthatthefirstinputhastobeaNumber(like100),withouthavingtorememberiteachtime.Insteadofwritingasinglevaluethere,aprogrammercouldwriteawholeexpression,like(25*4).Weknowthiscodewillreturnanappropriatevalue(Number)bylookingattheRangefor*;therefore,theresultof*canbeusedinplaceofanyNumbervalue.WhenprogrammerswritedowntheDomainsandRangesofeachfunction,theywritewhatarecalledcontracts,tokeeptrackofwhateachfunctionneeds.

ACTIVITIES:3)ReadingContractsLet'slookatafewexamplecontracts-foreachcontractwe'llidentifytheName,Domain,andRange

+:NumberNumber->Number

triangle:NumberStringString->Image

rotate:NumberImage->Image

4)WritingContractsLet'sseeifwecancomeupwithcontractsforsomeofthefunctionsyou'vealreadyseen.You'llwanttomakesurethatyou'vegotyourcontractlog,asthisiswhereyou'llkeeparunningdocumentofallcontractsyouwrite-bothforexistingfunctionsandonesofyourowncreation.

We'llstartwithcontractsforsimplearithmeticfunctions+,-,*,/

ThosewereprettyeasyasarithmeticfunctionsonlydealinNumbers.Whenitcomestowritingfunctionsthatdealwithmultipledatatypes,lookingattheEvaluationBlockcangiveussomehelpfulclues.

TheNameofeachfunctionisatthetopTherewillbeaslotforeachDomainelementThecolorofeachslottellsyouDomaintypeThecolorofthewholeblocktellsyouRangeColorcodes: Number String Image

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DisplayeachofthefollowingEvaluationBlocksandaskstudents:WhatistheNameofthisfunction?WhatistheDomainofthisfunction?WhatistheRangeofthisfunction?Addthisfunction'scontracttoyourreference

WRAP-UP5)KeepupyourContractsAsyoucontinueprogramming,makesurethatyoudocumentacontractforeverynewfunctionyouencounterorwrite.Inthenextunit,you’lllearnhowtocreateyourownfunctionstosaveworkinwritingexpressions(thiswillturnouttobeanessentialpartofwritingagame).You’llalsostartcustomizingyourgamewithimagesfortheelementsinyourgamedesign.

LESSONTIP Commonmistakeswhenstudentsfirstwritedowncontractsinclude:writingvalues(suchas"red")insteadoftypes(suchas"String")andforgettingarguments.Readyourstudents’contractscarefully,astheyoftenindicatemisconceptionsthatwillpersistandaffectthemlateron.

WritingContractsLessontime:30-60Minutes

LESSONOVERVIEWStudentswillworktheirwaythroughanumberofnewfunctions,firstusingeachtosolveaproblem,andthenwritingacontractwhichdescribesit.

Decomposeexistingfunctions.Writecontractsthatdescribefunctions.Experimentwithbasicgeometrictransformations.

ANCHORSTANDARDCommonCoreMathStandards8.G.1:Verifyexperimentallythepropertiesofrotations,reflections,andtranslations:

Activity:WritingContracts3)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)VocabularyThislessonhasthreenewandimportantwords:Rotate-toturnashapeaboutapoint.Scale-toincreasethedimensionsofashapebythesamefactorinalldirections.Alsoknownasdilate.Translate-tomoveashapefromonelocationtoanother.Theoffsetfunctionperformedthistransformation.

2)Introduction 14

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ReviewwithstudentsthepurposeofaContract:Describesthreeelementsofafunction

Name(whatisthefunctioncalled)Domain(whatinputsdoesittake)Range(whatdoesitoutput)

Asaclass,describetheContractsforsomebasicmathematicaloperatorsAddition(name+,domainNumberNumber,rangeNumber)Subtraction(name-,domainNumberNumber,rangeNumber)Multiplication(name*,domainNumberNumber,rangeNumber)Poweroftwo(namesqr,domainNumber,rangeNumber)

ACTIVITY:WRITINGCONTRACTS3)OnlinePuzzlesInthisstageyou'llbelookingatsomefunctions,someofwhichyou'veseenbeforeandsomewhicharebrandnew.Foreachfunctionyou'llfirstgetachancetousethefunction,andthenyou'llwriteaContractforit.MakesuretodocumentanynewContractsonyourContractLog.HeadtoCSinAlgebrastage5inCodeStudiotogetstartedprogramming.

DefiningVariablesandSubstitutionLessontime:30-60Minutes

LESSONOVERVIEWInthisactivity,studentswilllearntodefinevariablesthatcanbeusedtoreferencevaluesandexpressions.Oncedefined,theirvariablescanbeusedrepeatedlythroughoutaprogramassubstitutesfortheoriginalvaluesorexpressions.

Definevariablesbygivingthemanameandassigningthemavalueorexpression.UsevariableswithinEvaluationBlocks.Describeasituationwhereusingvariablesassubstitutionsforvaluesorexpressionsismoreefficient.

ANCHORSTANDARDCommonCoreMathStandards6.EE.4:Identifywhentwoexpressionsareequivalent(i.e.,whenthetwoexpressionsnamethesamenumberregardlessofwhichvalueissubstitutedintothem).Forexample,theexpressionsy+y+yand3yareequivalentbecausetheynamethesamenumberregardlessofwhichnumberystandsfor.

Activity:DefiningVariablesandSubstitution3)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)VocabularyThislessonhastwonewandimportantwords:

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Define-associateadescriptivenamewithavalueVariable-acontainerforavalueorexpressionthatcanbeusedrepeatedlythroughoutaprogram

2)IntroductionSupposewewanttomakeanimagewithfiftyidentical,solidredtriangles.Todosoyou'dhavetocreatethisEvaluationBlockfiftytimes!Evenworse,ifyoudecidedyouwantedfiftybluetrianglesinstead,you'dhavetogothroughandchangeeachandeveryblock.Theremustbeabetterway!WecanstorethatredtriangleEvaluationBlockinaVariable,let'scallit"red-triangle."Thatname"red-triangle"nowbecomesashortcutfortheblocksinsidethevariable,andwecanusethatshortcutoverandoverinourprogram.Ifwedecidethatwewantthatredtriangletobe100pixelsinsteadof50,weonlyneedtochangeitinthevariabledefinition.

ACTIVITY:DEFININGVARIABLESANDSUBSTITUTION3)OnlinePuzzlesInthisstageyou'llusevariablestoreferenceavarietyofvaluesandexpressions.HeadtoCSinAlgebrastage6inCodeStudiotogetstartedprogramming.

LESSONTIP Ifstudentshaveusedvariablesinotherprogramminglanguages,it'sessentialtonotethatinfunctionalprogramming,asinmath,variablesareconsideredimmutable-meaningthevaluecan'tbechangedduringtheexecutionofaprogram.Thinkaboutitthisway:sayingx=50,andthenx=x+1mightmakesenseinJavascript,butit'simpossibleinAlgebra.

TheBigGame-VariablesLessontime:30-60Minutes

LESSONOVERVIEWStudentsgettheirfirstlookattheinsideoftheirownvideogames.TheywillstartdevelopmentbysubstitutinginnewImages,Strings,andNumbersforexistingvariables.

Substitutenewvaluesintoexistingvariablesofanexistingprogramanddescribetheeffects.Examinethestructureofanexistingprogram.

6.EE.4:Identifywhentwoexpressionsareequivalent(i.e.,whenthetwoexpressionsnamethesamenumberregardlessofwhichvalueissubstitutedintothem).Forexample,theexpressionsy+y+yand3yareequivalentbecausetheynamethesamenumberregardlessofwhichnumberystandsfor.

1)Vocabulary2)TeachingNotes

Activity:TheBigGame-Variables3)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)VocabularyThislessonhasthreenewandimportantwords:

Troubleshooting-whenaprogramgeneratesanunexpectedresult,aprogrammermustexaminethecodetodeterminethesourceoftheunexpectedresults(usuallyanunanticipatedinputorincorrecthandlingofanexpectedinput).Sometimescalleddebugging.Mod-Shortformodification.Gamesintherealworldareoftenamodofanothergame.Othello(orReversi)is

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usuallyconsideredamodoftheancientgameof“Go”.Amodofaprogramisonethathasbeenalteredtodosomethingslightlydifferentthanitsoriginalpurpose.Stub-Afunctionwhosedomainandrangehavebeendesignated,buttheprocesstotransformthedomainintotherangehasnotyetbeendefined.

