Partners for Mathematics Learning

1. 1 PARTNERS forMathematicsLearning GradeFive Module5 QuickTime™anda decompressor areneededtoseethispicture. Partners forMathematicsLearning

2. 2 StatisticsEssentialStandards Lookatthestatisticsandprobability essentialstandardsacrossthegrades Whatdoyounotice? Whatarethesimilaritiesanddifferences betweengrades3,4and5? Partners forMathematicsLearning

3. 3 BigIdeas Datacanbeeithercategoricalornumerical Pose,Collect,Analyze,Interpret(PCAI)is amodelfortheprocessofstatistical investigations Differentrepresentationsandgraphs classifyandcommunicatedata Understandingbasicconceptsof probabilityallowsustomakemore accuratepredictions Partners forMathematicsLearning

4. 4 CategoricalData Valuesthatareoftenwordsandthat representpossibleresponseswithrespecttoa givencategory Representindividualsorobjectsbyoneormore characteristicsortraitsthattheyshare Examples: Monthsinwhichpeoplehavebirthdays FavoritecolorT-shirt Favoritefruits Kindsofpets Partners forMathematicsLearning

5. 5 NumericalData Valuesthatarenumberssuchascounts, measurements,andratings Representobjectsorindividualsbynumbers assignedtocertainmeasurableproperties- Examples: Numberofchildreninfamilies Pulseratesoftopathletes Timeinminutesthatstudentsspendwatching televisioneachday Numberofpets Partners forMathematicsLearning

6. 6 PCAIModel Partners forMathematicsLearning

7. 7 PCAIStep1:PosetheQuestion Identifyaspecificquestionto exploreanddecidewhat datatocollecttoaddress thequestion Partners forMathematicsLearning

8. 8 PCAIStep2:CollecttheData Studentsshould Collecttheirowndata Haveaplanfordatacollection Understandwheredatacomefrom Partners forMathematicsLearning

9. 9 FlawsinDataCollection Whatkindsofthings needtobeconsidered whencollectingdata? Whatdoesitmean tosaythedataare biased? Partners forMathematicsLearning

10. 10 What’stheProblem? Billyconductsasurveytodetermine computerownershipoutsideacomputer repairshop Whymightthedatacollectedinthis samplebeinaccurate? Partners forMathematicsLearning

11. 11 What’stheProblem? Keishasurveyseveryhouseina5block radiusofcityhallaskingifsubsidies shouldbecontinuedfordairyfarmers Whymightthedata collectedinthis samplebeinaccurate? Partners forMathematicsLearning

12. 12 What’stheProblem? Alocalradiostation askslistenerstocallin andexpresstheirviews onexpandingthe localairport Whymightthedatacollected inthissamplebeinaccurate? Partners forMathematicsLearning

13. 13 What’stheProblem? Fromthepagesofhistory… Inthe1936presidentialcampaignbetween FDRandAlfredLandon,awell-respected publicationconductedasurveysendingten millionballotstoasamplepopulation selectedfromclubmemberships,telephone directories,andmagazinesubscriptions ItincorrectlydeterminedthatLandonwould win;FDRwonbyalandslide Partners forMathematicsLearning

14. 14 ImplementingthePCAIModel “GettingtoKnowUs”projectwillinclude… Part1 Posingaquestionandcollectingdata Part2 Analyzingandinterpretthedata Part3 Presentation Partners forMathematicsLearning

15. 15 FormingTeams Formteamsof3-4people Theteamscanbeallgrade4andallgrade 5orteamswhoarefromthesameLEA Partners forMathematicsLearning

16. 16 ImplementingthePCAIModel “GettingtoKnowUs”-First… Generateatleastonenumericalquestion Formulateanhypothesis Preparetosampletwogroupsofpeople Partners forMathematicsLearning

17. 17 ImplementingthePCAIModel “GettingtoKnowUs” Second… Collectthedata Posethequestiontotwodifferentpopulations Partners forMathematicsLearning

18. 18 ImplementingthePCAIModel “GettingtoKnowUs” Maintainnotes abouttheprocess Bepreparedtoshare yourexperience Thinkaboutimplementing thiswithstudents

19. 19 ImplementingthePCAIModel “GettingtoKnowUs” Atanothersessionwewill… Analyzethedata Interpretthedata Presentthedatatotheclass Partners forMathematicsLearning

