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Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning Grade Four Module 6. Partners for Mathematics Learning. 2. Mathematics Learning…  Mathematics learning is about making sense of mathematics  Mathematics learning is about acquiring skills and insights to solve problems NCTM Standards 2000

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning GradeFour Module6 Partners forMathematicsLearning

  2. 2 MathematicsLearning… Mathematicslearningisaboutmaking senseofmathematics Mathematicslearningisaboutacquiring skillsandinsightstosolveproblems NCTMStandards2000 Mathematicslearningisaboutempowering students Partners forMathematicsLearning

  3. 3 BeaMathematicsLearner… Ibakedcookiesandleftonehalfofthemin aboothatthestatefair.ThenIateonehalf acookie Mybrotherwantedsomecookies,soI gavehimonehalfofthecookiesIhadleft andthenIateonehalfofacookie MymomwantedonehalfofthecookiesI hadleft.AfterIgavethemtoher,Iateone halfofacookie Partners forMathematicsLearning

  4. 4 BeaMathematicsLearner… Mylittlesisterlikescookies,soIgaveher onehalfofthecookiesIhadleftandIthen ateonehalfofacookie NowIhaveonecookieleft HowmanycookiesdidImake? Partners forMathematicsLearning

  5. 5 BeaMathematicsLearner… Howdidyousolvetheproblem? Whatproblemsolvingstrategiesdidyou employ? Howdidyoudealwithnothavingaready answertotheproblem? Whenstudentsdonotthinktheycansolve aproblem,howdoyouencouragethem withoutgivingtoomanyhints? Partners forMathematicsLearning

  6. 6 ImplementingthePCAIModel “GettingtoKnowUs” Part1 Poseaquestion Collectdata Part2 Analyzethedata Interpretthedata Partners forMathematicsLearning

  7. 7 Step3:AnalyzetheData Organize,summarize,describeand displaythedata Lookforpatternsinthedata Representthedatainordertoidentify patternsandtrends Mannerofrepresentationdependsonthetype ofdataandwhytheyhavebeencollected Partners forMathematicsLearning

  8. 8 AnalyzingData Graphicaldisplaysprovidevisual descriptionsof… Datasetvariability Datasetshape MeasuresofCenter Median Mode Mean Partners forMathematicsLearning

  9. 9 Graphs Graphsprovideameansfor Communicatingandclassifyingdata Comparingdataanddisplaying mathematicalrelationshipsthatoften cannotbeeasilyseeninnumericform Integratinggeometricideaswith computationskillsandclassification taskswithnumericunderstandings Partners forMathematicsLearning

  10. 10 DataDisplays PictorialGraphs LinePlots VennDiagrams StemandLeafPlots BarGraphs CircleGraphs Linegraphs Partners forMathematicsLearning

  11. 11 YourTurn… Prepareareviewofyourassignedgraph Howtocreateyourgraph Theusesofyourgraph Howtointerpretdataonyourgraph Partners forMathematicsLearning

  12. 12 PictorialGraphs Partners forMathematicsLearning

  13. 13 LinePlots TimeSpentPlayingVideo Games =1Student 0 1 2 3 4 5 6 7 8 NumberofHoursThisWeek Partners forMathematicsLearning

  14. 14 VennDiagram Partners forMathematicsLearning

  15. 15 StemandLeafPlot  Partners forMathematicsLearning

  16. 16 StemandLeafPlots 8 7 6 5 4 3 3 5 2258 35 875542 531 53300 55 Back-to-BackStem andLeafPlot Key: 35=35 20 98555 740 2 1 0 0001448 55557999 0023668 Partners forMathematicsLearning

  17. 17 DiscreteandContinuousData •DiscreteData: Basedoncounts Finitenumberofpossiblevalues Cannotbemeaningfullysubdivided •ContinuousData Canbemeasuredonascaleorcontinuum Canbemeaningfullysubdivided Partners forMathematicsLearning

  18. 18 SameData…DifferentAppearance FavoriteFoodsSurvey(circlegraph) FavoriteFoodsSurvey(bargraph) Tacos 13% 30 Pizza 27% 25 20 Hamburgers 23% NumberfoVotes 15 10 5 HotDogs 21% 0 Steak 16% Pizza HotDogs Steak Hamburgers Tacos Comparetheinformationonthesetwographs Partners forMathematicsLearning

  19. 19 LineGraphs TemperatureReadings 90 80 70 60 50 40 30 Fahrenheit) Temperature(Degrees 8:00 A.M. 9:0010:0011:0012:00 A.M.A.M.A.M.P.M. 1:00 P.M. 2:00 P.M. 3:00 P.M. 4:00 P.M. 5:00 P.M. 6:00 P.M. 7:00 P.M. 8:00 P.M. TimeofDay Partners forMathematicsLearning

  20. 20 ScaleMatters Partners forMathematicsLearning

  21. 21 Graphs: HandmadeorComputerGenerated? Inyourgroups,discussthe pro’sandcon’sof handmadeandcomputer generatedgraphs Trueorfalse:computers candisplaydatainappropriately Partners forMathematicsLearning

