Unit 3 Day 1 The Golden Ratio - OAME Welcome：3单元1天黄金比例- OAME欢迎.docx

Unit3:Day:TheGoldenRatioMindsOn:5Action:50Consolidate:20Total=75minLealTlinaGoal:Calculate,interpretandapplymeasuresofcentraltendency.Materials 10-12TapeMeasures GraphingcalculatorsAssessmentOpportunitiesMindsOn.WhOIeClaSS今DiSCUSSion1.eadstudentsinabrainstormingsessiontodiscusswhatitmeanstobeaverage".Whatdoesitmeantobeaboveorbelowaverage?WhOleClaSS->IntrOdUCtiOntoACtiVitVStudentscollectthemeasurementslistedinBLM3.1.1.Studentsmakeconnectionsbetweenterms,conceptsandprinciplesofcentraltendency.Themeancardcanbeheldbythestudentwhosevalueisclosesttothecalculatedmean.TheGoldenRatioisapproximately1.61803399.Discusswithstudentshowthisnumberrelatestotheresults.Action!WhOleClaSSTheGOIdenRatiOUsingBLM3.1.11studentscollectindividualdataandgenerateclassdataforthefourdifferentratios.Thestudentscalculatemeasurementsofcentraltendencyusingtechnology(TI-83,Fathom2,Excel)andrecordtheclassresultsinTable3.1.1a.Thestudentsstopwhenthetablehasbeencompletedandwaitforfurtherinstructionsfromtheteacher.SmallGroups÷Discussion(Home)ArrangethestudentsinascendingorderofL1ratio.Distributemean,median,mode,minimum,Qi,Q3,andmaximumcardstotheappropriatestudents.Breakthestudentsintofourgroupsusingthequartiles:eachquartilegroupisassignedoneofthefourratiosforanalysis.SmaIlGrOUPS-»DiSCUSSiOn(EXPert)Usingnumberedheads,breakthehomegroupsintosmallerexpertgroups(includerepresentationfromeachhomegroup)andhavethestudentscompletetheexpertgroupquestion.ProcessEXPeCtationS/Communicating/ObSerVatiOn:Observegroupsastheyconnecttheirresultstothemeasuresofcentraltendency.ListentodiscussionsandideaslookingforitemsthatstudentscansharewithothersduringtheConsolidateDebrief.ConsolidateDebriefWhOIeClaSS今DiSCUSSionDiscussresultsoftheexpertquestionwiththewholeclass,highlightingthedifferencesbetweenthemeasuresofcentraltendency.Includeadescriptionofquartiles,standarddeviationandvariance.ExplorationApplicationHomeActivityorFurtherClassroomConsolidationWhichmeasurewouldyoupreferforyourgrade-mean,median,ormode?Why?Performthefollowingmeasurements,standingstraightup,withyourarmsatyoursidesandrelaxed:A. Yourheight,shoesoff!B. TopofyourheadtoyourfingertipsC. TopofyourheadtoyourelbowsD. TopofyourheadtotheinsidetopofyourarmsE. Yourelbowtoyourfingertips1. Nowcalculateyourindividualratios,correcttotwodecimalplaces:2. 1.1=A/B3. 1.2=B/C4. 1.3=C/D5. 1.4=C/ERecordyourL1,L2,L3,L4ratiosonthechalkboardundertheappropriatecolumn.Copytheclassdatasetintothetablebelow.Table3.1.1a-StudentResultsL1L2L3L43.1.1: TheGoldenRatio(continued)Completethetablebelowforeachofthemeasures,correcttotwodecimalplaces.Table3.1.1b-MeasuresofCentralTendencyL1L2L3L4MeanMedianModeMinimumQiQ3MaximumVarianceStandardDeviationOnceyouhavecompletedthechart,waitforfurtherinstructionsfromyourteacher.HomeGroup:Withinyourassignedgroup,discussanswerstothefollowingquestions.1) Considerthedatasetforyourassignedratio(L1,L2,L3orL4).Whichmeasurement(mean,medianormode)ubestrepresents1'thisdata?Why?2) WhichmeasurementuIeastrepresents*1thisdata?Why?ExpertGroup:Withinyourassignedgroup,determinetheubestoveral,measureofcentraltendency.Med-anOP3.1.2: MeasuresofCentralTendencyCards(continued)MaX-mumUnit3:Day2:OnTargetMindsOn:5Action:50Consolidate:20Total=75minLealTlinaGoal:Calculate,interpretandapplystandarddeviationasameasureofcentraltendency.Materials Timer Graphingcalculators MaskingTape