AFRICAN INSTITUTE FOR MATHEMATICAL SCIENCES SCHOOLS ENRICHMENT CENTRE (AIMSSEC)

AIMING HIGH

SCISSORS, PAPER, ROCK Gamefor2players

Forscissorsholdout2fingerslikeapairofscissors.Forpaperholdyourhandoutflat.Forrockclenchyourhandintoafist.

Count3,2,1andthenbothplayers,atthesametime,makeoneofthesigns:scissors,orpaperorrock.

Scissorsbeatspaper,paperbeatsrockandrockbeatsscissors.

Itisadrawifbothplayersmakethesamesign.

Playthegameoftenandenjoyit.

SPRWide-Splits-InChinapeopleplaythisgamestandingupfacingtheiropponent.Theystartwiththeirfeettogetherandwhentheylosetheysteptoonesidesothattheirfeetgetfurtherapart.Afterawhiletheyaredoingthesplits.Playthisgameandseewhocanlastlongestbeforegivinguporfallingover.

SPRForward-Splits–Agamefortwoplayerswhoshouldberoughlythesame

height.Startthegametoetotoewiththeotherfoottoetoheelbehind.PlayoneroundofSPR.Whoeverwinstakestheirfrontfootandputsitdirectlybehindtheirbackfoot.Whoeverlosesthatroundmustslidetheirfrontfootforwardtomeettoetotoewiththeiropponentagain.AnotherroundofSPRisplayed.Whoeverwinstakestheirfrontfootandputsitdirectlybehindtheirbackfoot.Whoeverlosesthatroundmustslidetheirfrontfootforwardtomeettoetotoewiththeiropponentagain.Thiscontinuesuntilsomeonelosestheirbalanceandfallsoverorendsupinthesplits!Watchthisvideohttps://youtu.be/dN8xaC-g8Rktoseehowthegameisplayed.LEARNTHEMATHSPlaythegamewithafriend10timesandkeeparecordoftheresults.

Player1 Paper Scissors Isitafairgame?Didyoubothhavethesamechanceofwinning?

Player2 Rock Rock

Winner Player1 Player2

Listallthedifferentpossibleeventsthatcanhappeneachtimeyouplaythisgame.Didalltheseeventshappeninyour10games?

Whatmakesyoudecidewhichsigntomake?Giveyourreasons.

Areyouequallylikelytomakethescissorssign,thepapersignortherocksign?Explainwhy.

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HELP Thistableisnotforrecordingtheresultsofthegamesyouplay.Itgivesallthedifferentresultsthatcouldhappen.Fillintheotherboxes.Thetablehasbeenstartedforyou.

PLAYER 1 SCISSORS SCISSORS SCISSORS PLAYER 2 SCISSORS PAPER ROCK WINNER DRAW 1 2

NEXT Makeupasimilargamewith4actionsinsteadof3.Playyourgameandrecordtheresults.Isyourgameafairgame?

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NOTES FOR TEACHERS SOLUTION

PLAYER 1 SCISSORS SCISSORS SCISSORS PAPER PAPER PAPER ROCK ROCK ROCK PLAYER 2 SCISSORS PAPER ROCK SCISSORS PAPER ROCK SCISSORS PAPER ROCK WINNER DRAW 1 2 2 DRAW 1 1 2 DRAW

Tounderstandprobabilityyoumustunderstandwhateventscanhappen.Mathematicianscallthisthesamplespace.Learnersinprimaryschoolshouldhavetheexperienceofplayinggames,makinglistsofwhatcanhappenandcountingthenumberofeventsthatfitaparticulardescription,forexample‘Player2wins’,buttheydon’tneedtolearnthewordssamplespace.

Theninedifferenteventsinthissamplespacearelistedinbothtablesindifferentways.ThetablesshowthatPlayer1hasa1in3chanceofwinning,player2hasa1in3chanceofwinningandthereisa1in3chanceofadraw.Soitisafairgame.

Why do this activity? Learnerswillenjoyplayingthisgameanditwillintroducethemtosomefundamentalmathematicalthinkingaboutprobability.

Learning objectives Indoingthisactivitystudentswillhaveanopportunityto:• experienceinvolvementinagamethatrequiressomemathematicalthinkingabout

probability;• developofmathematicalthinkingaboutthedifferentpossibleeventsinasituation;• meettheconceptofasamplespace(withouttechnicallanguage);• exploretheconceptofequalchancesandafairgame.

Generic competences Indoingthisactivitystudentswillhaveanopportunityto:• thinkmathematicallyandreasonlogically;• communicateandexchangeideaswithothersabouttherulesofagameandthe

probabilityofwinning;• developlifeskillsandconsiderationforothersinplayinggames.

Suggestions for teaching ThisisaDO,TALK,RECORDlessoncyclethatyoumighttrytoplanformostofyourlessons.

Explainthegameandgettheclasstoplaythegame10timesinpairs.

Whiletheyareplayingwritethesequestionsontheboard:1. Isitafairgame?Doyoubothhavethesamechanceofwinning?2. Listallthedifferentpossibleeventsthatcanhappeneachtimeyouplaythisgame.3. Didalltheseeventshappeninyour10games?