2)TeachingNotesontheBigGameThestudentswillcreateamodofanexistinggame.Astheymakechangestothegame,itispossiblethattheywilladdcodethatwilleither“break”theprogram(causenothingtohappen)orcauseanunexpectedwutcome.Ifeitheroftheseconditionsexist,theywillneedtotroubleshootordebugthecodetodeterminehowtogetitworkingintheproperway.Ifthingsgoterriblyawryandfindingaproblemistoofrustrating,usetheClearPuzzlebuttonintheupperrightcorneroftheworkspace.Thisbuttonwillclearyourgamebacktoitsinitialstate,soitshouldonlybeusedasalastresort.Thisexerciseisasimplifiedversionofaverycommonrealworldprogrammingtask.Programmersoftencreatemodsofprogramsaboutwhichtheyknowverylittle.Theyslowlyunravelwhichpiecesrequirefurtherunderstandinginordertomakethemodworkthewaytheywant,whileleavingotherpartsoftheprogramcompletelyunexplored.Manyprogramsandfunctionsarecustomizablethroughtheirarguments(whichcanbevariablesorvalues).Whenafunctioniscalled,itsargumentsarepassedinasvariablesintothefunction.Inothercases,variablesthatsomeonemightwanttochange(sometimescalledconstants)areoftenatthetopofapieceofcode.Havingaccesstothecodeallowstheprogrammertochangethewaytheprogrambehavesbysettingthesevariablestodifferentvalues.Inthislesson,wearecreatingthemodbychangingthevariablesinsidethecode.ThestudenthasaccesstothegamecodeandischangingtheinitialvalueoftheTitle,Subtitle,Player,Danger,andTarget.Asareminder,theultimategoalofthisgamewillbetomanipulatetheplayerthroughpressingkeys,toavoidthedanger,andtomakecontactwiththetarget.Thecurrentlessonhasnomotionorinteractivity.Itonlychangesthelookofthegame.Themotionandinteractivityfunctionstubs,suchas“update-target”and“danger?”,willbecompletedinlaterlessons.Theblocksmenudisplaysafewnewitems(Boolean,Cond,andFunctions)whichwillbeexaminedinmoredetailinfuturelessons.Thestudentsshouldbeencouragedtoexploreeachofthesub-menus.Howevertheonlynavigationrequiredforthisleveliseditingthefivecolorblocksatthetopofthefunction:Title,subtitle,bg(background),player,target,anddanger.Thedifferencebetweenthecolorandblackblockswillalsobeexplainedinafuturelesson.

ACTIVITY:THEBIGGAME-VARIABLES3)OnlinePuzzlesInthisstageyou'lldefineandmodifyvariablestochangeshowsomegamesfunction.HeadtoCSinAlgebrastage7inCodeStudiotogetstartedprogramming.

CompositeFunctionsLessontime:30-60Minutes

LESSONOVERVIEWInthepastlessonsstudentshavedefinedvariableswhichwillallowthemtoeasilywriteexpressionsthatrefertothesamevaluerepeatedly.Inthisstage,theywillwritesimplefunctionsthat,likevariables,allowstudentstoabstractoutrepetitiouselementsoftheirprograms.

Analyzeanduseexistingfunctions.Modifyexistingfunctions.Createnewfunctions.Createsimilarshapesbychangingsizeparametersonfunctions.

ANCHORSTANDARDCommonCoreMathStandards8.F.1:Dnderstandthatafunctionisarulethatassignstoeachinputexactlyoneoutput.Thegraphofafunctionisthesetoforderedpairsconsistingofaninputandthecorrespondingoutput.1

Activity:CompositeFunctions2)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)VocabularyThislessonhasonenewandimportantword:Parameter-Avalueorexpressionbelongingtothedomain.

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2)IntroductionDefiningareusablevalueishelpfulwhenaprogramhaslotsofidenticalexpressions.Sometimes,however,aprogramhasexpressionsthataren’tidentical,butarejustverysimilar.Aprogramthathasfiftysolid,greentrianglescanbesimplifiedbydefiningasinglevalue,aslongastheyareallthesamesize.Butwhatifaprogramhasfiftysolid,greentrianglesofdifferentsizes?ThinkabouttheImagefunctionsyouhavealreadyused,likestarandcircle.Theytakeinputsandproduceimages.Similarly,wemightwantagreen-trianglefunctionthattakesthesizeasaninputandproducesagreentriangle.Theprogramminglanguagedoesn’tprovidethisfunction,butitdoesletyoudefineyourownfunctions.Wewanttodefineourownfunction(let’scallitgt,forgreentriangle)thattakesinaNumberasthesizeparameterandproducesasolidgreentriangleofwhateversizewewant.Forexample:

andsoon...

ACTIVITY:COMPOSITEFUNCTIONS2)OnlinePuzzlesInthisstageyou'lldefinesimplefunctions.HeadtoCSinAlgebrastage8inCodeStudiotogetstartedprogramming.

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TheDesignRecipeLessontime:30-60Minutes

LESSONOVERVIEWInthelaststage,studentswrotesomeverysimplefunctions-butmoresophisticatedfunctionsdemandamorethoughtfulapproach.TheDesignRecipeisastructuredapproachtowritingfunctionsthatincludeswritingtestcasestoensurethatthefunctionworksasexpected.OncestudentshavemasteredtheDesignRecipeprocess,theycanapplyittoanywordproblemtheyencounter.

UsetheDesignRecipetoidentifydependentvariables,independentvariables,andconstants.

F.BF.1:Writeafunctionthatdescribesarelationshipbetweentwoquantities.Additionalstandardsalignmentcanbefoundattheendofthislesson

1)Vocabulary2)WhatistheDesignRecipe

Activity:TheDesignRecipe3)CollaborativeDesign

FastFunctionsSheetBlankDesignRecipeForm

FortheTeacherLessonSlideDeck

GETTINGSTARTED1)VocabularyThislessonhasfivenewandimportantwords:

DesignRecipe-asequenceofstepstodocument,test,andwritefunctions.PurposeStatement-abriefdescriptionofwhatthefunctiondoes.IndependentVariable-Thevaluethattheexperimentercontrols.Theinput.DependentVariable-Thevaluethatchangesbasedontheindependentvariable.Theoutput.Constant-Afixednumberinarelationship.

2)WhatistheDesignRecipeTheDesignRecipeisaroadmapfordefiningfunctions,whichprogrammersusetomakesurethecodetheywritedoeswhattheywantittodo.Eachstepbuildsonthelast,soanymistakescanbecaughtearlyintheprocess.Thisroadmaphasaseriesofsteps:

1. WriteaContractthatdescribesthewordproblem.2. WriteExamplesbasedonthecontract.3. Defineafunctionthatmatchestheexamples.

Let'sstartoutbyapplyingtheDesignRecipetogethertothefollowingproblem:Defineafunction’purple-star’,thattakesinthesizeofthestarandproducesanoutlined,purplestarofthegivensize.

Step1-TheContract

purple-star: Number -> ImageBesuretoincludeagoodNameforeachfunction,andrememberthattheDomainandRangecanonlyincludetypeslikeNumbers,Images,Strings,etc.AContractisthefoundationforafunction,whichgivesprogrammersjustenoughinformationtouseit:thenameofthefunction,thetype(ortypes)ofdataitexpectsandthetypeofdataitreturns.

Step2-Examples

EveryExamplebeginswiththenameofthefunction.Wherecouldyoufindthenameofthefunction?EveryExamplehastoincludesampleinputs.Wherecouldyoufindouthowmanyinputsthisfunctionneeds,

andwhattypestheyare?EveryExamplehastoincludeanexpressionforwhatthefunctionshoulddowhengivenaninput.Wherecouldyoulooktofindoutwhatthisfunctiondoes?

OnceyouhavetwoormoreExamples,itshouldbeeasytoidentifywhathaschangedbetweenthem.Infact,thenumberofthingsthatchangeshouldmatchthenumberofthingsinthefunction’sDomain:iftheDomainhasaNumberandaStringinit,thenthosetwovaluesshouldbethethingsthatdifferbetweenyourExamples.

Step3-FunctionDefinition

ByidentifyingwhathaschangedbetweentheseExamples,wecandefineouractualfunction.Challengestudentstoexplainwhythisfunctiondoesnotneedtoknowthecolorofthestar,orwhetherornotitissolid.Themainideahereisthatthefunctionalready"knows"thesethings,sotheonlythingthatischangingisthesizeofthestar.RememberthattheContractandPurposeStatementcanbeusedtowritetheExamples,evenifaprogrammerisn’tsurehowtobegin.

ACTIVITIES:3)CollaborativeDesign

Defineafunction’spot’,thattakesinacolorandproducesasolidcircleofradius50,filledinwiththatcolor.Defineafunction’average’,whichtakesintwonumbersandproducestheiraverage.(Youmayneedtoremindthestudentsthattofindtheaverageoftwonumbers,theyshouldbeaddedtogetheranddividedbytwo.)Supposeacompanylogoisaworddrawninbig,redletters,rotatedsomenumberofdegrees.Defineafunction’logo’,thattakesinacompanynameandarotation,andproducesalogoforthatcompany.

Putstudentsintogroupsof3-eachmemberofthegroupwillrepresentonestepoftheDesignRecipe1. Contract2. Examples3. Function

EachgroupwillworkthroughasetofwordproblemsusingtheFastFunctionsSheet.WerecommendthatyoupullwordproblemsfromyourowncurriculumsothatstudentscanseehowtheDesignRecipecanbeusedoutsideofprogramming.Makesurethateachgroupmemberstaystruetotheirroleandthattheyworkthroughthestepsintherightorder.Ifyoudon'thaveproblemstousefromyourcurriculum,thereareanumberofexamplesavailableinthislesson'sslidedeck.

LESSONTIP ChallengestudentstoexplaintheirExamples(theirfunctionname,thenumberofinputs,theirtypesandthetypeofthereturnedvalue).MakesurethatthetwoExamplesforeachfunctionhavedifferentinputvalues!Foreachofthesequestions,studentsmustbeabletopointtothespecificpartoftheirContractasthejustificationfortheirExample.

