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Unit3:Day1:TheGoldenRatioMindsOn:5LearningGoal:Calculate,interpretandapplymeasuresofcentraltendency.Materials10-12TapeMeasuresGraphingcalculatorsAction:50Consolidate:20Total=75min Assessment
OpportunitiesMindsOn…WholeClassDiscussionLeadstudentsinabrainstormingsessiontodiscusswhatitmeanstobe“average”.Whatdoesitmeantobeaboveorbelowaverage?WholeClassIntroductiontoActivityStudentscollectthemeasurementslistedinBLM3.1.1.Studentsmakeconnectionsbetweenterms,conceptsandprinciplesofcentraltendency.Themeancardcanbeheldbythestudentwhosevalueisclosesttothecalculatedmean.TheGoldenRatioisapproximately1.61803399.Discusswithstudentshowthisnumberrelatestotheresults.Action!WholeClassTheGoldenRatioUsingBLM3.1.1,studentscollectindividualdataandgenerateclassdataforthefourdifferentratios.Thestudentscalculatemeasurementsofcentraltendencyusingtechnology(TI-83,Fathom2,Excel)andrecordtheclassresultsinTable3.1.1a.Thestudentsstopwhenthetablehasbeencompletedandwaitforfurtherinstructionsfromtheteacher.SmallGroupsDiscussion(Home)ArrangethestudentsinascendingorderofL1ratio.Distributemean,median,mode,minimum,Q1,Q3,andmaximumcardstotheappropriatestudents.Breakthestudentsintofourgroupsusingthequartiles:eachquartilegroupisassignedoneofthefourratiosforanalysis.SmallGroupsDiscussion(Expert)Usingnumberedheads,breakthehomegroupsintosmallerexpertgroups(includerepresentationfromeachhomegroup)andhavethestudentscompletetheexpertgroupquestion.ProcessExpectations/Communicating/Observation:Observegroupsastheyconnecttheirresultstothemeasuresofcentraltendency.ListentodiscussionsandideaslookingforitemsthatstudentscansharewithothersduringtheConsolidateDebrief.ConsolidateDebriefWholeClassDiscussionDiscussresultsoftheexpertquestionwiththewholeclass,highlightingthedifferencesbetweenthemeasuresofcentraltendency.Includeadescriptionofquartiles,standarddeviationandvariance.ExplorationApplicationHomeActivityorFurtherClassroomConsolidationWhichmeasurewouldyoupreferforyourgrade–mean,median,ormode?Why?3.1.1:TheGoldenRatioPerformthefollowingmeasurements,standingstraightup,withyourarmsatyoursidesandrelaxed:Yourheight,shoesoff!TopofyourheadtoyourfingertipsTopofyourheadtoyourelbowsTopofyourheadtotheinsidetopofyourarmsYourelbowtoyourfingertipsNowcalculateyourindividualratios,correcttotwodecimalplaces:L1=A/BL2=B/CL3=C/DL4=C/ERecordyourL1,L2,L3,L4ratiosonthechalkboardundertheappropriatecolumn.Copytheclassdatasetintothetablebelow.Table3.1.1a-StudentResultsL1L2L3L4
3.1.1:TheGoldenRatio(Continued)Completethetablebelowforeachofthemeasures,correcttotwodecimalplaces.Table3.1.1b–MeasuresofCentralTendencyL1L2L3L4MeanMedianModeMinimumQ1Q3MaximumVarianceStandardDeviationOnceyouhavecompletedthechart,waitforfurtherinstructionsfromyourteacher.HomeGroup:Withinyourassignedgroup,discussanswerstothefollowingquestions.Considerthedatasetforyourassignedratio(L1,L2,L3orL4).Whichmeasurement(mean,medianormode)“bestrepresents”thisdata?Why?Whichmeasurement“l(fā)eastrepresents”thisdata?Why?ExpertGroup:Withinyourassignedgroup,determinethe“bestoverall”measureofcentraltendency.
