Partners for Mathematics Learning

1. 1 PARTNERS forMathematicsLearning GradeSix Module1 Partners forMathematicsLearning

2. 2 VideoOverview Welcometothefirstofsixmodulesof Partnersprofessionaldevelopment forteachersofsixthgrade Partners forMathematicsLearning

3. 3 Problems,Problems,Problems SorttheBigIdeasfromyourbagaccording tothe5contentstrands Readtheproblemsaloudwithinyourgroup anddecidewhichproblemgoeswitheach BigIdea Bereadytosupportyouranswers Partners forMathematicsLearning

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

5. 5 WhatisESSENTIAL? Lookatthenew2009standardcourseof studyforgradesix Whatdoyounoticeaboutthewaytheyare written? Isthereanythingthat“jumpsout”thatis differentfromthecurrentcurriculum? Partners forMathematicsLearning

6. 6 ValueofTeachingwithProblems Focusesstudents’attentiononideasand sensemaking Developsabeliefthatstudentsareableto domath Providescontinuousassessment Providestheopportunityformultiplesolutions TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

7. 7 ValueofTeachingwithProblems Engagesstudents Developsmathematicalpower Makeslearningmathematicsfun Howdoyouselectactivitiesfor yourclassroom?Whatcriteria shouldbeused? Partners forMathematicsLearning

8. 8 FiddlingwithFactors Usethe“FiddlingwithFactors”activity sheet Worktogetherwithyourgrouptofind thefactorsoftheintegers1to30 Partners forMathematicsLearning

9. 9 FiddlingwithFactors PerfectNumber:Sumoftheproper factors(excludingthenumberitself)isequal tothenumber AbundantNumber:Sumoftheproper factors(excludingthenumberitself)isgreater thanthenumber DeficientNumber:Sumoftheproperfactors (excludingthenumberitself)islessthanthe number Partners forMathematicsLearning

10. 10 FiddlingwithFactors Definitionsofperfect,abundant,and deficientnumbersincludetheterm properfactors Determinewhichintegersfrom1to30 areperfect,abundant,ordeficient Partners forMathematicsLearning

11. 11 FiddlingwithFactors Howmanyperfectnumbersare therelessthanorequalto30? Abundantnumbers? Deficientnumbers? Isthereapatternfordeterminingthese numbers? Partners forMathematicsLearning

12. 12 FiddlingwithFactors WhichBigIdeawasthefocus ofthisactivity? Wheredoesthiscontentfitintothe essentialstandards? Howwouldyouusethisactivityinyour classroom? Partners forMathematicsLearning

13. 13 Three-PartFormatfor Problem-BasedLearning Beforebeginningthetask Getstudentsmentallyprepared Besurethetaskisunderstood Establishexpectations TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

14. 14 Three-PartFormatfor Problem-BasedLearning Beforebeginningthetask,studentsmight askthemselves WhatamIbeingaskedtodo? WhatfactsdoIknow? IsthereanyinformationIneedtopay particularattentionto? WhatkindofanswerdoIexpecttoget? Partners forMathematicsLearning

15. 15 Three-PartFormatfor Problem-BasedLearning Howwouldyoubegintodevelopthese behaviorsinyourstudents? Whatotherpreparationmaybeneeded? Partners forMathematicsLearning

16. 16 Three-PartFormatfor Problem-BasedLearning During-workingonthetask Letgo Providehints Listenactively Encouragetestingofideas TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

17. 17 Three-PartFormatfor Problem-BasedLearning During-workingonthetask Supportstudentsdoingthethinking Givepointersnotstep-by-stepadvice “Showmehowyougotyouranswer” “Howdoyouknowyouarecorrect?” Partners forMathematicsLearning

18. 18 Three-PartFormatfor Problem-BasedLearning After-whentheworkiscomplete Providefeedback Usepraisecautiously Engagethefullclassindiscussion TeachingStudentCenteredMathematicsGrades5–8 JohnA.VandeWalleandLouAnnH.Lovin Partners forMathematicsLearning

19. 19 Three-PartFormatfor Problem-BasedLearning After-whentheworkiscomplete “Actionable”feedbackhelpsstudentsknow whattotryagainandwhattoavoid “Veryclearexplanation”or“Youmadea goodprediction” “Howarethedifferentapproachessimilar?” Partners forMathematicsLearning

20. 20 InvestigatingCircles Whatdoyouknowaboutcircles? Whatdistinguishesalargercirclefroma smallercircle? WhatisPi(asopposedtopie)? Partners forMathematicsLearning

21. 21 What’sinaCircle? Usingoneofthecircularobjects, tracetheobjectonpattypaper Foldthecircleinhalfsothatopposites sidesoverlap Repeattheprocessintheopposite direction Partners forMathematicsLearning

22. 22 What’sinaCircle? Markandlabelthecenter Traceandlabelthediameter Traceandlabelaradius Foldthecirclesuchthatapointonthe outsideofthecircletouchesthecenter Traceandlabelthechord Partners forMathematicsLearning

23. 23 What’sinaCircle? Usingstringandarulerora measuringtape,findthedistancearound yourcircleincentimeters Traceyourobjectoncmgridpaperand approximatetheareaofyourcircle Approximatethelengthsofadiameter andaradiusincentimeters Partners forMathematicsLearning

24. 24 What’sinaCircle? CompletetheWhat’sInACircle recordingsheet Compareyourchartwiththeother membersofyourgroup Whatconclusionscanyoudraw? Partners forMathematicsLearning

25. 25 What’sinaCircle? Usingthestickydotsatyourtable, plotyourdataonthecorrespondinggraphs DiameterversusRadius CircumferenceversusDiameter CircumferenceversusTwicetheRadius AreaversusRadiusSquared Partners forMathematicsLearning

26. 26 What’sinaCircle? Let’sanalyze!Whatrelationships doyouseefrombothyourtablesand theclassgraphs? Usingtheserelationships,writeformulas forcircumferenceandareaofacircle Partners forMathematicsLearning

27. 27 What’sinaCircle? WhichBigIdeawasthefocus ofthisactivity? Whatwouldyoudotopreparestudents beforetheactivity? Whatguidingquestionswouldyouask studentsduringthisactivity? Howwouldyousharestudents’findings aftertheactivity? Partners forMathematicsLearning

28. 28 Reflection Reviewingthethree-partformatfor problem-basedlearning,whichofthethree phasesdoyouseeasastrengthinyour classroomandwhichphasedoyouwantto improveinyourinstructionalprogram? Explain Partners forMathematicsLearning

29. 29 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

30. 30 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

31. 31 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

32. 32 PARTNERS forMathematicsLearning GradeSix Module1 Partners forMathematicsLearning