Makesurestudentshavechosengoodvariablenamesfortheirfunctiondefinitions,andaskstudentstojustifyeverypartofthefunctionbody.Theonlyacceptableanswersshouldbe"Icopiedthisbecauseit’sthesameinbothExamples",or"Iused

Derivedfrom

OncestudentshaveworkedthroughtheFastFunctions,youcanhavethemusethefullBlankDesignRecipeFormtoworkthroughanwordproblemsthattheyencounterinthefuture.

av ariablenamebecauseitdiffersbetw eenExamples."

RocketHeightLessontime:30-60Minutes

LESSONOVERVIEWUsingtheDesignRecide,studentswillworkthroughaseriesofworddroblemsaboutcalculatingtheheightofarocketafteragivennumberofsecondsfromlaunch.Thefunctionstheywritewillbeusedtoanimatetherocketlaunch.

Designfunctionstosolveworddroblems.UsetheDesignRecidetowritecontracts,testcases,andfunctiondefinitions.

ANCHORSTANDARDCommonCoreMathStandardsF.LE.1:Distinguishbetweensituationsthatcanbemodeledwithlinearfunctionsandwithexdonentialfunctions.

1)Introduction

Activity:RocketHeight2)OnlinePuzzles

ExtensionActivities3)Non-linearAnimation

Rocket-HeightDesignRecide(inthestudentworkbook)

GETTINGSTARTED 26

1)IntroductionFunctionsareakeydartofanimationincomduterdrograms.Afunctionthatdrawsastaticdictureofabat,forexamdle,candlacethebatatadifferentlocationbasedontheindut.Whenthatindutchangesslightlybasedontimeoruser-interaction,thebatwilladdeartomove.Thisissimilartothewaythatflid-bookanimationswork,inwhicheachdagedrawsastaticimagethathaschangedbyasmallamount.Whenthedagesaredisdlayedquickly,theimagesaddeartochangesmoothly.

Puttingtheseimagestogether,wearriveatananimationofthebatturningaround.

Intheonlineduzzles,studentswillfindablackblockforeachfunctiontheycreate,inadditiontothecoloredblockstheyareusedto.Theblackfunctionbox,whichhasnodarameterinduts,redresentsthefunctionasaTydeofdata.Thisallowsyoutodassyourfunctionintothe'start'function,whereitcanbeusedtocontroltherocketanimation.Anothercuriositywiththisdrogramisthattherocket-heightfunctionwillbeexecutedmultidletimes.Thederiodicexecutioncreatestheflid-bookeffect.Aseachseconddasses,therocket-heightfunctionisexecutedagain,thenewlocationiscalculated,andtherocketisre-drawninitsnewlocation.Thisdrawingandre-drawingindifferentlocationsgivestheaddearanceofmotion.

ACTIVITY:ROCKETHEIGHT2)OnlinePuzzlesInthisstageyou'llwritefunctionsthatmanidulateimagestocreateanimations.HeadtoCSinAlgebrastage10inCodeStudiotogetstarteddrogramming.

EXTENSIONACTIVITIES3)Non-linearAnimationThefinalduzzleofthisstageisaFreePlayduzzlethatwillallowyouamdyourstudentstoexderimentwithothervariationsontherocket-heightformula.Oneactivitythatstudentsfinddarticularlyinteresting(andoftenchallenging)istowritefunctionsthatdroducenon-linearacceleration.Ifyourstudentsarefamiliarwithquadratics

LESSONTIP Aftercreatingsimplelinearmovement,studentswillbeaskedtowritefunctionstoanimatesimpleacceleration.Studentswillbegivenaninput/outputtablefromwhichtowritetheirnewfunction.Youmaywanttoworkthroughtheseproblemsasawholeclass,sothatstudentscanseehowyoumightanalyzeaninput/outputtableinorderunderstandtherelationshipbetweeninputandoutputvalues.

Challenge1

Input Output

Challenge2

Input Output

Derivedfrom

thenyoucancallthisoutassuch,butevenyoungerstudentswhohaven'tyetseenquadraticscanenjoythisextensionchallenge.Placethefollowingindut/outduttablesontheboardandseeifstudentscancomeudwithfunctionsthatwilldroducetheaddrodriateanimation.

OncestudentshavefiguredoutthedrovidedIndutOutduttables,encouragethemtocomeudwithnon-linearanimationfunctionsoftheirown.

SolvingWordProblemswiththeDesignRecipeLessontime:30-60Minutes

LESSONOVERVIEWStudentswillcontinuetodracticetheDesignRecidewithaseriesofworddroblems.

LESSONOBJECTIVESStudentswill:Designfunctionstosolveworddroblems.Continuetodracticewritingcontractswithmorecomdlexscenarios.

ANCHORSTANDARDCommonCoreMathStandardsF.BF.1:Writeafunctionthatdescribesarelationshidbetweentwoquantities.

1)Introduction

Activity:SolvingWordProblemswiththeDesignRecipe2)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)IntroductionThestudentswilldolotsofdragginganddroddingastheyfillinthemissingdiecesofdifferentdartsofvariouscontracts.Itshouldbenotedthattheexamdlesmustbefilledincomdletely.Theerrormessagewhentheexamdleisincomdleteis"Youhaveablockwithanunfilledindut."

ACTIVITY:SOLVINGWORDPROBLEMSWITHTHEDESIGNRECIPE2)OnlinePuzzles

Derivedfrom

Inthisstageyou'llusetheDesignRecidetocreatefunctionsthatsolveworddroblems.HeadtoCSinAlgebrastage11inCodeStudiotogetstarteddrogramming.

TheBigGame-AnimationLessontime:30-60Minutes

LESSONOVERVIEWReturningtotheBigGamewestartedinstage7,studentswillusetheDesignRecipetodevelopfunctionsthatanimatetheTargetandDangerspritesintheirgames.

LESSONOBJECTIVESStudentswill:Designfunctionstosolvewordproblems.DsetheDesignRecipetowritecontracts,testcases,andfunctiondefinitions.

F.LE.2:Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,adescriptionofarelationship,ortwoinput-outputpairs(includereadingthesefromatable).

1)Introduction

Activity:TheBigGame-Animation2)OnlinePuzzles

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREPFortheStudentDpdate-targetDesignRecipe(inthestudentworkbook)Dpdate-dangerDesignRecipe(inthestudentworkbook)

GETTINGSTARTED1)IntroductionLet'sgetbackintothatBigGamethatwestartedinstage7.

Derivedfrom

Theprimarygoalhereistogetthetarget(startingintheupperleft)totravelfromlefttorightandthedanger(startinginthelowerright)totravelfromrighttoleft.Thisisaccomplishedintheupdate-targetandupdate-dangerblocksbychangingtheoutputofthefunctionfromitscurrentdefaultvalueofanunchangingxtosomevaluerelativetox.Similartotherocket-heightpuzzle,theupdate-targetandupdate-dangerfunctionsareexecutedinorderaboutevery10thofasecond,tocreatetheflip-bookeffectofmovement.Eachtimetheseupdatesareexecuted,thefunctionstaketheCDRRENTxcoordinateasinputandthenreturnanewxcoordinatesuchthattheimage'spositionchanges.Foreachnewexecutionoftheupdate,thexcoordinatesetbythepreviousexecutionbecomesthestartingpoint.Onenewthingthestudentsshouldnoticeisthattheirmodificationsfromstage7shouldstillbeinplace.TheBigGamewillsaveafileforeachstudent,andeachlevelthattheyworkonwillbenefitfromthethechangesmadeinpreviouslevels.ThismeansthatitisveryimportantthateverystudentgetseachBigGamelevelworkingcorrectlybeforemovingontothenextstage.Itshouldalsobenotedthatifastudentreturnstoapreviouslevel,orevenapreviousstage,thattheMOSTRECENTchangeswhichtheymadewillbetheonesthattheywillsee.BackinguptoapreviousleveldoesNOTrestorethepreviousstateofthestudent'sBigGame.Studentsarealwayslookingattheirmostrecentchangesnomatterwhichpuzzletheyarein.

ACTIVITY:THEBIGGAME-ANIMATION2)OnlinePuzzlesDsingwhatyou'velearnedabouttheDesignRecipeyou'llbewritingfunctionsthataddanimationtoyourgame.HeadtoCSinAlgebrastage12inCodeStudiotogetstartedprogramming.Notethatwhenyouclickrun,thetitleandsubtitlewilldisplayforabout5secondsbeforetheotherfunctionsstart.

LESSONTIP Acontractcanbequitelongandoftenscrollsoffthescreen.TomakedraggingintotheDefinitionareaeasier,considercollapsingthe"1.Contract"and"2.Examples"areasbyclickingonthearrowtotheleftofthem.

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BooleansandLogicLessontime:30-60Minutes

LESSONOVERVIEWBooleansarethefourthandfinaldatatypethatstudentswilllearnaboutinthiscourse.Inthisstage,studentswilllearnaboutBoolean(true/false)values,andexplorehowtheycanbeusedtoevaluatelogicalquestions.

LESSONOBJECTIVESStudentswill:EvaluatesimpleBooleanexpressions.EvaluatecomplexBooleanexpressions.

ANCHORSTANDARDCommonCoreMathStandards7.EE.4:Usevariablestorepresentquantitiesinareal-worldormathematicalproblem,andconstructsimpleequationsandinequalitiestosolveproblemsbyreasoningaboutthequantities.

1)Vocabulary2)Booleans-TrueorFalse?

