Partners for Mathematics Learning

1. 1 PARTNERS forMathematicsLearning Grade3 Module5 Partners forMathematicsLearning

2. 2 BigIdeasinData Datacanbeeithercategoricalornumerical Pose,Collect,Analyze,Interpretisamodel fortheprocessofstatisticalinvestigations Differentrepresentationsandgraphs classifyandcommunicatedata Understandingbasicconcepts ofprobabilityallowustomake moreaccuratepredictions

3. 3 CategoricalandNumericalData Studentsneedtodistinguishbetween questionsthatgivecategoricaland numericaldatabeforetheyposea questionandtrytointerpretthedata Justbecausenumbersareinvolved, dataarenotautomaticallynumerical Partners forMathematicsLearning

4. 4 CategoricalData Valuesthatareoftenwordsthatrepresent possibleresponseswithrespecttoagiven category Representindividualsorobjectsbyoneormore characteristicsortraitsthattheyshare Examples: Monthsinwhichpeoplehavebirthdays Bestplacestoeat Favoritefruits StatesVisited

5. 5 CategoricalData Valuesofthedatacanbeclassifiedand graphedbuthavenoinherentorder Somesetsofcategoricaldatahavemany differentvalues Questionsarerelatedtohowthedata areorganized Partners forMathematicsLearning

6. 6 ProcessofStatisticalInvestigation Posethequestion Collectthedata Analyzethedata Interpretthedata Partners forMathematicsLearning

7. 7 PosingaQuestion Posethequestion Identifyaspecificquestiontoexplore Thinkabouttheinformationyouwanttoknow Decidewhatdatatocollecttoaddressthe question Whataresomeissuesthatwillarisewhen 3rdgraderscreatequestions? Partners forMathematicsLearning

8. 8 PosetheQuestion Alldatainvestigationsbeginwith aproblemorquestion Questionsshouldbefocused&precise Questionsmayneedtoberefined Studentsneedmultipleexperiences withposingquestionsandcarrying-out investigations Eachquestionshouldhaveapurpose

9. 9 DevelopingCategories Whatwouldyouchooseasyourdream occupation? Howmightyouorganizeorclassify thedata? Differentquestionscanbeanswered byorganizingthedataindifferentways

10. 10 RefiningtheQuestion Somesetsofcategoricaldata canhavemanydifferentvalues orcategories Tomakesenseofthedata,classifythe dataintoafewmajorcategories Toofewcategoriesmaygivelimited information Toomanycategoriesmayresultinfew datapiecesineachcategory Partners forMathematicsLearning

11. 11 RefiningtheQuestion Whatdoyounoticeaboutyourdata? Whatmakesagoodcategory? Discussdifferentwaysyoumight categorizethedata Aretherewaystorearrangethedatato makethemeasiertounderstand Howcouldwearrangethedatatosee whethermorepeoplewereinterestedina professioninthearts?Inmedicine? Partners forMathematicsLearning

12. 12 Organize-RefinetheQuestion Cananyofthesedatabeconsidered together? Aretherewaysinwhichsomeofourdata arethesame?Different? Whatdowedowhenapieceofdatadoes notfitinanycategory? Whatotherideasdoyouhaveaboutways toclassifythesedata? Partners forMathematicsLearning

13. 13 CategoricalData Whatquestionsmightbe posedbythirdgraders? Whatdoyouwanttodowhenyougrowup? WhatisyourfavoriteWiigame? Whatdoyouliketodoinyourfreetime? Ifyoucouldbeanyanimalforaday,what animalwouldyoube? Wheredoyouliketoplay? Wheredoyouliketoeat?) Partners forMathematicsLearning

14. 14 BarGraph showing ungrouped data BarGraph HowManyBooksReadSoFarThisSchoolYear 6 5 4 3 2 1 0 Students NumberofBooksRead ic am b ad ia y in e e ne co Er si rg ar Er Br Li s Ja M Jo rt Ca ou C

15. 15 BarGraph HowManyBooksReadThisYear? 4 3 2 1 0 NumberofStudents 1 2 3 4 5 NumberofBooksRead

