Partners for Mathematics Learning

1. PARTNERS forMathematicsLearning Grade7 Module1 Partners forMathematicsLearning

2. 2 VideoOverview Welcometothefirstofsixmodulesof Partnersprofessionaldevelopment forteachersofseventhgrade Partners forMathematicsLearning

3. 3 Problems,Problems,Problems SorttheBigIdeasfromyourbagaccording tothe5strands Readtheproblemsaloudwithinyourgroup anddecidewhichproblemgoeswitheach BigIdea Bereadytosupportyouranswers Partners forMathematicsLearning

4. 4 ReviewingtheBigIdeas Werethereproblemsthatfitwithmore thanoneBigIdea?Ifso,whichones? Howcouldyouusesomeofthese problemsinyourclassroom? Partners forMathematicsLearning

5. 5 WhatisESSENTIAL? Lookatthenew2009StandardCourse ofStudyforgradeseven Whatdoyounoticeaboutthewaythe essentialsarewritten? Isthereanythingthat“jumpsout”thatis differentfromthecurrentcurriculum? Partners forMathematicsLearning

6. 6 SumsandWhiskers Completetheadditionchartwiththe sumsthatrepresenttherollingoftwo numbercubes Findandrecordthetheoretical probabilitiesofrollingeachpossiblesum Whatdothedatatellyou? Partners forMathematicsLearning

7. 7 SumsandWhiskers Rollthenumbercubes25timesandrecord thesumofthefacesinafrequencytableor lineplot Findandrecordtheexperimentalprobabilities ofrollingeachpossiblesum Compareandcontrastyourexperimental probabilitieswiththetheoreticalprobabilities Partners forMathematicsLearning

8. 8 SumsandWhiskers Usingyour25sums,findthemeasuresof center(mean,median,andmode) Howdothesedatarelatetothetheoretical probabilities? Createabox-and-whiskerplotusingyour 25sums Howdothesedatarepresentedonthe box-and-whiskerplotrelatetothe theoreticalprobabilities? Partners forMathematicsLearning

9. 9 SumsandWhiskers Whatdatacharacteristicsaremasked bythebox-and-whiskerplot? Compareyourresultswithanotherpairof participants Doesvariabilityexistbetweenthetwo samples? Partners forMathematicsLearning

10. 10 SumsandWhiskers Whatbigideaisthefocusofthisactivity? Howdoesthisactivityhelpstudentsrelate probabilitytodataanalysis? Howdoesthisactivityhelpstudentsthink aboutmeasuresofcenterinrelationto probabilityanddistribution? Partners forMathematicsLearning

11. 11 Three-PartFormatfor Problem-BasedLearning Beforebeginningthetask Getstudentsmentallyprepared Besurethetaskisunderstood Establishexpectations TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

12. 12 Three-PartFormatfor Problem-BasedLearning Beforebeginningthetask,studentsmight askthemselves WhatamIbeingaskedtodo? WhatfactsdoIknow? IsthereanyinformationIneedtopay particularattentionto? WhatkindofanswerdoIexpecttoget? Partners forMathematicsLearning

13. 13 Three-PartFormatfor Problem-BasedLearning Howwouldyoubegintodevelopthese behaviorsinyourstudents? Whatotherpreparationmaybeneeded? Partners forMathematicsLearning

14. 14 Three-PartFormatfor Problem-BasedLearning During-workingonthetask Letgo Providehints Listenactively Encouragetestingofideas TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

15. 15 Three-PartFormatfor Problem-BasedLearning During-workingonthetask Supportstudentsdoingthethinking Givepointersnotstep-by-stepadvice “Showmehowyougotyouranswer” “Howdoyouknowyouarecorrect?” Partners forMathematicsLearning

16. 16 Three-PartFormatfor Problem-BasedLearning After-whentheworkiscomplete Providefeedback Usepraisecautiously Engagethefullclassindiscussion TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

17. 17 Three-PartFormatfor Problem-BasedLearning After-whentheworkiscomplete “Actionable”feedbackhelpsstudentsknow whattotryagainandwhattoavoid “Veryclearexplanation”or“Youmadea goodprediction” “Howarethedifferentapproachessimilar?” Partners forMathematicsLearning

18. 18 XMarkstheSpot Makeaprediction:Usingyourrighthand, howmanyx’scanyoumarkoncmgrid paperin30seconds? Collectthedata:Whentheinstructorsays go,beginmarkingx’s(fromcornerto corner,diagonally)usingyourrighthand Theinstructorwilltellyouwhentostop Partners forMathematicsLearning

19. 19 XMarkstheSpot Recordyourresultonastickynoteand placestickynoteontheclasslineplot Usingtheclassdata,completethetable onthehandout Repeattheprocesswithyourlefthand Partners forMathematicsLearning

20. 20 XMarkstheSpot Usingthetwosetsofdata,createaback tobackstemandleafplotorstackedbox andwhiskerplotsongraphpaper Answerthequestionsonparttwoofthe handoutandbereadytodiscussyour findings Partners forMathematicsLearning

21. 21 XMarkstheSpot Whichsetofdatahasthegreatermedian? Howcanyoutellthisbylookingatyour displayofdata? Whichsetofdatahasthegreatermean?Why doyouthinkthissethasthegreatermean? Whichsetofdatahasthegreaterrange?Do outliersaffecttherange?Explain Partners forMathematicsLearning

22. 22 XMarkstheSpot Analyzethedatabydescribingtheshape andvariability Interpretthedata:Whatconjecturesand inferencescanbemaderegardingthe classpopulation? Whydowehavetobecarefultryingto makeconjecturesaboutalarger populationbasedonthisdata? Partners forMathematicsLearning

23. 23 XMarkstheSpot Howdoescollectingandanalyzing authenticdatamakeconnectionsfor students? Howdoeslookingattwosamplesof relateddataallowstudentstomake conjecturesandinferencesabouta population? Partners forMathematicsLearning

24. 24 Problem-BasedLearning Inouractivitiesweprovidedstructureand organizationforthetasks Howdostructuredtaskssuchastheseset thestageforgreaterindependencein solvingproblems? Whatwouldbegoodproblemsforstudents whohaveexperiencedthesetasks? Partners forMathematicsLearning

25. 25 Reflection Reviewingthethree-partformatfor problem-basedlearning,whichofthe threephasesdoyouseeasastrengthin yourclassroomandinwhichphasedo youwanttoimprove? Writeanotetoyourself andputitinyour planningbook Partners forMathematicsLearning

26. 26 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

27. 27 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

28. 28 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

29. PARTNERS forMathematicsLearning Grade7 Module1 Partners forMathematicsLearning