  22. 22 Graphs: HandmadeorComputerGenerated? Thevalueofhavingstudentsactually constructtheirowngraphsisnotsomuch thattheylearnthetechniquesbutthatthey arepersonallyinvestedinthedataand theylearnhowagraphconveys information TeachingStudentCenteredMathematics JohnVandeWalle Partners forMathematicsLearning

  23. 23 FourthGradeData:FingerSnaps FingerSnapsforGirls FingerSnapsforBoys Partners forMathematicsLearning

  24. 24 DataAnalysisVocabulary Minimum:thelowestnumerical valueinthedataset Maximum:thelargestnumerical valueinthedataset Range:thedifferencebetweenthe minimumandmaximumvalues Partners forMathematicsLearning

  25. 25 DataAnalysisVocabulary Mode:thedatavalueoccurringmost frequentlyinadataset Median:themiddlevalue inanordereddataset Mean:thearithmetic average;thevalueif eachdataintheset werethesamevalue Partners forMathematicsLearning

  26. 26 ModeandMedian Createasetofnumericaldatainwhichthe modeisnotthebestmeasureofcenter Createasetofnumericaldatainwhichthe medianisnotthebestmeasureofcenter Partners forMathematicsLearning

  27. 27 UnderstandingMean Buildtowerswiththefollowing numbersofcubes:4,6,7,7,3,3 Findthemeanbyadjustingtheheightsof thetowers Partners forMathematicsLearning

  28. 28 Mean Fourboyscollectbaseballcards Whensharedfairlyamongthe4boys, eachboyhas7cards Jackhas5cards,Marcushas10cards andTyronehas8 Howmanycardsdoes Albertohave? Partners forMathematicsLearning

  29. 29 Mean Createasetofnumericaldatainwhichthe meanisnotthebestmeasureofcenter Talktoyourneighbor:Suggestacontextin whichmeanwouldnotbethebest measureofwhatistypical Partners forMathematicsLearning

  30. 30 MysteryGraphs CompletetheMysteryGraphshandoutby matchingthegraphswiththeirtitles Next,analyzethegraphsbasedonthe SHAPEofthedata Partners forMathematicsLearning

  31. 31 MysteryGraphs Writequestionsyoumightaskchildren aboutyourgroup’sassignedgraph Partners forMathematicsLearning

  32. 32 WhatCouldThisRepresent? Partners forMathematicsLearning

  33. 33 Duke,Carolina,orState? Partners forMathematicsLearning

  34. 34 BacktoYourQuestion… Handout2:DataQuestions Followdirectionsandrespondtothequestions Useasaguidelineforpresentation Handout3:Presentationguidelines Usetohelporganizeyourpresentationtothe group Partners forMathematicsLearning

  35. 35 It’sShowTime… Shareyourinformation Partners forMathematicsLearning

  36. 36 IntegrationofStrands Whatothermathematicsobjectivesare incorporatedintothisDataTask? Partners forMathematicsLearning

  37. 37 Reflection:ProcessStandards Didyouuse… Problem-Solving Communication Representation Connections ReasoningandProof Givespecificexamples Partners forMathematicsLearning

  38. 38 PCAIwithStudents Makeaplanforclassroomimplementation Whatkindsofscaffoldingdo childrenneedtobesuccessful inunderstandingthemath? Whenistheredangerintoo muchscaffolding? Partners forMathematicsLearning

  39. 39 MathematicsLearning… Mathematicslearningisaboutmaking senseofmathematics Mathematicslearningisaboutacquiring skillsandinsightstosolveproblems NCTMStandards2000 Mathematicslearningisaboutempowering students Partners forMathematicsLearning

  40. 40 DevelopingMathematicalPower Empoweringstudentsto… Understandmathematics Usemathematics Enjoymathematics Haveconfidenceinthemselvesas mathematicsstudents Partners forMathematicsLearning

  41. 41 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

  42. 42 PMLDisseminationConsultants SusanAllman JuliaCazin RuafikaCobb AnnaCorbett GailCotton JeanetteCox LeanneDaughtry LisaDavis RyanDougherty ShakilaFaqih PatriciaEssick DonnaGodley ShanaRunge YolandaSawyer PennyShockley PatSickles NancyTeague MichelleTucker KanekaTurner BobVorbroker JanWessell DanielWicks CarolWilliams StacyWozny CaraGordon TeryGunter BarbaraHardy KathyHarris JulieKolb ReneeMatney TinaMcSwain MarilynMichue AmandaNorthrup KayonnaPitchford RonPowell SusanRiddle JudithRucker Partners forMathematicsLearning

  43. 43 2009Writers PartnersStaff KathyHarris RendyKing TeryGunter JudyRucker PennyShockley NancyTeague JanWessell StacyWozny AmandaBaucom JulieKolb FredaBallard,Webmaster AnitaBowman,OutsideEvaluator AnaFloyd,Reviewer MeghanGriffith,AdministrativeAssistant TimHendrix,Co-PIandHigherEd BenKlein,HigherEducation KatieMawhinney,Co-PIandHigherEd WendyRich,Reviewer CatherineStein,HigherEducation PleasegiveappropriatecredittothePartners forMathematicsLearningprojectwhenusingthe materials. JeaneJoyner,Co-PIandProjectDirector Partners forMathematicsLearning

  44. 44 PARTNERS forMathematicsLearning GradeFour Module6 Partners forMathematicsLearning

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