16. 16 NumericalData Valuesthatarenumbers(counts, measurements,ratings) Representobjectsorindividualsby numbersassignedtocertainmeasurable properties Numberofyearsineducation Milesdriventoprofessional development Timeinminutestogettowork

17. 17 NumericalData Thequestionposedshould resultindatathatarequantities Doesthequestion,“Whatisyourfavorite number”resultinquantitativedata? Giveexamplesandnonexamplesof questionsthatresultinquantitativedata? Answerstoquestionsshouldbean “amountofsomething” Partners forMathematicsLearning

18. 18 TalkwithaPartner Whataresomenumericaldata questionsyourstudentscould explore? Partners forMathematicsLearning

19. 19 PCAIModel Processof Statistical Investigation Partners forMathematicsLearning

20. 20 PosetheQuestion Poseaquestiontodeterminethe distanceofyourgiantstep Questionshouldbefocusedandprecise Whatdoyouexpecttolearnfromthis investigation? Question(s)mayneedtoberefined Partners forMathematicsLearning

21. 21 ProcessofMeasurement Determine typeofgiantsteptobemeasured attributetobemeasured appropriateunit processformeasuringthe distanceofthegiantstep thenumberofunitsmeasured Partners forMathematicsLearning

22. 22 CollecttheData Step2:Firstdecide howtocollectthedata Notetheprocessofmeasurementis thesameforallattributes Anappropriateunithavingthesame attributeisneeded Sizeoftheunitshouldrelate reasonablytosizeofobjectbeing measured Partners forMathematicsLearning

23. 23 Guidelines Insmallgroups,suggest guidelinesneededto collectdata Startingline?Positionoffeetonline Howtomeasurethedistanceofagiantstep Measuringdistanceofstep–beginandend Practicetrials?Bestoutof2tries? Howwilldataberecorded? Othersourcesofvariations? Partners forMathematicsLearning

24. 24 Decisions Decidehowtorecord thedata Partners forMathematicsLearning

25. 25 RecordtheData Decideonthemethod ofrecordingdataand collectthedata Whentousecentimeter Whentousehalfcentimetermeasure Willtherebepracticetrials? Shareyourdata Partners forMathematicsLearning

26. 26 AnalyzetheData Step3: Organize,summarize,describe,and displaythedata;andlookfor patternsinthedata Partners forMathematicsLearning

27. 27 DataAnalysisVocabulary Mode:thedatavalueoccurringmost frequentlyinadataset Minimum:thelowestnumericalvalue inthedataset Maximum:thelargestnumerical valueinthedataset Range:thedifferencebetweenthe minimumandmaximumvalues Partners forMathematicsLearning

28. 28 UsesofGraphs Graphsprovideameansfor: Communicatingandclassifyingdata Comparingdataanddisplaying mathematicalrelationshipsthatoften cannotbeeasilyseeninnumericform Integratinggeometricideaswith computationskillsandclassification taskswithnumericunderstandings

29. 29 LinePlots Quick,simplewaytoorganizedata UsesX’s(orothersamesizedsymbols) onasinglehorizontalaxis Includesallnumberswithintherangeof thedatasetontheaxistoshowholes andtheshapeofthedata Partners forMathematicsLearning

30. 30 PocketDataShownTwoWays 012345678910 Orderedsetof“pockettowers”showingdata Partners forMathematicsLearning

31. 31 LinePlot x x x xx xx Howmanytotal pocketsareinthe class? x x xxxxx xxxxxxx 012345678910 Pockets Partners forMathematicsLearning

32. 32 012345678910 Comparing x x x xx xx xxxxxx xxxxxxxx 012345678910 Partners forMathematicsLearning

33. 33 LinePlot–Clumps,Gaps,Trends Howmanystarscanyoudrawinone minute?x x x xxx xxxxx xxxxxxxx 343536373839404142434445 Partners forMathematicsLearning

34. 34 InterpretingtheData InterprettheResults Whatdoyouknowaboutthetypicalnumberof starsdrawninthisclass? Howarethedataspreadout? Whatdoyounoticeabouttheshapeofthe data? Whatmightyoupredictiftheclasscollected dataonanotherday? Partners forMathematicsLearning