20. 20 ImplementingthePCAIModel “GettingtoKnowUs” Thingstokeepinmind… Havedatacollectedby… Anyquestions? Partners forMathematicsLearning

21. 21 PARTNERS forMathematicsLearning Movinginto Decimals

22. 22 DecimalConcepts Decimalnumbersareanotherwayof writingfractions Thebase-tenplace-valuesystem extendsinfinitelyintwodirections,to everlargervaluesandtoeversmaller values Thedecimalpointindicatestheunits position(toitsimmediateleft) Partners forMathematicsLearning

23. 23 Decimals:Base-TenFractions Theadditionandsubtractionofdecimal numbersisasimpleextensionfrom wholenumbers,involvingnumbersinlike positionvalues Whatismeantby“likepositionvalues”? Howcanwehelpchildrenseethe connectionbetweenfractionsand decimals? Partners forMathematicsLearning

24. 24 Decimals:Base-TenFractions Usefamiliarfractionconceptsandmodels toexploretenths,hundredths,and thousandths(rationalnumberseasily representedbydecimals) Helpthemseehowthebase-tensystem extendstoincludenumberslessthanone Helpchildrenusemodelstomake meaningfultranslationsbetweenfractions anddecimals Partners forMathematicsLearning

25. 25 Decimals:Base-TenFractions Models: 10x10square Base-tenplacevaluestripsandsquares Meterstick Numberline Moneyisnotrecommendedasamodel,but asanapplication Exploremultiplenamesandformats Partners forMathematicsLearning

26. 26 DecimalModels Whatnumberis Whatpartofthe gridisshaded? representedonthegrid?Giveyouranswer asafractionand asadecimal Howmanywhole tenthsare shaded? Howmanyextra hundredths? Partners forMathematicsLearning

27. 27 DecimalModels Whatnumberis representedonthe grid? Whatpartofthe gridisshaded? Whatpartisnot shaded? Giveyouranswer asafractionand asadecimal Partners forMathematicsLearning

28. 28 DevelopingDecimalNumberSense NumberLines(RelativeMagnitude) WhatnumbersdopointsCandDrepresent? HowfarapartareAandB? Whydoyouthinkso? A B CD E F G 2.0 1.25 Whichletterrepresents1.5? Partners forMathematicsLearning

29. 29 Decimals:Base-TenFractions Whenthesenumbersareputonanumber line,whichtwonumbershavetheleast spacebetweenthem? 1.3 1.12 1.30 0.04 0.4 Whichtwohavethemostemptyspace betweenthem?Howdoyouknow? Partners forMathematicsLearning

30. 30 Decimals:Base-TenFractions ImportantExplorationsafterModeling: Example:73 100 Isthisfractionmoreorlessthan½?⅔?¾? Differentwaystosaythefraction:“7tenthsand3 hundredths,”“73hundredths”) Showmultiplewaystowritethisfraction: 73or7 + 3or.73or.7+.03 10010100or.70+.03 Partners forMathematicsLearning

31. 31 Decimals:BaseTenFractions Reviewideasofwholenumberplacevalue 10-1relationshipbetweenthevalueofanytwo adjacentpositions 10ofonepiecewillmake1ofthenextlargerand viceversa The10to1relationshipcontinuesinfinitelyin bothdirections Withagivenmodel,anypiececouldbechosen astheonespiece;thusthedecimalpointhas theimportantroleofdesignatingtheunits (ones)position(totheleftofthedecimalpoint). Partners forMathematicsLearning

32. 32 Decimals:BaseTenFractions Rewritethesenumbers Putindecimalpointssothatthe7isinthe givenplace 4672 4672 7469 7469 tenths hundredths ones ten thousands 467 47 7469 187 tenths thousandths hundreds thousandths Partners forMathematicsLearning

33. 33 Decimals:BaseTenFractions Rewritethesenumbers Putindecimalpointssothatthe7isinthe givenplace 46.72 7.469 tenths ones 4.672 74,690.tenthousands hundredths 46.7 .047 746.9 .187 tenths thousandths hundreds thousandths Partners forMathematicsLearning

34. 34 Decimals:Base-TenFractions Useacalculatortocountby0.1 Whathappenswhenyougetto0.9? Whydoesitnotcount0.8,0.9,0.10,0.11…? Does0.8,0.9,1.0,1.1…makesense? Why? Countby0.01and0.001 Howlongdoesittakeyoutogetto1? Partners forMathematicsLearning

