1 / 49

Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning Grade Five Module 5 QuickTime™ and a decompressor are needed to see this picture. Partners for Mathematics Learning. 2. Statistics Essential Standards  Look at the statistics and probability essential standards across the grades

palmere
Télécharger la présentation

Partners for Mathematics Learning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related