Computer Science in Algebra

Computer Sciencein Algebra

Instructor Handbook

2015-2016

Powered by

Bootstrap

UUNPLUGGED

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.

2

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).

3

Derivedfrom

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).

4

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.

6

Derivedfrom

7


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

8

Derivedfrom

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.

9

UUNPLUGGED

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

10


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

11

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

12

Derivedfrom

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.

13


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

Derivedfrom

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.

15


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:

16

Derivedfrom

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.

17


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

18

Derivedfrom

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.

19


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.

20

Derivedfrom

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.

21

UUNPLUGGED

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

22

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,

23

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

24

Derivedfrom

OncestudentshaveworkedthroughtheFastFunctions,youcanhavethemusethefullBlankDesignRecipeFormtoworkthroughanwordproblemsthattheyencounterinthefuture.

av ariablenamebecauseitdiffersbetw eenExamples."

25


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.

27

Challenge1

Input Output

1 10

2 40

3 90

4 160

Challenge2

Input Output

1 15

2 45

3 95

4 165

Derivedfrom

thenyoucancallthisoutassuch,butevenyoungerstudentswhohaven'tyetseenquadraticscanenjoythisextensionchallenge.Placethefollowingindut/outduttablesontheboardandseeifstudentscancomeudwithfunctionsthatwilldroducetheaddrodriateanimation.

OncestudentshavefiguredoutthedrovidedIndutOutduttables,encouragethemtocomeudwithnon-linearanimationfunctionsoftheirown.

28


SolvingWordProblemswiththeDesignRecipeLessontime:30-60Minutes

LESSONOVERVIEWStudentswillcontinuetodracticetheDesignRecidewithaseriesofworddroblems.

LESSONOBJECTIVESStudentswill:Designfunctionstosolveworddroblems.Continuetodracticewritingcontractswithmorecomdlexscenarios.

ANCHORSTANDARDCommonCoreMathStandardsF.BF.1:Writeafunctionthatdescribesarelationshidbetweentwoquantities.



1)Introduction

Activity:SolvingWordProblemswiththeDesignRecipe2)OnlinePuzzles

TEACHINGGUIDEGETTINGSTARTED1)IntroductionThestudentswilldolotsofdragginganddroddingastheyfillinthemissingdiecesofdifferentdartsofvariouscontracts.Itshouldbenotedthattheexamdlesmustbefilledincomdletely.Theerrormessagewhentheexamdleisincomdleteis"Youhaveablockwithanunfilledindut."

ACTIVITY:SOLVINGWORDPROBLEMSWITHTHEDESIGNRECIPE2)OnlinePuzzles

29

Derivedfrom

Inthisstageyou'llusetheDesignRecidetocreatefunctionsthatsolveworddroblems.HeadtoCSinAlgebrastage11inCodeStudiotogetstarteddrogramming.

30


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.

31

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.

32

UUNPLUGGED

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?

34

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

35

Derivedfrom

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

36


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.

37

�erive✁from

ACTIVITY:BOOLEANOPERATORS2)OnlinePuzzlesHeadtoCSinAlgebrastage14inCodeStudiotogetstarteddrogramming.

38


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)

39

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.

40

✂erivedfrom

problemsintosimplerpieces,whichmakeitpossibletodesignelegantsolutionstodifficultproblems.

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

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

41


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)

42

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.

43

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

44

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

45

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{

46

(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}

47

Derivedfrom

Anotherverycommonpiecewisefunctionsisfortaxicabs.$3for0to2miles$1foreachpartialmileafterthat

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

48


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

49

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.

50

✝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!

51

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

52

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?

53

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)

54

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.

55


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)

56

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.

57

Student Workbook

Name: ____________________________ Course: ____________________________

Computer Sciencein Algebrapowered by

Name: ___________________________ Date: ___________ Per: __________

Reverse EngineeringUStage 1

1Code.org Computer Science in Algebra

2

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

Name: ___________________________ Date: ___________ Per: __________

UStage 1

1Code.org Computer Science in Algebra

3

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

4

*

Stage 2

2Evaluation Blocks

4

-/

3

*

+

*

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: __________


5

___________________ : ____________________________________ -> ________________ name domain range

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________


Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________


Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________


Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Define: ________________ ( _______________ ) = ______________________________

Stage 9

9Fast Functions!

Name: ___________________________ Date: ___________ Per: __________


6

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: __________


7

DesignRecipe

DThe Design Recipe



Examples



Definition



Description:





Name: ___________________________ Date: ___________ Per: __________


8

DesignRecipe

DThe Design Recipe



Examples



Definition



Description:





Name: ___________________________ Date: ___________ Per: __________


9

rocket-height (word problem)

Stage 10

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: __________


10

Stage 12

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: __________


11

Stage 12

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: __________


12

Stage 15

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: __________


13

Stage 15

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: __________


14

Stage 15

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: __________


15

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________


___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________________________________________________

Stage 18

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: __________


16

Key Code ReferenceStage 18

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: __________


17

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

Example: ________________ ( _______________ ) = ______________________________

update-player 38 240 240 + 10

240 - 10update-player 40 240

update-player 38 250

update-player 40 250


___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________________________________________________

Stage 18

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: __________


18

1 53 7 102 6 94 8 11 12

1

5

3

7

2

6

4

00

A

B

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

19

Name: ___________________________ Date: ___________ Per: __________


19

1 53 7 102 6 94 8 11 12

1

5

3

7

2

6

4

00

On the graph:

Draw a segment from point A to point B


Draw a right triangle using segment c as the hypotenuse.




A

B








8. What is a2 + b2 ___________

Graph #2


19

Name: ___________________________ Date: ___________ Per: __________


20

1 53 7 102 6 94 8 11 12

1

5

3

7

2

6

4

00

On the graph:

Draw a segment from point A to point B


Draw a right triangle using segment c as the hypotenuse.




A

B








8. What is a2 + b2 ___________

Graph #3


19

Name: ___________________________ Date: ___________ Per: __________


21



line-length 10 5 10 - 5

line-length 2 8 8 - 2


___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________ ___________________________________

___________________________________________________________________________

Stage 20

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: __________


22

The Distance FormulaStage 20

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: __________


23

Stage 20

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: __________


24

Stage 20

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

Computer Science in Algebra

Documents

Transcript of Computer Science in Algebra