3.1.2:MeasuresofCentralTendencyCardsMeanMean
3.1.2:MeasuresofCentralTendencyCards(continued)MedianMedian
3.1.2:MeasuresofCentralTendencyCards(continued)ModeMode
3.1.2:MeasuresofCentralTendencyCards(continued)QQ1
3.1.2:MeasuresofCentralTendencyCards(continued)QQ3
3.1.2:MeasuresofCentralTendencyCards(continued)MinimumMinimum
3.1.2:MeasuresofCentralTendencyCards(continued)MaximumMaximum
Unit3:Day2:OnTargetMindsOn:5LearningGoal:Calculate,interpretandapplystandarddeviationasameasureofcentraltendency.MaterialsTimerGraphingcalculatorsMaskingTapeIntegerchipsorflatdiscsAction:50Consolidate:20Total=75min Assessment
OpportunitiesMindsOn…SmallGroupsPassthePaperStudentseachstartwithapaperandatitleof“mean”,“median”or“mode”ingroupsofthree.Allow1minuteforstudentswritedownwhattheyknowabouttheterm,limitationsandexamples.After1minute,instructstudentstopasstheirpapertothepersonbesidethemandcontinueinthiswayforthreeturns.Afteractivityiscompleted,studentsengageinadiscussionregardingthelimitationsofmean,medianandmodeasmeasuresofcentraltendency.Thatis,theyprovideacentralvalue,butdonotindicatethespreadandconsistencyofthedata.Studentsmakeconnectionsbetweenconsistencyandstandarddeviation.Action!WholeClassHittingtheMark!UsingBLM3.2.1,studentscollectindividualscoresforthreetrialsofthegame.WholeClassDiscussionWithreferencetoBLM3.2.2,leadstudentsinadiscussiononthedifferencebetweenprecisionandaccuracy.Commentontheconnectionbetweenprecisionandconsistencyandhowthesetermsrelatetostandarddeviation.ProcessExpectations/Observation/ChecklistObservegroupsastheydeveloptheirunderstandingofconsistencyasameasureofdispersion.Listentodiscussionsandideaslookingforconnectionstothenextactivity,BLM3.2.3.WholeClassAllChargedUp!Studentscompletethe.ProcessExpectations/PerformanceTask/RubricAssessthestudentsontheAllChargedUpactivityusingBLM3.2.4.ConsolidateDebriefWholeClassDiscussionLeadstudentsinadiscussionontheinterplayofprecision,accuracy,consistencyandstandarddeviation.ExplorationApplicationHomeActivityorFurtherClassroomConsolidationThinkofasituationfromeverydaylife.Inthissituation,isitbettertohavehighaccuracyorhighprecision?Canyouthinkofasituationinwhichlowprecision(orlowaccuracy)wouldbeacceptable?3.2.1:HittingtheMark(ScoringSheet)StudentName:____________________________ScoringInstructions:Keepatallychartofyourpartner’sperformancebelowtocalculatetheirtotalscore.Trial123Points10510TotalForeachtoss,recordthespotwherethemarkerlandsonthetargetsbelowTrial#1 Trial#2 Trial#3Withreferencetothegroupingofyourmarkers,howdidyourresultschange?
3.2.2:HittingtheMark(TeacherInstructions)GameSetup:Constructagameboardonthefloorwithmaskingtape.Usethefollowingdimensions:11105Outersquare: 150cmby150cmMiddlesquare: 100cmby100cmInnersquare: 50cmby50cmAddastartinglinethatis2mawayfromtheouteredgeofthetarget.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:Usethetargetanalogytoleadadiscussionregardingtheclassresultson“HittingtheMark”.Commentontheconnectionbetweenprecisionandconsistencyandhowthesetermsrelatetostandarddeviation.Highprecision,butlowaccuracy Highaccuracy,butlowprecision
3.2.3: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.