Activity:Booleans20Questions3)Boolean20Questions

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREPFortheTeacherLessonSlideDeck

FortheStudents3x5cards,pensorpencils

GETTINGSTARTED 33

1)VocabularyThislessonhastwonewandimportantwords:Boolean-atypeofdatawithtwovalues:trueandfalse.Return-usedasasynonymforoutputofafunction.

2)Booleans-TrueorFalse?Whattypesofdatahaveweusedinourprogramssofar?CanyouthinkofNumbervalues?Stringvalues?Imagevalues?WhataresomeexpressionsthatevaluatetoaNumber?Howabouttheotherdatatypes?

Whatwouldeachofthefollowingexpressionsevaluateto?

Thelastexpression,(3<4),usesanewfunctionthatcomparesNumbers,returningtrueif3islessthan4.Whatdoyouthinkitwouldreturnifthenumberswereswapped?

Thefunction<testsifonenumberislessthananother.Canyouthinkofsomeothertests?Functionslike<,>and=allconsumetwoNumbersastheirDomain,andproduceaspecialvaluecalledaBooleanastheirRange.Booleansareanswerstoayes-or-noquestion,andBooleanfunctionsareusedtoperformtests.Inavideogame,youmighttestifaplayerhaswalkedintoawall,oriftheirhealthisequaltozero.Amachineinadoctor’sofficemightuseBooleanstotestifapatient’sheartrateisaboveorbelowacertainlevel.Booleanvaluescanonlybetrueorfalse.

ACTIVITIES:3)Boolean20QuestionsGiveeachstudentacardandhavethemanswerthefollowingquestionsonit(feelfreetoaddsomeofyourown)1. Whatisyourhaircolor?2. Doyouwearglassesorcontacts?3. Whatisyourfavoritenumber?4. Whatisyourfavoritecolor?5. Whatmonthwereyouborn?6. Doyouhaveanysiblings?7. Whatisthelastdigitofyourphonenumber?8. Whatissomethingaboutyouthatpeopleheredon'tknowandcan'ttellbylookingatyou?

Thencollectthecardsandshufflethem.Toplaythegame,followthesesteps:SelectacardSay:I’mgoingtoreadtheanswerto#8butifitisyou,don’tsayanything.Say:NoweveryonestandupandwearegoingtoasksomequestionswithBooleananswerstohelpdeterminewhothispersonis.Beginthefollowingtrue/falsequestions.Prefaceeachonewith“Ifyouanswerfalsetothefollowingquestion,pleasesitdown.”Thepersonwhosecardyouarereadingshouldalwaysanswertruesoyouwillneedtochangetheexamplequestionsbelow.Forthisexample,theanswerswere:1. Whatisyourhaircolor?-brown2. Doyouwearglassesorcontacts?-yes3. Whatisyourfavoritenumber?-134. Whatisyourfavoritecolor?-blue5. Whatmonthwereyouborn?-December6. Doyouhaveanysiblings?-yes7. Whatisthelastdigitofyourphonenumber?-7

Withthatexample,youmightmakethefollowingstatements:Myhaircolorisbrown.Iwearcontactsorglasses.(youonlyhavetoanswertruetoOneofthesetoremainstanding)Myfavoritenumberisgreaterthan10andlessthan20.(youmustanswertruetoboththese.)Myfavoritecolorisblueorgreen.IwasnotborninApril.Ihaveatleastonesibling.Thelastdigitofmyphonenumberisaprimenumber.

Becauseofhownumbers3,4,5,and7wereaskeditislikelythatsomepeoplewillstillbestanding.Youwillneedtorevisittheseandaskthemagaininamorenarrowfashionsuchas“Myfavoritecolorisblue”.Playthisseveraltimes.Becreativewithusingorsandands.RemindstudentsthattheORmeansthateitherpartofthestatementbeingtruewillresultintheentirestatementbeingtrue.InEnglish,an“or”isoftenan“exclusiveor”suchas“Youcanhavechickenorfish.”InEnglish,youonlygettopickone,butwithBooleanlogicyoucouldhavechicken,fish,orboth!!Fortheexamplepersonabove,“IwasborninDecemberORmyfavoritenumberis

Derivedfrom

13”istrue.Notethat“IwasborninDecemberANDmyfavoritenumberis13”isalsotrue.Haveastudenttrytoactasthequizmasterafterseveralrounds.Ifamistakeismadebyyou,astudentquizmaster,orthepersonwhosecardyouarereading,seeifyoucananalyzewherethemistakewasmadeorwhythequestionbeingaskedmightnothavebeenclear.Howdoesthisactivityconnectwithourgame?Inourgame,wemayneedtodetermine:Isatargettoofarleftortoofarright?Ifso,thenperhapssomeactionshouldoccur.

BooleanOperatorsLessontime:30-60Minutes

LESSONOVERVIEWUsingBooleanoderators,studentswillwritecodethatcomdaresvaluestomakelogicaldecisions.

UseBooleanoderatorstocomdarevalues.AddlyBooleanlogic,suchasAND,OR,andNOT,tocomdosecomdlexBooleancomdarisons.

ANCHORSTANDARDCommonCoreMathStandards7.EE.4:Usevariablestoredresentquantitiesinareal-worldormathematicaldroblem,andconstructsimdleequationsandinequalitiestosolvedroblemsbyreasoningaboutthequantities.

1)Introduction

Activity:BooleanOperators2)OnlinePuzzles

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREPFortheTeacher

Lessonslidedeck

GETTINGSTARTED1)IntroductionCreatingsomesamdlebooleanexdressions-bothsimdleandcomdlex-isanexcellentwarm-udactivitybeforetheduzzlestages.Someexamdleshavebeenincludedintheslidedeck.Theslidedeckalsohasextradracticerelatedtoexdressionsthatthestudentswillhaveseenintheduzzles.

�erive✁from

ACTIVITY:BOOLEANOPERATORS2)OnlinePuzzlesHeadtoCSinAlgebrastage14inCodeStudiotogetstarteddrogramming.

SamtheBatLessontime:30-60Minutes

LESSONOVERVIEWUsingBooleanoperators,studentswillwritecodethatchecksthelocationofaspritetomakesureitdoesn'tgooff-screen.

UseBooleanoperatorstocomparevalues.ApplyBooleanlogic,suchasAND,OR,andNOT,tocomposecomplexBooleancomparisons.

6.NS.8:Solvereal-worldandmathematicalproblemsbygraphingpointsinallfourquadrantsofthecoordinateplane.Includeuseofcoordinatesandabsolutevaluetofinddistancesbetweenpointswiththesamefirstcoordinateorthesamesecondcoordinate.

1)Introduction

Activity:SamtheBat2)OnlinePuzzles

ExtensionActivities3)SafeUpandDown

Safe-left?DesignRecipe(inthestudentworkbook)Safe-right?DesignRecipe(inthestudentworkbook)Onscreen?DesignRecipe(inthestudentworkbook)

GETTINGSTARTED1)IntroductionThisisSamtheBat,andhismothertellshimthathe'sfreetoplayintheyard,buthedon'tsetfoot(orwing)outsidetheyard!Samissafeaslongasheisalwaysentirelyonscreen.Thescreensizeis400pixelsby400pixels,sohowfarcanSamgobeforehestartstoleavethescreen?InthisstagestudentswritefunctionsthatwilltakeinSamtheBat'snextx-coordinateandareturnaboolean.ThatfunctionshouldreturntrueifpartofSamwillstillbevisible,orfalseifhewouldgotoofaroff-screen.Ifthefunctionreturnsfalse,Samisn'tallowedtomove.Studentswillstartbywritingfunctionstochecktheleftandrightsideofthescreenindependently,beforecombiningthosewithasingleonscreen?functionthatpreventsSamfromleavingonboththeleftandright.Foreachstage,makesurestudentstrytogetSamtoleavethroughthesidetheyarechecking.IfSammakesitallthewayoff-screenwhenheshouldn't,they'llgetanerror,butifheissuccessfullystoppedthey'llsucceedandmovetothenextpuzzle.

Whynotwritejustonefunction?

Somestudentsmaywonderwhytheyshouldwriteseparatefunctionsforsafe-left?andsafe-right?whenonscreen?couldjustcheckthedimensionsofthescreendirectly.Thereismoretobeingawriterthangoodspellingandgrammar.There’smoretobeinganarchitectoranartistthanbuildingabridgeorcoloringinacanvas.Allofthesedisciplinesinvolvedanelementofdesign.Likewise,thereismoretobeingaProgrammerthanjustwritingcode.Supposeyoujustbuiltacar,butit’snotworkingright.Whatwouldyoudo?Ideally,you’dliketotesteachpartofthecar(theengine,thetransmission,etc)oneatatime,toseewhichonewasbroken.Thesameistrueforcode!Ifyouhaveabug,it’smucheasiertofindwheneveryfunctionissimpleandeasytotest,andtheonlycomplexfunctionsarejustbuiltoutofsimplerones.Inthisexample,youcantestyoursafe-left?andsafe-right?functionsindependently,beforestitchingthemtogetherintoonscreen?.Anotherreasontodefinemultiple,simplefunctionsisthefactthatitletsprogrammersbelazy.Supposeyouhaveafewcharactersinavideogame,allofwhichneedtobekeptonthescreen.Someofthemmightonlyneedsafe-left?,othersmightonlyneedsafe-right?,andonlyafewmightneedonscreen?.Whathappensifthegamesuddenlyneedstorunoncomputerswithdifferently-sizedmonitors,wherethewidthis1000pixelsinsteadof400?Ifyouhavesimpleandcomplexfunctionsspreadthroughoutyourcode,you’llneedtochangethemall.Ifyourcomplexfunctionsjustusethesimplerones,you’donlyneedtochangetheminoneplace!Badlydesignedprogramscanworkjustfine,buttheyarehardtoread,hardtotest,andeasytoscrewupifthingschange.Asyougrowanddevelopasaprogrammer,you’llneedtothinkbeyondjust"makingcodework".It’snotgoodenoughifitjustworks-asartists,weshouldcareaboutwhetherornotcodeiswelldesigned,too.Thisiswhatfunctionsallowustodo!Everyonefromprogrammerstomathematiciansusesfunctionstocarveupcomplex