35. 35 BarGraph Horizontalorverticalbars ofuniformwidth Heights(orlengths)areproportionalto thequantitiestheyrepresent Comparesfrequenciesofgrouped, discretequantitiesorofungroupedvalues Axesarelabeledtoindicatevalueor frequency Partners forMathematicsLearning

36. 36 BarGraph HowManyBooksReadThisYear? 4 3 2 1 0 NumberofStudents 1 2 3 4 5 NumberofBooksRead

37. 37 AnalyzetheData Representingthedatainorderto identifypatternsofvariationinthedata Mannerofrepresentationdependsonwhy thedatahavebeencollectedandwhat typeofdatahavebeencollected Graphicaldisplaysprovidevisual descriptionsofvariabilityindata(clusters, outliers)andwaystoanalyzethedata (range,median,mode)

38. 38 AnalyzingData Eachgroupwillcreatealine plotandabargraphoftheclassdata Howdoesthedatarelatetoyour question? Describethe“shapeofthedata” Howarethedataspreadout? Arethereanycluster?Gaps? Arethereanyunusualdatavalues? Partners forMathematicsLearning

39. 39 AnalyzeandInterpret: Interprettheresults Relatetheanalysestothe investigationquestion Drawandjustify conclusions Communicatetheresults andconclusions Partners forMathematicsLearning

40. 40 InterpretResults Whatdoyounoticeaboutthedistribution of“GiantStep”data?” Arethereanyclusters?Gaps?Unusual datavalues? Whatmightyousayistypical?Other predictions? Partners forMathematicsLearning

41. 41 CompareRepresentations Discussthedifferentaspectsofthedata shownbythelineplotandthebargraph Whyisitimportantfor studentstocompare representationsofdata? Partners forMathematicsLearning

42. 42 ConnectingDataandMeasurement HowLongisOurGiantStep? Wherearetheconnections tomeasurement? Iteration Partitioning Transitivity CompensatoryPrinciple Partners forMathematicsLearning

43. 43 Extensions Howfarcanyou“frog”jump? Howfarcanyou“rabbit”jump? Partners forMathematicsLearning

44. 44 IfYouHoppedLikeaFrog Ifyouhoppedlikeafrog, youcouldjumpfrom homeplatetofirstplate inonemightyleap Partners forMathematicsLearning

45. 45 MysteryData Whatmightthegraphbelowshow? x x xx xx xxxx xxxxx xxxxxxxx 012345678 Partners forMathematicsLearning

46. 46 MysteryData Chooseoneofthelineplots Explainwhatthedatacouldrepresent withabriefstory Usethedatainthegraphyouchooseto createabargraph Titleandlabelthegraphappropriately Partners forMathematicsLearning

47. 47 ProcessisImportant Processisasmuchapartofdoing mathematicsasthecontentitself ReviewtheEssential Standardsfor Statistics Identifyexperiences thatwillsupport studentsinattaining datasense Partners forMathematicsLearning

48. 48 “Theemphasisonworking withdataentailsstudents’ meetingnewideasand proceduresasthey progressthroughthe gradesratherthanrevisiting thesameactivitiesandtopics” NCTM,2000 Partners forMathematicsLearning

49. 49 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

50. 50 PMLDisseminationConsultants SusanAllman JuliaCazin RuafikaCobb AnnaCorbett GailCotton JeanetteCox LeanneDaughtry LisaDavis RyanDougherty ShakilaFaqih PatriciaEssick DonnaGodley CaraGordon TeryGunter BarbaraHardy KathyHarris JulieKolb ReneeMatney TinaMcSwain MarilynMichue AmandaNorthrup KayonnaPitchford RonPowell SusanRiddle JudithRucker ShanaRunge YolandaSawyer PennyShockley PatSickles NancyTeague MichelleTucker KanekaTurner BobVorbroker JanWessell DanielWicks CarolWilliams StacyWozny Partners forMathematicsLearning