35. 35 Decimals:Base-TenFractions Findanumberthatcomesbetweenthe twodecimalfractionsthataregiven Theremaybemorethanonepossible answers .43.45 3.193.21 .099 .011 .5 .08 .799 .6 .09 .801 Partners forMathematicsLearning

36. 36 WhereistheDecimal? Placeadecimalineachstatementif neededtomakethestatementmake sense Halfof9is45 75isthesameasthreefourths Myheightisabout175meters 245isalittlelessthantwoandone-half Partners forMathematicsLearning

37. 37 TheDecimal-FractionConnection 64 Usemodelstoseethat2100isthe sameas2.64andviceversa Whatmodelswouldworkwell? Useacalculatorwithafraction- decimalconversionkey Whatpatternsdoyounotice? Partners forMathematicsLearning

38. 38 TheDecimal-FractionConnection Choosetwonumbersfromthegrid Decidewhichoneisgreaterthantellhow youknow Partners forMathematicsLearning

39. 39 DecimalComputation AdditionandSubtraction Agoodplacetobeginiswithestimation Agoodtimetobeginisassoonasa conceptualbackgroundindecimalnumeration hasbeendeveloped -VandeWalleandLovin,TeachingStudent–CenteredMathematics,Grades3-5 Partners forMathematicsLearning

40. 40 DecimalAdditionandSubtraction Makequick,easywhole-number estimatesofthefollowing: 4.908+123.02+56.123 17.3+25.04+91.015 479.8–12.543 197.03–53.119 Partners forMathematicsLearning

41. 41 DecimalAdditionandSubtraction LashondaandMandaranthequarter-mile Mandaranitin76.05seconds Lashondaranthequarterin82.436 seconds HowmanysecondsfasterdidLashonda runthanManda? Estimateawholenumberanswer Thenfigureouttheexactdifference Partners forMathematicsLearning

42. 42 DecimalAdditionandSubtraction Givenasuminvolvingdifferentnumbers ofdecimalplaces: 76.23+7.8+0.597 Task1:Makeanestimateandexplainhowit wasmade Task2:Computetheexactanswerandexplain howitwasdone(nocalculators!) Task3:Deviseamethodforaddingand subtractingdecimalnumbersthatcanbeused withanytwonumbers Shareyourstrategieswiththeclassandtest themonanewcomputation Partners forMathematicsLearning

43. 43 BalancingDecimals Findthemissingvalues. Figuresthatarethesamesizeandshapemusthavethesamevalue. AdaptedfromWheatleyandAbshire,DevelopingmathematicalFluency,MathematicalLearning,2002 Partners forMathematicsLearning

44. 44 FocusofInstruction Workonsubstantialmathematics Takestudentthinkingseriously Treattheconstructionofmathematical knowledgeastheworkofanintellectual collectivewithjustificationcrucial -HymanBass,UniversityofMichigan,fromapresentationatICME-10, Copenhagen,Denmark,July,2004 Partners forMathematicsLearning

45. 45 Connections Whichoftheprocessstandardsdidweuse? ProblemSolving ReasoningandProof Communication Connections Representation Writethreethingsontheindexcardthatyou willincorporateintoyourinstructional programinthecomingyear Partners forMathematicsLearning

46. 46 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

47. 47 PMLDisseminationConsultants SusanAllman JuliaCazin CaraGordon TeryGunter ShanaRunge YolandaSawyer BarbaraHardyPennyShockley KathyHarris JulieKolb ReneeMatney TinaMcSwain MarilynMichue AmandaNorthrup KayonnaPitchford RonPowell StacyWozny JudithRucker Partners forMathematicsLearning RuafikaCobb AnnaCorbett GailCotton JeanetteCox LeanneDaughtry LisaDavis RyanDougherty ShakilaFaqih PatriciaEssick DonnaGodley PatSickles NancyTeague MichelleTucker KanekaTurner BobVorbroker JanWessell DanielWicks CarolWilliams SusanRiddle

48. 48 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

49. 49 PARTNERS forMathematicsLearning GradeFive Module5 QuickTime™anda decompressor areneededtoseethispicture. Partners forMathematicsLearning