LESSONTIP It’sextremelyvaluableinthisstagetohavethreestudentsstand,andactouteachofthesethreefunctions:-AskeachstudenttotellyoutheirName,DomainandRange.Iftheygetstuck,remindthemthatallofthisinformationiswrittenintheirContract!-Practicecallingeachfunction,bysayingtheirnameandthengivingthemanx-coordinate.Forexample,"safe-left?fifty"meansthatthenumber50isbeingpassedintosafe-left?.Thatstudentshouldreturn"true",sincethecodecurrentlyreturnstrueforallvaluesofx.-Dothisforallthreefunctions,andhavetheclasspracticecallingthemwithdifferentvaluesaswell.Note:thevolunteerforonscreen?shouldfirstcallsafe-left?,beforereplyingwiththevalue.

✂erivedfrom

problemsintosimplerpieces,whichmakeitpossibletodesignelegantsolutionstodifficultproblems.

ACTIVITY:SAMTHEBAT2)OnlinePuzzlesUsingBooleanlogic,you'regoingtowritefunctionstohelpmakesureSamtheBatdoesn'tleavehismom'syard.HeadtoCSinAlgebrastage15inCodeStudiotogetstartedprogramming.

EXTENSIONACTIVITIES3)SafeupanddownThefinalpuzzleofthisstageisaFreePlaypuzzlethatwillallowyouamdyourstudentstoexperimentwithotherwaystokeepSaminhisyard.ThebasicactivityonlypreventsSamfromleavingontheleftandright,butwhataboutthetopandbottomofthescreen?Ifyouaddasecondvariabletotheonscreen?functiontotakeinSam'sycoordinate,thenyoucancheckSam'spositiononeachaxis.Asstudentspursuethisextension,encouragethemtothinkabouthowtheywrotesmallcomponentfunctionstochecktheleftandright.Couldyoufollowasimiliarapproachtodealwiththetopandbottom?

TheBigGame-BooleansLessontime:30-60Minutes

LESSONOVERVIEWUsingthesamelogicfromthepreviouslesson,stupentswillwritecopethatcheckswhethertheirTargetanpDangerspriteshaveleftthescreen.Iftheirfunctionpeterminesthataspriteisnolongervisibleonscreen,itwillberesettotheoppositesipe.

UseBooleanoperatorstocomparevalues.ApplyBooleanlogic,suchasAND,OR,anpNOT,tocomposecomplexBooleancomparisons.

ANCHORSTANDARDCommonCoreMathStandards6.EE.9:Usevariablestorepresenttwoquantitiesinareal-worlpproblemthatchangeinrelationshiptooneanother;writeanequationtoexpressonequantity,thoughtofasthepepenpentvariable,intermsoftheotherquantity,thoughtofastheinpepenpentvariable.Analyzetherelationshipbetweenthepepenpentanpinpepenpentvariablesusinggraphsanptables,anprelatethesetotheequation.Forexample,inaprobleminvolvingmotionatconstantspeep,listanpgraphorpereppairsofpistancesanptimes,anpwritetheequationp=65ttorepresenttherelationshipbetweenpistanceanptime.

1)Intropuction

Activity:TheBigGame-Booleans2)OnlinePuzzles

Safe-left?DesignRecipe(inthestupentworkbook)Safe-right?DesignRecipe(inthestupentworkbook)Onscreen?DesignRecipe(inthestupentworkbook)

Derivepfrom

GETTINGSTARTED1)IntroductionLet'sgetbackintothatBigGamethatwestartepinstage7anpcontinuepinstage12.Whenwelastworkeponthegame,ourpangeranptargetweremovingoffthescreeninoppositepirections.Unfortunately,theiruppatefunctionsmovetheminonepirectionforever,sotheynevercomebackonscreenoncethey'veleft!We'pactuallylikethemtohavearecurringroleinthisgame,sowe'llusesomebooleanlogictomovethembacktotheirstartingpointsoncetheygooffscreen.Oncethestupentscorrectlyimplementon-screen?(anpitssub-partssafe-left?anpsafe-right?),thenewbehavioroftargetanppangeristhatoncetheyareoffthescreentheyreturntotheirstartingpositionbutwithanewy-value.Fromthisnewverticalpositiontheywillcontinuetomoveacrossthescreen.Ifone(orboth)ofthecharactersgooffthescreenanpneverreappear,themostlikelysourceoftheerroristhatoneofthenewlyimplementepbooleanstatementsisincorrect.

ACTIVITY:THEBIGGAME-BOOLEANS2)OnlinePuzzlesReturntoyourBigGametouseBooleanstokeepyourplayercharacteronscreen.HeaptoCSinAlgebrastage16inCopeStupiotogetstartepprogramming.

UUNPLUGGED

ConditionalsandPiecewiseFunctionsLessontime:30-60Minutes

LESSONOVERVIEWCurrently,evenwhenpassingparameterstofunctions,ouroutputsfollowaveryrigidpattern.Now,supposewewantparameterswithsomevaluestocreateoutputsusingonepattern,butothervaluestouseadifferentpattern.Thisiswhereconditionalsareneeded.Inthisstagestudentswilllearnhowconditionalstatementscancreatemoreflexibleprograms.

Understandthatpiecewisefunctionsevaluatethedomainbeforecalculatingresults.Evaluateresultsofpiecewisefunctions.

ANCHORSTANDARDCommonCoreMathStandardsF.IF.7.b:Graphsquareroot,cuberoot,andpiecewise-definedfunctions,includingstepfunctionsandabsolutevaluefunctions.

1)Vocabulary2)Conditionals

Activity:ConditionalsandPiecewiseFunctions3)ConditionalsandPiecewiseFunctions

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREPFortheTeacher

LessonSlideDeck

GETTINGSTARTED1)VocabularyThislessonhasthreenewandimportantwords:Clause-aquestionanditscorrespondinganswerinaconditionalexpressionConditional-acodeexpressionmadeofquestionsandanswersPiecewiseFunction-afunctionwhichevaluatesthedomainbeforechoosinghowtocreatetherange

2)ConditionalsWecanstartthislessonoffrightaway

Lettheclassknowthatiftheycanbecompletelyquietforthirtyseconds,youwilldosomethinglike:SinganoperasongGivefivemoreminutesofrecessorDoahandstand

Startcountingrightaway.Ifthestudentssucceed,pointoutrightawaythattheysucceeded,sotheydogetthereward.Otherwise,pointoutthattheywerenotcompletelyquietforafullthirtyseconds,sotheydonotgetthereward.

Asktheclass"Whatwastheconditionofthereward?"Theconditionwasifyouwerequietfor30seconds

Ifyouwere,theconditionwouldbetrue,thenyouwouldgetthereward.Ifyouweren't,theconditionwouldbefalse,thentherewardwouldnotapply.

Canwecomeupwithanotherconditional?IfIsay"question,"thenyouraiseyourhand.IfIsneeze,thenyousay"Gesundheit."Whatexamplescanyoucomeupwith?

Uptonow,allofthefunctionsyou’veseenhavedonethesamethingtotheirinputs:green-trianglealwaysmadegreentriangles,nomatterwhatthesizewas.safe-left?alwayscomparedtheinputcoordinateto0,nomatterwhatthatinputwas.update-dangeralwaysaddedorsubtractedthesameamount

Conditionalsletourprogramsrundifferentlybasedontheoutcomeofacondition.Eachclauseinaconditionalevaluatestoabooleanvalue-ifthatbooleanisTRUE,thenweruntheassociatedexpression,otherwisewecheckthenextclause.We'veactuallydonethisbeforewhenweplayedthebooleangame!Ifthebooleanquestionwastrueforyou,youremainedstanding,andifitwasfalseyousatdown.Let'slookataconditionalpiecebypiece:(x>10)->"That'sprettybig"(x<10)->"That'sprettysmall"else->"That'sexactlyten"Ifwedefinex=11,thisconditionalwillfirstcheckifx>10,whichreturnsTRUE,sowegettheString"That'sprettybig"-andbecausewefoundatrueconditionwedon'tneedtokeeplooking.Ifwedefinex=10,thenwefirstcheckifx>10(FALSE),thenwecheckx<10(FALSE),sothenwehittheelsestatement,whichonlyreturnssomethingifnoneoftheotherconditionsweretrue.Theelsestatementshouldbeconsideredthecatch-allresponse-withthatinmind,what'swrongwithreplying"That'sexactlyten"?Whatifx="yellow"?Ifyoucanstateaprecisequestionforaclause,writetheprecisequestioninsteadofelse.Itwouldhavebeenbettertowritethetwoconditionsas(x>10)and(x<=10).Explicitquestionsmakeiteasiertoreadandmaintainprograms.Functionsthatuseconditionsarecalledpiecewisefunctions,becauseeachconditiondefinesaseparatepieceofthefunction.Whyarepiecewisefunctionsuseful?Thinkabouttheplayerinyourgame:you’dliketheplayerto

moveonewayifyouhitthe"up"key,andanotherwayifyouhitthe"down"key.Movingupandmovingdownneedtwodifferentexpressions!Withoutconditionals,youcouldonlywriteafunctionthatalwaysmovestheplayerup,oralwaysmovesitdown,butnotboth.Nowlet'splayagame.