3.2.4:AllChargedUp!RubricReasoningandProvingCriteriaLevel1Level2Level3Level4Makinginferences,conclusionsandjustificationsJustificationoftheanswerpresentedhasalimitedconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhassomeconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhasadirectconnectiontotheproblemsolvingprocessandmodelspresentedJustificationoftheanswerpresentedhasadirectconnectiontotheproblemsolvingprocessandmodelspresented,withevidenceofreflectionConnectingCriteriaLevel1Level2Level3Level4MakingconnectionsamongmathematicalconceptsandproceduresMakesweakconnectionsMakessimpleconnectionsMakesappropriateconnectionsMakesstrongconnections
Unit3:Day3:GraphIt!MindsOn:5LearningGoal:Generateagraphicalsummary(boxandwhiskerplot,histogram)ofaonevariabledataset.MaterialsRulersTechnology(Fathom2,Excel,TI-83)Action:55Consolidate:15Total=75min Assessment
OpportunitiesMindsOn…PairsPicturePerfectStudentworkinpairsanddiscussthequestionsinBLM3.3.1regardingthegraphicalrepresentationofdata.Whyisitimportanttorepresentdatainagraphicalformat?Iftechnologyisnotavailable,thestudentsgeneratetherepresentationsbyhand.Action!WholeClassReachingNewHeightsUsingBLM3.3.2,studentsgenerateaboxandwhiskerplotandahistogramforagivendataset.SmallGroupsDiscussionWithreferencetoBLM3.3.2,studentsdiscusstheirresponsetothelastquestionregardingwhichrepresentation(boxandwhiskerorhistogram)“best”representsthisdataset.ProcessExpectations/Communicating/Observation:Observegroupsastheydeveloptheirunderstandingofgraphicalrepresentationsofdata.Listentodiscussionsandideaslookingforconnectionstothenextactivity,BLM3.3.2.WholeClassBetweenFriends!Ifavailable,studentsusetechnology(Fathom2,Excel,TI-83)tocompleteBetweenFriends(BLM3.3.3).ProcessExpectations/Representing/Observation:Observestudentsastheygenerategraphicalrepresentationsofdata;checktheboxandwhiskerplotsandhistogramsforaccuracyandcompleteness.ConsolidateDebriefWholeClassDiscussionLeadstudentsinadiscussiononthechallengesofgraphicalrepresentationsofdata(howarescaleschosen,whatrepresentationsaremostappropriate).SkillDevelopmentHomeActivityorFurtherClassroomConsolidationDescribehowahistogramcanbeconvertedintoaboxandwhiskerplot.Isitpossibletoconvertaboxandwhiskerplottoahistogram?Why?3.3.1:PicturePerfectWhichhasmorevariability–AorB?Why?GraphA GraphBWhichclassdidbetter?Howdoyouknow?BlueClass YellowClass3.Aretherethesamenumberofraisinsineachbox?Howcanyoutell?3.3.2:ReachingNewHeights4.Thefollowingarejumpheights(incm)fromelevendifferentcats.Illustratethedatawithaboxandwhiskerplotusingthenumberlinebelow.72,40,95,58,62,35,56,65,74,68,905.Determineappropriateintervalsandrepresentthejumpingheightsinahistogram.Properlylabelyouraxesandprovideatitle.6.Whichtoolisthebettergraphicalrepresentationofthedata?Why?
3.3.3:BetweenFriendsPickoneofthequestionsbelowandsurveyyourclassmates.Whatisyourbirthmonthbynumber(January=1,February=2,…)?Whatisthelastdigitofyourphonenumber?Howmanyhoursoftelevisiondidyouwatchlastweek?Howmanybookshaveyoureadthisyear?Howmanylettersareinyourlastname?Recordtheresponsesbelow.__________________________________________________________________________________________________________________________________________________________________________________________________________________Prepareaboxandwhiskerplotofyourdata.Besuretoindicatethescaleandlabeltheimportantdatapoints(minimum,Q1,median,Q3,maximum).Determineapropriateintervalsandrepresentyourdatainahistogram.Properlylabelyouraxesandprovideatitle.