IntegerchipsorflatdiscsAssessmentOpportunitiesMindsOn.SmallGrOUPS今PaSSthePaPerStudentseachstartwithapaperandatitleof"mean”,"median"or4,mode"ingroupsofthree.Allow1minuteforstudentswritedownwhattheyknowabouttheterm,limitationsandexamples.After1minute,instructstudentstopasstheirpapertothepersonbesidethemandcontinueinthiswayforthreeturns.Afteractivityiscompleted,studentsengageinadiscussionregardingthelimitationsofmean,medianandmodeasmeasuresofcentraltendency.Thatis,theyprovideacentralvalue,butdonotindicatethespreadandconsistencyofthedata.Studentsmakeconnectionsbetweenconsistencyandstandarddeviation.Action!WhOleCIaSSHittinatheMark!UsingBLM3.2.1,studentscollectindividualscoresforthreetrialsofthegame.WhOIeClaSSDiSCUSSiOnWithreferencetoBLM3.2.2,leadstudentsinadiscussiononthedifferencebetweenprecisionandaccuracy.Commentontheconnectionbetweenprecisionandconsistencyandhowthesetermsrelatetostandarddeviation.ProcessExpectationsObservationChecklistObservegroupsastheydeveloptheirunderstandingofconsistencyasameasureofdispersion.Listentodiscussionsandideaslookingforconnectionstothenextactivity,BLM3.2.3.WhOIeClaSS»AIlCharaedUp!Studentscompletethe.ProcessExpectationsZPerformanceTask/RubricAssessthestudentsontheAllChargedUpactivityusingBLM3.2.4.ConsolidateDebriefWholeClaSS今DiSCiJSSiOn1.eadstudentsinadiscussionontheinterplayofprecision,accuracy,consistencyandstandarddeviation.ExplorationApplicationHomeActivityorFurtherClassroomConsolidationThinkofasituationfromeverydaylife.Inthissituation,isitbettertohavehighaccuracyorhighprecision?Canyouthinkofasituationinwhichlowprecision(orlowaccuracy)wouldbeacceptable?StudentName:ScoringInstructions:Keepatallychartofyourpartner'sperformancebelowtocalculatetheirtotalscore.12310510TotalTrialSIUdForeachtoss,recordthespotwherethemarkerlandsonthetargetsbelowWithreferencetothegroupingofyourmarkers,howdidyourresultschange?3.1.3: HittingtheMark(TeacherInstructions)GameSetup:Constructagameboardonthefloorwithmaskingtape.Usethefollowingdimensions:Outer square:Middle square: Inner square:150cmby150cm100cmby100cm50cmby50cmAddastartinglinethatis2mawayfromtheouteredgeofthetarget.Withtheadditionofextrastartinglinesarrangedaroundthetarget,uptofourstudentscanplayatonce.Pointvalues:OuterSquare(1point);MiddleSquare(5points);InnerSquare(10points);outsideofthetargetareascoresnopoints.Playingthegame:studentsapproachthestartingline,andtosseachoftheir5markers(integerchips,coins,colouredtiles)intothetargetareaoneatatime.Apartnerrecordswherethechipslandontheprovidedscoringsheet.Eachplayertriesthegamethreetimes.Recording:studentsrecordtheirresultsonthesheetprovided(BLM3.2.1)inbothatableandadiagram.Observations:UsethetargetanalogytoleadadiscussionregardingtheclassresultsonuHittingtheMark,Commentontheconnectionbetweenprecisionandconsistencyandhowthesetermsrelatetostandarddeviation.Highprecision,butlowaccuracyHighaccuracy,butlowprecision3.1.4: AllChargedUp!YouhavebeenhiredbyLowTechEnterprises,acompanythatmanufacturesportableMP3players,tochooseabatterysupplier.LowTechoffersawarrantyprogramthatguarantees200rechargesoftheirplayers;thatis,LowTechwillrepairorreplaceanyMP3playerthatdoesnotrecharge200times.TheoriginalsupplierofthebatterywassupplierX.Theircompetition,SupplierY,wantstobethenewexclusivebatterysupplierforLowTech.Youchoosearandomsampleoftwentybatteriesfromeachsupplierandexperimentallydeterminethenumberofrechargesforeachbattery.Thedatafromyourexperimentisasfollows(thenumbergivenishowmanytimeseachbatterywascapableofbeingrecharged):SupplierX:254, 