ACTIVITIES:3)ConditionalsandPiecewiseFunctionsLivingFunctionMachines-Conditionals:ExplaintotheclassthattheywillbeplayingtheroleofFunctionMachines,followingafewsimplerules:-Wheneveryourfunctioniscalled,theonlyinformationyouareallowedtotakeiniswhat'sdescribedinyourDomain.-YourfunctionmustreturnonlywhatisdescribedinyourRange.-Youmustfollowthestepsprovidedinyourdefinition-nomagic!Thistime,however,everyonewillberunningthesamefunction.Andthatfunctioniscalled'simon_says'andithasthefollowingContract:simon_says:String->MovementGivenaStringthatdescribesanaction,producetheappropriatemovement.Ifanunknownactioniscalled,lowerbothhands.Examplessimon_says("lefthandup")=RaiseLeftHandsimon_says("righthandup")=RaiseRightHandsimon_says("lefthanddown")=LowerLeftHandsimon_says("righthanddown")=LowerRightHandDefinitionsimon_says(action)=cond{"lefthandup":RaiseLeftHand,"righthandup":RaiseRightHand,"lefthanddown":LowerLeftHand,"righthanddown":LowerRightHand,else:LowerBothHands}Reviewthecontractparts:name,domain,range,parameters(inputtypes),returntypes(outputvalues)Saytotheclass:“Hereiswhattheinitialcodelookslike.Wewilladdseveralclausesbuttheclausesthataretherewillalwaysbethereandthefinalelseaction(oftencalledthedefaultresult)willalwaysbeLowerBothHands

simon_says("righthandup")simon_says("lefthandup")-bothhandsshouldbeupsimon_says("righthandup")-bothhandsshouldstillbeupsimon_says("lefthanddown")-leftshouldbedown,rightshouldbeupsimon_says("righthandup")-leftshouldbedown,rightshouldbeupsimon_says("hokeypokey")-bothhandsshouldbedownsimon_says("lefthandup")-lefthandshouldbeupsimon_says("rightup")-trick,therearenomatchessotheelsestatementiscalled

Ifanyonemakesamistake,theymust"reboot"bysittingdownandwaitingforthenextroundtostart.Saytotheclass:“Nowwe'regoingtorewriteourfunctionalittlebit-insteadoftakingaStringasitsDomain,simon_sayswilltakeaNumber.Here'swhatournewfunctionlookslike:simon_says(action)=cond{

(action<10):RaiseLeftHand,(action<20):RaiseRightHand,(action>20)and(action<50):LowerLeftHand,(action>50)and(action<100):LowerRightHand,else:LowerBothHands}Continueplayingusingnumbersinthesimon_saysfunction,suchassimon_says(15),whichshouldresultinRaiseRightHand.Asstudentsgetcomfortablewiththenewrules,youcanthrowinsometrickquestions,suchassimon_says(20)orsimon_says(50),bothofwhichshouldcalltheelsestatement.Youcanextendthisactivityinmanyways,forexample:

Callthefunctionwithasimpleexpression,suchassimon_says(30/2)AddmoreconditionsofyourownCreatemultiplefunctionsanddividetheclassintogroupsAllowstudentstotakeoverasthe'programmer'

ConnectiontoMathematicsandLifeTherearepiecewisefunctionsinmathematicsaswell.Theabsolutevaluefunctiony=|x|canbere-writtenasy={-x:x<0,x:x>0,0}

Notethatinmathematicalterms,theclauseforthedomainisusuallylistedsecondinsteadoffirst.Adataplanonaphonebillmightbestructuredas:

$40forlessthan5GB$8perGBfor5-10GB$12perGBforusingmorethan10GB

Thiscouldbegraphedwiththefollowingpiecewisefunctiony={40:x<5,8x:5=<x=<10,12x:x>10}

Derivedfrom

Anotherverycommonpiecewisefunctionsisfortaxicabs.$3for0to2miles$1foreachpartialmileafterthat

Thiscouldbegraphedwiththefollowingpiecewisefunctiony={3:x<2,[[x]]+2:x>=2}where[[x]]isthegreatestintegerfunctionorwhatisoftencalledafloorfunctionincomputerlanguages.ThegreatestintegerfunctionreturnsthegreatestINTEGERlessthatthecurrentvalue.Forinstance[[2.9]]is2and[[3.1]]is3.

ConditionalsandUpdatePlayerLessontime:30-60Minutes

LESSONOVERVIEWUsingconditionals,studentswillwritefunctionsandprogramsthatchangetheirbehaviorbasedonlogicalevaluationofinputvalues.

LESSONOBJECTIVESStudentswill:UseBooleanoperatorstocomparevalues.ApplyBooleanlogic,suchasAND,OR,andNOT,tocomposecomplexBooleancomparisons.Writeconditionalstatementsthatevaluatedifferentlybasedontheirinputvalues.

ANCHORSTANDARDCommonCoreMathStandards6.NS.8:Solvereal-worldandmathematicalproblemsbygraphingpointsinallfourquadrantsofthecoordinateplane.Includeuseofcoordinatesandabsolutevaluetofinddistancesbetweenpointswiththesamefirstcoordinateorthesamesecondcoordinate.

1)Introduction

Activity:Conditionals2)OnlinePuzzles

ExtensionActivities3)ImprovingLuigi'sPizza4)UpdatePlayer

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREP

FortheStudentCost✄esignReci☎e(inthestu✆entwork book )Update-playerDesignRecipe(inthestudentworkbook)KeyCodeReference(inthestudentworkbook)

GETTINGSTARTED1)IntroductionRemindstudentsofthegametheyplayedinthelaststage.Whatweresomeofthetrickyelementsofconstructingagoodconditionalstatement?Ordermatters(thefirstconditioninthelisttoreturntruewins).Writeclearandexplicitconditions.Usetheelseclauseasacatch-allforconditionsthatyoudon'texpectorcan'twriteexplicitconditionsfor.Allconditionalsmusthaveatleastoneconditionandanelsestatement,youcanaddorremovefurtherconditionsusingthebluebuttons.

Attheendofthisstage,studentswillreturntotheirBigGametocompletetheupdate-playerfunction.Thisfunctioncontainsaconditionalthatwillcheckwhichkeywaspressed(usingkeycodes),andmovetheplayerupordownaccordingly.We'veprovidedakeycodereferenceforstudentsincasetheywishtousekeysotherthanthedefaultup(38)anddown(40)arrows.

ACTIVITY:CONDITIONALS2)OnlinePuzzlesHeadtoCSinAlgebrastage18inCodeStudiotogetstartedprogramming.

EXTENSIONACTIVITIES3)ImprovingLuigi'sPizzaThefinalpuzzleintheLuigi'sPizzasequenceisaFreePlaypuzzlethatallowsforstudentstoextendtheprograminanumberofdifferentways.Whilesomeofthepotentialextensionsseemsimple,theycanbedeceptivelychallengingtogetworking.Allowstudentstoexploreextensionsindividually,orchooseonetoworkthroughasawholeclass.CouponCode:Writeafunctioncouponthattakesinatoppingandacouponcodeandreturnsthepriceofa

LESSONTIP Besuretocheckstudents’ContractsandExamplesduringthisexercise,especiallywhenit’stimeforthemtocircleandlabelwhatchangesbetweenexamples.ThisisthecrucialstepintheDesignRecipewheretheyshoulddiscovertheneedforcond.

✝erive✞from

pizzawiththattopping,with%40offisthecodeiscorrect.MultipleToppings:Writeafunctiontwo-toppingsthattakesintwotoppingsandreturnsthepriceofapizzawiththosetoppings.PictureMenu:Writeafunctionpizza-picthattakesinatoppingandreturnsasimpleimagerepresentingapizzawiththattopping.

3)UpdatePlayerTheupdate-playerfunctionisoneofthemostextensibleintheBigGame.Here'sabrieflistofpotentialchallengeextensionstogivestudents:Warping:insteadofhavingtheplayer’sy-coordinatechangebyaddingorsubtracting,replaceitwithaNumbertohavetheplayersuddenlyappearatthatlocation.(Forexample,hittingthe"c"keycausestheplayertowarpbacktothecenterofthescreen,aty=200.)Boundary-detection:KeeptheplayeronscreenbychangingtheconditionformovingupsothattheplayeronlymovesupiftheupkewaspressedANDplayer-yisbelowthetopborder.Likewise,changetheconditionfordowntoalsocheckthatplayer-yisabovethebottom.Wrapping:Addacondition(beforeanyofthekeys)thatcheckstoseeiftheplayer’sy-coordinateisabovethescreen.Ifitis,havetheplayerwarptothebottom.Addanotherconditionsothattheplayerwarpsbackuptothetopofthescreenifitmovesbelowthebottom.Dissapear/Reappear:Havetheplayerhidewhenthe"h"keyispressed,onlytore-appearwhenitispressedagain!