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4. Whatmakesyoudecidewhichsigntomake?Giveyourreasons.5. Areyouequallylikelytomakethescissorssign,thepapersignortherocksign?Explain

why.Thenaskthelearnerstotalkaboutthequestionsandtotrytofindanswers.Afterabout5minutesaskthemtowritedowntheiranswersintheirnotebooks.

Thenhaveaplenaryclassdiscussionabouttheanswersandlistallthedifferentpossibleeventsontheboard.Ask“howcanwerecordthesepossibilitiesclearly?”andintroducethistable:

PLAYER 1 SCISSORS SCISSORS SCISSORS PLAYER 2 SCISSORS PAPER ROCK WINNER DRAW 1 2

Getthelearnerstotellyouwhattofillinthedifferentcells.Forolderlearnersthisisagoodcontextinwhichtousea2-waytable.Whenthelearnersunderstandthatthereare9eventsthatcanhappen,askthelearnerswhatchancePlayer1hasofwinning?Tellthemthattheword‘probability’means‘chance’.Askthemwhatistheprobabilityofadraw.TheDiagnosticQuizcanbeusedattheendofthelessontofindoutifthelearnershaveunderstoodthefundamentalidea.YoucanintroducetheChineseSplitsversionofthegameattheendofthelessonorinanotherlesson.Key questions Whatarethedifferentthingsthatcanhappenwhenyouplaythisgame?Howmanydifferenteventshappenwhenyouplaythisgame?Areyousurethatyouhavemadealistofallthepossibilities?Howdoyouknow?Howmanyofthoseeventsendinadraw?Howmanyofthoseeventsendinyouwinning.Howmanyofthoseeventsendinyouropponentwinning?

Diagnostic Assessment Thisshouldtakeabout5–10minutes.1. Writethequestionontheboard,saytotheclass:

“Putup1fingerifyouthinktheanswerisA,2fingersforB,3fingersforCand4fingersforD”.2. Noticehowthelearnersresponded.AskalearnerwhogaveanswerAtoexplainwhyheorshegavethatanswerandDONOTsaywhetheritisrightorwrongbutsimplythankthelearnerforgivingtheanswer.3. ThendothesameforanswersB,CandD.Trytomakesurethatlearnerslistentothesereasonsandtrytodecideiftheirownanswerwasrightorwrong.

4. Asktheclassagaintovotefortherightanswerbyputtingup1,2,3or4fingers.Noticeifthereisachangeandwhogaverightandwronganswers.Itisimportantforlearnerstoexplainthereasonfortheiranswerotherwisemanylearnerswilljustmakeaguess.

ThecorrectanswerisC.Thereare7eventsinthesamplespace.Choosingaredcountergivestwooftheseevents.https://diagnosticquestions.com

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Follow up InaBoxhttps://aiminghigh.aimssec.ac.za/years-6-12-in-a-box/SameSweetshttps://aiminghigh.aimssec.ac.za/years-4-7-same-sweets/ PLAY SCISSORS PAPER ROCK LIZARD SPOCK - 5 ACTIONS IN PLACE OF 3 .

5 ACTIONS

SPR GAME

Scissors

Paper

Rock

Lizard

Spock Scissors D Sc R Sc S

Paper Sc D P L P

Rock R P D R S

Lizard Sc L R D L

Spock S P S L D

7 ACTIONS

SPR GAME

Rock

Water

Air

Paper

Sponge

Scissors

Fire Rock D W A P R R R

Water W D A P S W W

Air A A D P S Sc A

Paper P P P D S Sc F

Sponge R S S S D Sc F

Scissors R W Sc Sc Sc D F

Fire R W A F F F D

GototheAIMSSEC AIMING HIGH websiteforlessonideas,solutionsandcurriculumlinks:http://aiminghigh.aimssec.ac.zaSubscribetotheMATHS TOYSYouTubeChannelhttps://www.youtube.com/c/mathstoysDownloadthewholeAIMSSECcollectionofresourcestouseofflinewith

theAIMSSECAppseehttps://aimssec.apporfinditonGooglePlay.

Note:TheGradesorSchoolYearsspecifiedontheAIMINGHIGHWebsitecorrespondtoGrades4to12inSouthAfricaandtheUSA,toYears4to12intheUKandschoolyearsuptoSecondary5inEastAfrica.NewmaterialwillbeaddedforSecondary6.ForresourcesforteachingAlevelmathematics(Years12and13)seehttps://nrich.maths.org/12339MathematicstaughtinYear13(UK)&Secondary6(EastAfrica)isbeyondtheSACAPScurriculumforGrade12

LowerPrimaryApprox.Age5to8

UpperPrimaryAge8to11

LowerSecondaryAge11to15

UpperSecondaryAge15+

SouthAfrica GradesRand1to3 Grades4to6 Grades7to9 Grades10to12EastAfrica NurseryandPrimary1to3 Primary4to6 Secondary1to3 Secondary4to6USA KindergartenandG1to3 Grades4to6 Grades7to9 Grades10to12UK ReceptionandYears1to3 Years4to6 Years7to9 Years10to13

PapercoversRock.RockcrushesLizard.LizardbitesSpock.

SpocksmashesScissors.ScissorsdecapitateLizard.

LizardeatsPaper.PapercriticisesSpock.SpockvaporizesRock.RockcrushesScissors.ScissorscutPaper.

OR PLAY THE 7 ACTIONS GAMETherulesareinthecontingencytable.

Butyouneedtomakeupyourown‘stories’.