259,256,253,252,250,250,249,256,254,250,251,250,248,248,254,258,255,258,255SupplierY:257,306,179,245,192,164,325,283,289,293,287,305,155,267,331,192,265,279,312,274Xclaimsthattheirbatterieswilllastforanaverageof253recharges,whileYclaimsthattheirbatterieswilllastforanaverageof260recharges.Whichbatterysupplierwouldyourecommend?Justifyyourchoicebyconsideringappropriatemeasuresofcentraltendency.3.1.5: AllChargedUp!RubricReasoningandProvingCriteriaLevel1Level2Level3Level4Makinginferences,conclusionsandjustificationsJustificationoftheanswerpresentedhasalimitedconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhassomeconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhasadirectconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhasadirectconnectiontotheproblemsolvingprocessandmodelspresented,withevidenceofreflectionConnectingCriteriaLevel1Level2Level3Level4MakingconnectionsamongmathematicalconceptsandproceduresMakesweakconnectionsMakessimpleconnectionsMakesappropriateconnectionsMakesstrongconnectionsUnit3:Day:GraphIt!MindsOn:5Action:55Consolidate:15Total=75minLealTlinaGoal:Generateagraphicalsummary(boxandwhiskerplot,histogram)ofaonevariabledataset.MaterialsRulersTechnology(Fathom2,Excel,TI-83)AssessmentOpportunitiesMindsOn.PairS今PiCtUrePerfeCtStudentworkinpairsanddiscussthequestionsinBLM3.3.1regardingthegraphicalrepresentationofdata.Whyisitimportanttorepresentdatainagraphicalformat?Iftechnologyisnotavailable,thestudentsgeneratetherepresentationsbyhand.Action!WholeClass÷ReachinqNewHeiqhtsUsingBLM3.3.21studentsgenerateaboxandwhiskerplotandahistogramforagivendataset.SmallGroUDS-»DiSeUSSionWithreferencetoBLM3.3.2,studentsdiscusstheirresponsetothelastquestionregardingwhichrepresentation(boxandwhiskerorhistogram)“best”representsthisdataset.ProcessExpectations/Communicating/Observation:Observegroupsastheydeveloptheirunderstandingofgraphicalrepresentationsofdata.Listentodiscussionsandideaslookingforconnectionstothenextactivity,BLM3.3.2.WhOleClaSSfBetWeenFriends!Ifavailable,studentsusetechnology(Fathom2,Excel,TI-83)tocompleteBetweenFriends(BLM3.3.3).ProcessExpectations/Representing/Observation:Observestudentsastheygenerategraphicalrepresentationsofdata;checktheboxandwhiskerplotsandhistogramsforaccuracyandcompleteness.ConsolidateDebriefWhOIeClaSS今DiSCIJSSiOn1.eadstudentsinadiscussiononthechallengesofgraphicalrepresentationsofdata(howarescaleschosen,whatrepresentationsaremostappropriate).SkillDevelopmentHomeActivityorFurtherClassroomConsolidationDescribehowahistogramcanbeconvertedintoaboxandwhiskerplot.Isitpossibletoconvertaboxandwhiskerplottoahistogram?Why?3.3.1: PicturePerfect1. Whichhasmorevariability-AorB?Why?Graph AGraph B2. Whichclassdidbetter?Howdoyouknow?StudentMarkStudentMarkBlue ClassYellowClass3. Aretherethesamenumberofraisinsineachbox?Howcanyoutell?HlrtIir史36声3.3.2: ReachingNewHeights4. Thefollowingarejumpheights(incm)fromelevendifferentcats.Illustratethedatawithaboxandwhiskerplotusingthenumberlinebelow.72,40,95,58,62,35,56,65,74,68,9020304050607080901005. Determineappropriateintervalsandrepresentthejumpingheightsinahistogram.Properlylabelyouraxesandprovideatitle.6. Whichtoolisthebettergraphicalrepresentationofthedata?Why?3.3.3: BetweenFriendsPickOneofthequestionsbelowandsurveyyourclassmates. Whatisyourbirthmonthbynumber(January=1,February=2,.)