Unit3:Day4:DazedbyDataMindsOn:10LearningGoal:Exploredifferenttypesofdata(numerical,categorical-ordinal,nominal,interval,continuous,discrete)Establishtheattributesthatinformationmusthavetobemeaningful.MaterialsAcetatesOverheadprojectorAction:25Consolidate:40Total=75min Assessment
OpportunitiesMindsOn…PairsDataintheRealWorldPairschooseoneoftheoccupationssuggestedonBLM3.4.1.Studentsintervieweachotheraboutthekindsofdatausedintheirwork.Studentsdiscussthedataintermsofthetwoattributesthatinformationmusthavetobemeaningful:numericaldata(thenumberorscalar)andcategoricaldata(thelabelsorunitstellinguswhatthenumbersaremeasuring).Ina2-Dimensionalgraphwhichaxisisusuallynumericalandwhichisusuallycategorical?Thinkofa2-Dgraphwherebothaxesarenumerical.Howmuchinformationdoesitconvey?Example:73147314Km7314KmfromVictoria,B.C.toSt.John’s,Nfld.Answers:Linegraph:Horizontalaxismustbecategorical.Histogram:Eitherhorizontalorverticalaxiscanbecategorical.ScatterPlot:Bothaxesarenumerical.Action!WholeClassOnTheRoadAgainUsingBLM3.4.2,studentsattempttoestablisharelationshipbetweendatapointsprovidedonagraphwithoutnumericalorcategoricaldescriptors.SmallGroupsDiscussionWithreferencetoBLM3.4.2,studentsdiscusstheirresponsetothethreequestions.ProcessExpectations/Communicating/Observation:Observegroupsastheydeveloptheirunderstandingofgraphicalrepresentationsofdata.WholeClassOnTheRoadAgainUsingBLM3.4.2(Hints)provideahinttothestudents.WholeClassDiscussionUsingBLM3.4.2(TeacherNotes)presentthesolutiontothestudents.Studentsengageinadiscussionofthethreequestionsasked.UsingBLM3.4.3onacetateshowtheoverlaynamingthecapitalcities.ConsolidateDebriefSmallGroupsWhat’sMyWord?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?NumericalDataCategoricalData
3.4.2:OnTheRoadAgainWorkingingroupsofthree,determineapossiblepatternorrelationshipbetweenthedatapointsthatwouldaccountforthescatterplotshownbelow.Withinyourassignedgroups,discussanswerstothefollowingquestions:Withoutascale,howmuchinformationisthisscatterplotconveying?Whatpossibletypesofrelationshipscouldthesedatapointshave?Isitnecessarytohaveapredeterminedscaletoestablisharelationship,assumingthedotsareplacedaccordingtosomerepresentativescale?
3.4.2:OnTheRoadAgain(Hints)Hint:Scalefactorshavebeenaddedandthescatterplothasbeenturnedintoalinegraph.Doesthishelpyouestablisharelationshipbetweenthedatapoints?Hascategoricaldatabeenaddedyet?
3.4.2:OnTheRoadAgain(TeacherNotes)Doesthismapoverlayhelpyouestablisharelationship?ThedotsrepresentCanada’sprovincialandterritorialcapitalcitiesandthescalefactorsarethedistance(inthousandsofkilometres)betweenthecities.WholeClassDiscussion:Whatwasthecategoricaldatathatwasadded?Howdiditveryquicklyallowyoutoestablisharelationshipbetweenthedatapoints?Canyounamethecitythateachdotrepresents?
3.4.3:OnTheRoadAgain(Supplemental)IqaluitSt.John’sCharlottetownHalifaxFrederictonQuebecCityTorontoWinnipegReginaEdmontonYellowknifeWhitehorseVictoriaIqaluitSt.John’sCharlottetownHalifaxFrederictonQuebecCityTorontoWinnipegReginaEdmontonYellowknifeWhitehorseVictoria
3.4.4:What’sMyWord? CreateWordAssociationcardstohelpyourememberthevocabularytermsthatyoulearnedintoday’slesson.Oneachcard,drawarectangledividedinto4sections.Eachsectionofthecardislabelledbelow.Thetermiswritteninthefirstsection.Theremainingsectionsincludeavisualrepresentation,adefinitionwritteninyourownwords,andapersonalassociationthatwillhelpyouremembertheterm.Thevocabularytermcanbewrittenonthebackofthecardandusedinawordwall.VocabularyTermVocabularyTermPersonalAssociationVisualRepresentationInyourownwords… PersonalAssociationVisualRepresentationInyourownwords…
3.4.4:What’sMyWord?(continued)VerbalandVisualWordAssociationPrinttemplateoncardstock.Printthevocabularywordonthereversesidethenplacethecardonawordwallforfuturereference.CONTINUOUSDATADISCRETEDATANOMINALSCALEORDINALSCALEINTERVALDATA
3.4.5:IdentifyingNumericalandCategoricalScalesTheabovegraphshowstheaveragemarksforGrades9through12byreportingperiod.Questions:Identifythecategoricalscaleandthenumericalscale.Howmuchusefulinformationwouldbeprovidedifeitherthecategoricalornumericalscalewheremissing?Mathematically,doesitmakesensetoconnectthedatapointsbyaline?Whyorwhynot?