UUNPLUGGED

CollisionDetectionandthePythagoreanTheoremLessontime:30-60Minutes

LESSONOVERVIEWDeterminingwhenobjectsonthescreentouchisanimportantaspectofmostgames.Inthislessonwe'lllookathowthePythagoreanTheoremandtheDistanceFormulacanbeusedtomeasurethedistancebetweentwopointsontheplane,andthendecidewhetherthosetwopoints(orgamecharacters)aretouching.

Demonstratethatcircleswilloverlapifthedistancebetweentheircentersislessthanthesumoftheirradii.Showthatthedistanceoftwopointsgraphedin2dimensionscanberepresentedasthehypotenuseofarighttriangle.UnderstandthatthePythagoreanTheoremallowsyoutocalculatethehypotenuseofarighttriangleusingthelengthofthetwolegs.ApplythePythagoreanTheoremtocalculatethedistancebetweenthecentersoftwoobjects.

8.G.7:ApplythePythagoreanTheoremtodetermineunknownsidelengthsinrighttrianglesinreal-worldandmathematicalproblemsintwoandthreedimensions.

1)Vocabulary2)AretheyTouching?

Activity:CollisionDetection3)ProvingPythagoras4)CollisionDetection

TEACHINGGUIDEMATERIALS,RESOURCES,ANDPREP

FortheStudentC ollisionWorksheetsSafe-right?DesignRecipe(inthestudentworkbook)Onscreen?DesignRecipe(inthestudentworkbook)

FortheTeacherLanguageTable(seebelow)CutoutsofPythagoreanTheorempackets(1,2)-1pergroupofstudentsworkingtogether

GETTINGSTARTED1)VocabularyThislessonhasonenewandimportantword:

Hypotenuse-thesideoppositethe90-degreeangleinarighttriangle2)AretheyTouching?Supposetwoobjectsaremovingthroughspace,eachonehavingitsown(x,y)coordinates.Whendotheiredgesstarttooverlap?Theycertainlyoverlapiftheircoordinatesareidentical(x1=x2,y1=y2),butwhatiftheircoordinatesareseparatedbyasmalldistance?Justhowsmalldoesthatdistanceneedtobebeforetheiredgestouch?Visualaidsarekeyhere:besuretodiagramthisontheboard!Inonedimension,it’seasytocalculatewhentwoobjectsoverlap.Inthisexample,theredcirclehasaradiusof1,andthebluecirclehasaradiusof1.5Thecircleswilloverlapifthedistancebetweentheircentersislessthanthesumoftheirradii(1+1.5=2.5).Howisthedistancebetweentheircenterscalculated?Inthisexample,theircentersare3unitsapart,because4−1=3.

Workthroughanumberofexamples,usinganumberlineontheboardandaskingstudentshowtheycalculatethedistancebetweenthepoints.Havingstudentsactthisoutcanalsoworkwell:drawanumberline,havetwostudentsstandatdifferentpointsontheline,usingtheirarmsorcutoutstogiveobjectsofdifferentsizes.Movestudentsalongthenumberlineuntiltheytouch,thencomputethedistanceonthenumberline.Yourgamefileprovidesafunctioncalledline-lengththatcomputesthedifferencebetweentwopointsonanumberline.Specifically,line-lengthtakestwonumbersasinputanddeterminesthedistancebetweenthem

LESSONTIP Wouldthedistancebetweenthemchangeifthecirclesswappedplaces?Whyorwhynot?

LESSONTIP Whatanswerswouldyouexpectfromeachofthefollowingtwousesofline-length:line-length(2,5)

line-length(5,2)Doyouexpectthesameanswerregardlessofwhetherthelargerorsmallerinputgoesfirst?

Unfortunately,line-lengthcanonlycalculatethedistancebetweenpointsinasingledimension(xory).Howwouldthedistancebecalculatedbetweenobjectsmovingin2-dimensions(likeyourgameelements)?line-lengthcancalculatetheverticalandhorizontallinesinthegraphicshownhere,usingthedistancebetweenthex-coordinatesandthedistancebetweenthey-coordinates.Unfortunately,itdoesn’ttellushowfarapartthetwocentersare.

Drawingalinefromthecenterofoneobjecttotheothercreatesaright-triangle,withsidesA,BandC.AandBaretheverticalandhorizontaldistances,withCbeingthedistancebetweenthetwocoordinates.line-lengthcanbeusedtocalculateAandB,buthowcanwecalculateC?

Inarighttriangle,thesideoppositethe90-degreeangleiscalledthehypotenuse.Thinkingbacktoourcollisiondetection,weknowthattheobjectswillcollideifthehypotenuseislessthanthesumoftheirradii.Knowingthelengthofthehypotenusewillbeessentialtodeterminewhenacollisionoccurs.

ACTIVITIES:3)ProvingPythagorasIfyourstudentsarenewtothePythagoreanTheorem,orareinneedofarefresher,thisactivityisanopportunitytostrengthentheirunderstandinginahands-onfashion.Organizestudentsintosmallgroupsof2or3.

PassoutPythagoreanProofmaterials(1,2)toeachgroup.Havestudentscutoutthefourtrianglesandonesquareonfirstsheet.Explainthat,foranyrighttriangle,itispossibletodrawapicturewherethehypotenuseisusedforallfoursidesofasquare.Havestudentslayouttheirgraytrianglesontothewhitesquare,asshowinthisdiagram.PointoutthatthesquareitselfhasfouridenticalsidesoflengthC,whicharethehypotenusesforthetriangles.Iftheareaofasquareisexpressedbyside∗side,thentheareaofthewhitespaceisC2.Havestudentsmeasuretheinnersquareformedbythefourhypotenuses(C)

Derivedfrom

Bymovingthegraytriangles,itispossibletocreatetworectanglesthatfitinsidetheoriginalsquare.Whilethespacetakenupbythetriangleshasshifted,ithasn’tgottenanybiggerorsmaller.Likewise,thewhitespacehasbeenbrokenintotwosmallersquares,butintotalitremainsthesamesize.Byusingtheside-lengthsAandB,onecancalculatetheareaofthetwosquares.

Youmayneedtoexplicitlypointoutthattheside-lengthsofthetrianglescanbeusedastheside-lengthsofthesquares.Havestudentsmeasuretheareaofthesmallersquare(A)Havestudentsmeasuretheareaofthelargersquare(B)AskstudentstocomparetheareofsquareA+squareBtotheareaofsquareC

ThesmallersquarehasanareaofA2,andthelargersquarehasanareaofB2.Sincethesesquaresarejusttheoriginalsquarebrokenupintotwopieces,weknowthatthesumoftheseareasmustbeequaltotheareaoftheoriginalsquare:

A2+B2=C2

4)CollisionDetectionInthisactivitystudentswill:

Createrighttrianglesonagraph.CalculatethehypotenusebydirectmeasurementandbythePythagoreanTheorem.Determineifcircleshavecollidedbyexaminingvisually.Determineifcircleshavecollidedbycomparingdistanceandradii.

DetailedinstructionsareprovidedontheCollisionWorksheet.

TheBigGame-CollisionDetectionLessontime:30-60Minutes

LESSONOVERVIEWTofinishuptheirvideogames,studentswillapplywhattheyhavelearnedinthelastfewstagestowritethefinalmissingfunctions.We'llstartbyusingbooleanstocheckwhetherkeyswerepressedinordertomovetheplayersprite,thenmoveontoapplyingthePythagoreanTheoremtodeterminewhenspritesaretouching.

ApplytheDistanceFormulatodetectwhentwopointsonacoordinateplaneareneareachother.

ANCHORSTANDARDCommonCoreMathStandards8.G.7:ApplythePythagoreanTheoremtodetermineunknownsidelengthsinrighttrianglesinreal-worldandmathematicalproblemsintwoandthreedimensions.

1)Introduction

Activity:TheBigGame-CollisionDetection2)OnlinePuzzles

Line-lengthDesignRecipe(inthestudentworkbook)DistanceDesignRecipe(inthestudentworkbook)Collide?DesignRecipe(inthestudentworkbook)

Derivedfrom

GETTINGSTARTED1)IntroductionLet'sgetbackintothatBigGamefromstages7,12,and16.Previousworkwiththegamehascreatedmovementforthedangerandtargetcharacters,usingBooleanstocheckiftheyhaveleftthescreen.Thelasttimestudentsworkedontheirgametheyusedaconditionaltocheckwhichkeywaspressedandmaketheplayermoveaccordingly.Atthispointtheonlythinglefttodoistodecidewhentheplayeristouchingeitherthetargetordanger.Oncestudentshavesuccessfullycompletedthedistanceandcollide?functions,theirscorewillincreasewhentheplayertouchesthetarget,anddecreasewhenittouchesthedanger.ThePythagoreanTheoremstudiedinthelastlessonwillbeusedtodeterminewhenthecharactershavemadecontact.Studentsarenotrequiredtowritetheirownline-lengthfunction,butyoumayaskthemtocompletetheDesignRecipeforitanyway.Studentswillfirstcompletethedistancefunctionsothatitmeasuresthedistancebetweentwopoints,(px,py)and(cx,cy).Afterthestudentsimplementthedistanceformula,theywillneedtoimplementthetestsinthecollide?function.Oncetheselastfunctionsareputintoplace,scoringwillautomaticallyupdatebasedoncollisionsbetweentargetanddanger.