? Whatisthelastdigitofyourphonenumber? Howmanyhoursoftelevisiondidyouwatchlastweek? Howmanybookshaveyoureadthisyear? Howmanylettersareinyourlastname?Recordtheresponsesbelow.Prepareaboxandwhiskerplotofyourdata.Besuretoindicatethescaleandlabeltheimportantdatapoints(minimum,Qbmedian,Q3,maximum).Determineapropriateintervalsandrepresentyourdatainahistogram.Properlylabelyouraxesandprovideatitle.Unit3:Day4:DazedbyDataMindsOn:10Action:25Consolidate:40Total=75minLealTlinaGoal: Exploredifferenttypesofdata(numerical,categorical-ordinal,nominal,interval,continuous,discrete) Establishtheattributesthatinformationmusthavetobemeaningful.MaterialsAcetatesOverheadprojectorAssessmentOpportunitiesMindsOn.PairS今DataintheRealWOrldPairschooseoneoftheoccupationssuggestedonBLM3.4.1.Studentsintervieweachotheraboutthekindsofdatausedintheirwork.Studentsdiscussthedataintermsofthetwoattributesthatinformationmusthavetobemeaningful:numericaldata(thenumberorscalar)andcategoricaldata(thelabelsorunitstellinguswhatthenumbersaremeasuring).Ina2-Dimensionalgraphwhichaxisisusuallynumericalandwhichisusuallycategorical?Thinkofa2-Dgraphwherebothaxesarenumerical.Howmuchinformationdoesitconvey?5Example:73147314Km7314KmfromVictoria,B.C.toSt.John's,Nfld.Answers:1.ineraph:Horizontalaxismustbecategorical.Histoaram:Eitherhorizontalorverticalaxiscanbecategorical.SCatterPlot:Bothaxesarenumerical.Action!WholeCIaSSOnTheROadAqainUsingBLM3.4.2,studentsattempttoestablisharelationshipbetweendatapointsprovidedonagraphwithoutnumericalorcategoricaldescriptors.SrnaIlGroUPSDiSCUSSiOnWithreferencetoBLM3.4.2,studentsdiscusstheirresponsetothethreequestions.ProcessEXPeCtationS/CommunicatingZObservation:Observegroupsastheydeveloptheirunderstandingofgraphicalrepresentationsofdata.WhOIeClaSSOnTheROadAqainUsingBLM3.4.2(Hints)provideahinttothestudents.WhOIeClaSS-»DiSCUSSiOnUsingBLM3.4.2(TeacherNotes)presentthesolutiontothestudents.Studentsengageinadiscussionofthethreequestionsasked.UsingBLM3.4.3onacetateshowtheoverlaynamingthecapitalcities.ConsolidateDebriefSmailGrOUPS今What'sMVWoreI?Studentsengageinadiscussiononthechallengesofdatarepresentation.Studentscreatewordassociationcardstohelpdistinguishbetweencontinuousdataanddiscretedataandthethreetypesofcategoricalscales:nominal,ordinalandinterval.StudentsuseBLM3.4.4asaguidetotheactivityifwordassociationcardshavenotbeencreatedbefore.ProcessEXPeCtationS/Communicating/ObSerVatiOn:Circulateandassessforunderstandingmakingmentalnotesofincompleteorincorrectillustrationsanddefinitions.PracticeHomeActivityorFurtherClassroomConsolidationCompleteBLM3.4.4.ClassifythegraphsonBLM3.4.5accordingtodatatype.3.4.1: DataintheRealWorldChooseanoccupation.Interviewyourpartnerwiththequestionsprovided.Discussthetypesofdatayouuseinyourlineofworkandsortthemintonumericalorcategoricaldatasets.EnvironmentPublicSectorSciencesandEngineeringBusinessTransportationOccupationsMeteorologistPolicemanForensicScientistArchitectChemicalEngineerAccountantStockbrokerAirTrafficControllerInterviewQuestions:Whatdoyoufindchallenginginyourjob?Whatkindsofdatadoyouuseinyourwork?Howisthedatacollected?Whattypesoftoolsdoyouusetoworkwiththedata?NumericalDataCategoricalData3.4.2: OnTheRoadAgainWorkingingroupsofthree,determineapossiblepatternorrelationshipbetweenthedatapointsthatwouldaccountforthescatterplotshownbelow.Withinyourassignedgroups,discussanswerstothefollowingquestions:1) Withoutascale,howmuchinformationisthisscatterplotconveying?2) Whatpossibletypesofrelationshipscouldthesedatapointshave?3) Isitnecessarytohaveapredeterminedscaletoestablisharelationship,assumingthedotsareplacedaccordingtosomerepresentativescale?3.4.2:OnTheRoadAgain(Hints)Hint:Scalefactorshavebeenaddedandthescatterplothasbeent