3.4.6:ClassifyingCategoricalScalesForeachgraphbelowindicatethetypeofcategoricalscaleandwhetherthegraphisappropriate(i.e.shouldlinesbeusedorisahistogrammoreappropriate?)ANALYSIS:ANALYSIS:ANALYSIS:ANALYSIS:
3.4.6:ClassifyingCategoricalScales(Continued)Overview:Linesinagraphsuggesttrendsandpatternsinthedata.Changeisimpliedasyoumovefromoneitemtothenext.Ifthedatapointsarenotcloselyrelatedthroughacontinuousrangeofvalues,thenthepointscannotbeconnectedbyaline.Linegraphsshouldonlybeusedtolinkdatapointsalonganintervalscale.Unitsoftime(seconds,minutes,hours,days,weeks,months,years,etc.)arethemostcommonintervalscales.Linegraphsorhistogramscanalwaysbeusedwithtimeasacategoricalscale.Ifyouwishtoemphasizetheshapeorchangeinthedata,thenlinegraphsarethemostappropriate.Ifyouwishtoemphasizeindividualitems,thenhistogramscanbemosteffective.
3.4.6:ClassifyingCategoricalScales(TeacherNotes)Foreachgraphbelowindicatethetypeofcategoricalscaleandwhetherthegraphisappropriate(i.e.shouldlinesbeusedorisahistogrammoreappropriate?)ANALYSIS:Nominalcategoricalscale.ANALYSIS:Nominalcategoricalscale.Linegraphinappropriate.Histogramappropriatelyused.ANALYSIS:IntervalcategoricalscaleANALYSIS:Intervalcategoricalscale.Linegraphappropriatelyused.Histogramappropriatelyused.ANALYSIS:Intervalcategoricalscale.ANALYSIS:Intervalcategoricalscale.Linegraphappropriatelyused.Eachgraderepresentsanequalintervaloftime.Histogramappropriatelyused.Withintervalscales,youmayuselinegraphsorhistograms.
3.4.6:ClassifyingCategoricalScales–(TeacherNotes)(continued)ANALYSIS:Ordinalscale.ANALYSIS:Ordinalscale.LinegraphinappropriateHistogramappropriate
Unit3:Day6:TennisAnyone?(Part1)MindsOn:10LearningGoal:Generateagraphicalsummary(boxandwhiskerplot,histogram)ofaonevariabledataset.Calculatemeasuresofcentraltendencyforaone-variabledataset.MaterialsTechnology(Fathom2,Excel,TI-83)Action:55Consolidate:10Total=75min Assessment
OpportunitiesMindsOn…WholeClassDiscussionStudentsengageinadiscussionregarding“theprimeofyourlife”.Whendoesanathletepeak?Istheprimeageforathleticactivitydifferentformenandwomen?Whatdatawouldyouneedtorespondtothisquestion?UsetheWimbledonDataSet,attachedinBLM3.6.1.Inthedatasets,theagesofthedoubleschampionsarebothgiven–studentswillhavetodecideifusingtheaverageageoftheteamisappropriate.Action!SmallGroupsTennisAnyone?Studentsgetintogroupsoffour.Eachmembertakesoneofthedatasetsandperformsstatisticalanalysisusingthetoolslearnedsofar(mean,median,mode,standarddeviation,graphicalrepresentations)todeterminetheprimeageofatennischampion.ProcessExpectations/Observation/MentalNoteObservestudents’communicationskillsastheydiscussthestatisticalanalysisnecessarytoanswerthequestion.Checkthatthestudentshaveanaccurateunderstandingofmeasuresofcentraltendency.ConsolidateDebriefWholeClassDiscussionStudentengageinadiscussionregardinganyobstaclesfacedandhowtheywereovercome.ProcessExpectations/Observation/ChecklistObservestudents’communicationskillsastheydiscusswhataspectsoftheanalysisweredifficult.ReflectionHomeActivityorFurtherClassroomConsolidationInyourjournal,completethesentence“Inmygroup,myroleisto…”3.6.1:TennisAnyone?Question:Domenandwomenreachtheir“athleticprime”atdifferentages?OneofthemostprestigioustennistournamentsintheworldisTheChampionships,Wimbledon,heldeverysummerattheAllEnglandLawnTennisandCroquetClubinLondon,England.EachmemberofyourgroupisbeingassignedonedatasetfromthistournamentthatlistschampionsfromWimbledonsince1968.Inthespacesbelow,recordwhichgroupmemberisresponsibleforeachdataset.WomensSingles:________________ MensSingles:________________WomensDoubles:________________ MensDoubles:________________Plan:Whatstatisticalmeasuresandgraphicalrepresentationswillassistyouinansweringthequestion?Decideasagrouphowyouwillanalysethedatasets(whattoolswillbeused)andhowyourfindingswillbereportedbacktothegroup.Summarizeyourplaninthespacebelow.