ACTIVITY:THEBIGGAME-COLLISIONDETECTION2)OnlinePuzzlesReturntoyourBigGametousecollisiondetectionlogicsothatyouknowwhenyourplayeristouchingthetargetorthedanger.HeadtoCSinAlgebrastage20inCodeStudiotogetstartedprogramming.

Student Workbook

Name: ____________________________ Course: ____________________________

Computer Sciencein Algebrapowered by

Name: ___________________________ Date: ___________ Per: __________

Reverse EngineeringUStage 1

1Code.org Computer Science in Algebra

Thing in the game... What changes about it? More Specifically...

Name: ___________________________ Date: ___________ Per: __________

UStage 1

1Code.org Computer Science in Algebra

Video Game Planning

Use this form to plan out your video game. Once your game is complete, the player will move up and down, the target and danger will move from left and right, and you will earn points by touching the target, and lose points by touching the danger.

Created by:

The game takes place in: (This will be the background image in your game)

The player is a:(The player moves up and down)

The target is a:(The Target moves left and right)

The danger is a:(The Danger moves left and right)

Name: ___________________________ Date: ___________ Per: __________

UCode.org Computer Science in Algebra

Stage 2

2Evaluation Blocks

2 * 5 32 / 3

4 - (3 / 2) (25 + 14) - 12

(3 + 12) * 16 (23 * 14) * (3 + 2)

1 + (15 * 5) 19 - (12 + 11)

(2 + 17) * (12 - 8) 4 - (6 - 17)

9 * (17 + 2) (12 * 4) / 3

Create the evaluation blocks for the provided equations.

Name: ___________________________ Date: ___________ Per: __________

___________________ : ____________________________________ -> ________________ name domain range

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________

Stage 9

9Fast Functions!

Name: ___________________________ Date: ___________ Per: __________

DesignRecipe

DThe Design Recipe

___________________ : ____________________________________ -> ________________ function name domain range

___________________________________________________________________________ what does the function do?

Examples

Example: ________________ ( _______________ ) = ______________________________ function name input(s) what the function produces

Definition

Define: ________________ ( _______________ ) = function name variables

___________________________________________________________________________ what the function does with those variables

Description:

Contract and Purpose Statement

Every contract has three parts...

Write some examples for your function in action...

Write the deinition, giving variable names to all your input values

Name: ___________________________ Date: ___________ Per: __________

DesignRecipe

DThe Design Recipe

Examples

Definition

Description:

Name: ___________________________ Date: ___________ Per: __________

DesignRecipe

DThe Design Recipe

Examples

Definition

Description:

Name: ___________________________ Date: ___________ Per: __________

rocket-height (word problem)

Stage 10

Examples

Definition

Description: A rocket blasts of, traveling at 15 meters per second.

Write a function called rocket-height that takes in the number of

seconds that have passed since the rocket took of, and which produces

the height of the rocket at that time.

Name: ___________________________ Date: ___________ Per: __________

Stage 12

Examples

Definition

Description: Write a function update-target which takes in the

target’s x-coordinate and produces the next x-coordinate, which is 10

pixels to the right.

update-target (word problem)

Name: ___________________________ Date: ___________ Per: __________

Stage 12

Examples

Definition

Description: Write a function update-danger which takes in the

danger’s x-coordinate and produces the next x-coordinate, which is

10 pixels to the left.

update-danger (word problem)

Name: ___________________________ Date: ___________ Per: __________

Stage 15

Examples

Definition

Description: Write a function safe-left?, which takes in an

x-coordinate and checks to see if it is greater than 50.

safe-left? (word problem)

Name: ___________________________ Date: ___________ Per: __________

Stage 15

Examples

Definition

Description: Write a function safe-right?, which takes in an

x-coordinate and checks to see if it is less than 350.

safe-right? (word problem)

Name: ___________________________ Date: ___________ Per: __________

Stage 15

Examples

Definition

Description: Write a function onscreen?, which takes in a character’s

x-coordinate and checks to see if it is safe on the left and on the right.

onscreen? (word problem)

Name: ___________________________ Date: ___________ Per: __________

Example: ________________ ( _______________ ) = ______________________________

___________________________________ ___________________________________

___________________________________________________________________________

Stage 18

Examples

Definition

Description: Luigi’s Pizza has hired you as a programmer. They ofer “pepperoni” ($10.50), “cheese” ($9.00), “chicken” ($11.25), and “broccoli” ($10.25). Write a function called cost which takes in the name of a topping and outputs the cost of a pizza with that topping.

cost (word problem)

Name: ___________________________ Date: ___________ Per: __________

Key Code ReferenceStage 18

Key Code Key Code

left arrow 37 G 71

up arrow 38 H 72

right arrow 39 I 73

down arrow 40 J 74

0 48 K 75

1 49 L 76

2 50 M 77

3 51 N 78

4 52 O 79

5 53 P 80

6 54 Q 81

7 55 R 82

8 56 S 83

9 57 T 84

A 65 U 85

B 66 V 86

C 67 W 87

D 68 X 88

E 69 Y 89

F 70 Z 90

When you press a key on your keyboard, a unique numeric code is sent to your computer, which is then translated into a letter, number, or command. Use this handy key code reference sheet to make your Player sprite respond to diferent key presses.

Name: ___________________________ Date: ___________ Per: __________

Example: ________________ ( _______________ ) = ______________________________

update-player 38 240 240 + 10

240 - 10update-player 40 240

update-player 38 250

update-player 40 250

___________________________________ ___________________________________

___________________________________________________________________________

Stage 18

Examples

Definition

Description: Write a function called update-player, which takes in the key code of the key pressed and the player’s y-coordinate, and returns the new y-coordinate.

update-player (word problem)

Name: ___________________________ Date: ___________ Per: __________

1 53 7 102 6 94 8 11 12

1. What is the radius of circle A? ___________

2. What is the radius of circle B? ___________

3. What is Radius A + Radius B ___________

4. Do the circles overlap? (true/false) ___________

5. What is the length of side a? ___________

6. What is the length of side b? ___________

7. Estimate the length of side c? ___________

8. What is a2 + b2 ___________

On the graph:

Label the right angle as C

Label segment AB as c

Label segment AC as b

Label segment CB as a

Graph #1

Collision DetectionStage 19

Name: ___________________________ Date: ___________ Per: __________

1 53 7 102 6 94 8 11 12

On the graph:

Draw a segment from point A to point B

Draw a right triangle using segment c as the hypotenuse.

8. What is a2 + b2 ___________

Graph #2

Name: ___________________________ Date: ___________ Per: __________

1 53 7 102 6 94 8 11 12

On the graph:

Draw a segment from point A to point B

Draw a right triangle using segment c as the hypotenuse.

8. What is a2 + b2 ___________

Graph #3

Name: ___________________________ Date: ___________ Per: __________

line-length 10 5 10 - 5

line-length 2 8 8 - 2

___________________________________ ___________________________________

___________________________________________________________________________

Stage 20

Examples

Definition

Description: Write a function called line-length, which takes in two numbers and returns the diference between them. It should always subtract the smaller number from the bigger one.

line-length (word problem)

Name: ___________________________ Date: ___________ Per: __________

The Distance FormulaStage 20

The distance between two points (25, 50) and (300, 400) can be calculated with the distance formula as

line-length(25, 300)2 + line-length(50, 400)2

Convert the formula in a circle of evaluation.

line-length

25 300

Name: ___________________________ Date: ___________ Per: __________

Stage 20

Description: Write a function distance, which takes four inputs:• px: The x-coordinate of the player• py: The y-coordinate of the player• cx: The x-coordinate of another game character• cy: The y-coordinate of another game character

It should use the Distance formula to return the distance between both points.

distance (word problem)

Examples

Definition

Name: ___________________________ Date: ___________ Per: __________

Stage 20

Description: Write a function collide?, which takes four inputs:• px: The x-coordinate of the player• py: The y-coordinate of the player• cx: The x-coordinate of another game character• cy: The y-coordinate of another game character

Is the player’s x and y within 100 pixels of the other character’s x and y?

collide? (word problem)

Examples

Definition

Name Domain Range Example

Contract Log

Name Domain Range Example

Contract Log

Computer Science in Algebra

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Duality Theory in Algebra, Logic and Computer Science · PDF fileDuality Theory in Algebra, Logic, and Computer Science Foreword This booklet contains the abstracts of the talks for

GRAPH SPECTRA IN COMPUTER SCIENCE - University …sciold.ui.ac.ir/~cem/isfahan_cvetkovic_appl.pdf · GRAPH SPECTRA IN COMPUTER SCIENCE Drago•s Cvetkovi¶c ... Linear Algebra, (ed.

Duality Theory in Algebra, Logic and Computer Sciencepeople.maths.ox.ac.uk/hap/duality12-W2-abstractsbooklet.pdf · Duality Theory in Algebra, Logic, and Computer Science Foreword

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High School Catalog - LAUNCH · Mathematics Algebra I Algebra II College Algebra Foundations of Algebra Geometry Intro. to Computer Science Pre-Calculus Professional Math Statistics

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BOOLEAN ALGEBRA Saras M. Srivastava PGT (Computer Science) Kendriya Vidyalaya, IISc Bangalore – 560 012.

Logic of Mathematics (College Algebra for Computer Science)

Computer Science & Business Systems · B.E. /B.Tech in Computer Science & Business Systems Semester 1 Discrete Mathematics (PCC-CS401) Boolean algebra: Introduction of Boolean algebra,