3.6.1:TennisAnyone?(continued)WomensSinglesChampions,Wimbledon,1968topresentYearWomensChampionAge1968BillieJeanKing241969BillieJeanKing251970BillieJeanKing261971AnnHaydon-Jones321972MargaretSmithCourt291973EvonneGoolagong211974BillieJeanKing301975BillieJeanKing311976ChrisEvert211977VirginiaWade321978MartinaNavrátilová211979MartinaNavrátilová221980EvonneGoolagong-Cawley281981ChrisEvert-Lloyd261982MartinaNavrátilová251983MartinaNavrátilová261984MartinaNavrátilová271985MartinaNavrátilová281986MartinaNavrátilová291987MartinaNavrátilová301988SteffiGraf191989SteffiGraf201990MartinaNavrátilová331991SteffiGraf221992SteffiGraf231993SteffiGraf241994ConchitaMartínez221995SteffiGraf261996SteffiGraf271997MartinaHingis161998JanaNovotná291999LindsayDavenport232000VenusWilliams202001VenusWilliams212002SerenaWilliams202003SerenaWilliams212004MariaSharapova172005VenusWilliams252006AmélieMauresmo272007VenusWilliams27
3.6.1:TennisAnyone?(continued)WomensDoublesChampions,Wimbledon,1968topresentYearWomensDoublesChampionsAges1968RosieCasals/BillieJeanKing19/241969MargaretSmithCourt/JudyTegartDalton26/311970RosieCasals/BillieJeanKing21/261971RosieCasals/BillieJeanKing22/271972BillieJeanKing/BettyStove28/271973RosieCasals/BillieJeanKing24/291974EvonneGoolagong/PeggyMichel22/251975AnnKiyomura/KazukoSawamatsu19/241976ChrisEvert/MartinaNavrátilová21/191977HelenGourlayCawley/JoAnneRussell30/221978KerryReid/WendyTurnbull30/251979BillieJeanKing/MartinaNavrátilová35/221980KathyJordan/AnneSmith20/211981MartinaNavrátilová/PamShriver24/191982MartinaNavrátilová/PamShriver25/201983MartinaNavrátilová/PamShriver26/211984MartinaNavrátilová/PamShriver27/221985KathyJordan/ElizabethSmylie25/221986MartinaNavrátilová/PamShriver29/241987ClaudiaKohde-Kilsch/HelenaSuková23/221988SteffiGraf/GabrielaSabatini19/181989JanaNovotná/HelenaSuková20/241990JanaNovotná/HelenaSuková21/251991LarisaNeiland/NatashaZvereva24/201992GigiFernandez/NatashaZvereva28/211993GigiFernandez/NatashaZvereva29/221994GigiFernandez/NatashaZvereva30/231995JanaNovotná/ArantxaSánchezVicario26/231996MartinaHingis/HelenaSuková15/311997GigiFernandez/NatashaZvereva33/261998MartinaHingis/JanaNovotná17/291999LindsayDavenport/CorinaMorariu23/212000SerenaWilliams/VenusWilliams18/202001LisaRaymond/RennaeStubbs27/302002SerenaWilliams/VenusWilliams20/222003KimClijsters/AiSugiyama20/272004CaraBlack/RennaeStubbs25/332005CaraBlack/LiezelHuber26/282006ZiYan/JieZheng21/232007CaraBlack/LiezelHuber28/30
3.6.1:TennisAnyone?(continued)MensSinglesChampions,Wimbledon,1968topresentYearMensChampionAge1968RodLaver291969RodLaver301970JohnNewcombe251971JohnNewcombe261972StanSmith251973JanKode?271974JimmyConnors211975ArthurAshe321976Bj?rnBorg201977Bj?rnBorg211978Bj?rnBorg221979Bj?rnBorg231980Bj?rnBorg241981JohnMcEnroe221982JimmyConnors291983JohnMcEnroe241984JohnMcEnroe251985BorisBecker171986BorisBecker181987PatCash221988StefanEdberg221989BorisBecker211990StefanEdberg241991MichaelStich221992AndreAgassi221993PeteSampras211994PeteSampras221995PeteSampras231996RichardKrajicek241997PeteSampras251998PeteSampras261999PeteSampras272000PeteSampras282001GoranIvani?evi?29200
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