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Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning Grade 2 Module 6. Partners for Mathematics Learning. 2. Reflecting Back to Earlier Modules  Analyzed whole numbers 0 to 1000 for patterns, relationships, comparing and ordering  Discussed strategies for solving addition and subtraction equations

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning Grade2 Module6 Partners forMathematicsLearning

  2. 2 ReflectingBacktoEarlierModules Analyzedwholenumbers0to1000for patterns,relationships,comparingand ordering Discussedstrategiesforsolvingaddition andsubtractionequations Relatedoperationstophysicalmodels Stressedtheimportanceofdeveloping numbersense Partners forMathematicsLearning

  3. 3 ProblemBasedLessons Researchhasindicatedthat beginningwithproblem situationsyieldsgreater problem-solvingcompetence andequalorbetter computationalcompetence

  4. 4 BigIdeas:ProblemSolving Processes(makingconnections, communications,representations, mathematicalreasoning)arewaysthat studentslearnmathematicsandwaysthat theydemonstratewhattheyhavelearned Mathematicalreasoningiswhenstudents usetheirknowledgeofmathematicsand theconnectionstheyhavemade (internalized)toresolvenewsituations Partners forMathematicsLearning

  5. 5 BigIdeas:ProblemSolving Problemsolvingiswhatyoudowhena solutionpath(orsolution)isnotimmediately recognized Experienceswithabroadrepertoireof strategies(suchas,drawapicture,use manipulatives,actitout,makeatableor chart,tryasimplerproblem,workbackwards, guessandcheck)leadtoconfidenceand greaterlikelihoodforsuccessinsolving problems Partners forMathematicsLearning

  6. 6 TeachingAddition&Subtraction Strategies Contextual Problems Connectedtochildren’s lives;Developmodelingof therealworld Models Counters, drawings,numberlines Partners forMathematicsLearning

  7. 7 TeachingAdditionandSubtraction Teachersneedtoplanlessonsinwhich studentsusemodelsandsolvecontextual problems Routinedrills-nocontext Routineapplications-inacontext Multi-stepdrills-nocontext Multi-stepapplications-inacontext Non-routine-noobvioussolutionpath Partners forMathematicsLearning

  8. 8 Howwouldyousolvethis? Joanhad48booksonherbookcase Aftershecleanedherroom,shefound somemorebooksandputthemonher shelf Whenshecountedallthebooks, therewere74inall HowmanybooksdidJoanfind andputontheshelf? Partners forMathematicsLearning

  9. 9 Howwouldyousolvethis? Agroupofpenguinswassunning themselvesonthebeach 12jumpedinthewater Thentherewere22 onthebeach Howmanywere onthebeachbefore the12left? Partners forMathematicsLearning

  10. 11 BasicStructureofProblems AccordingtoCGI,therearefourbasic structuresforproblems,regardlessofthe magnitudeofnumbers     JoinProblems SeparateProblems Part-Part-WholeProblems CompareProblems Partners forMathematicsLearning

  11. 10 ComparingProblems Joanhad48bookson herbookcase.Aftershe cleanedherroom,she foundsomemorebooks andputthemonher shelf. Whenshecountedall thebookstherewere74 inall.Howmanybooks didJoanfindandputon theshelf? Agroupofpenguins wassunningthem- selves.12jumpedin thewater.Thenthere were22onthebeach. Howmanywere onthebeachbefore the12left? Partners forMathematicsLearning

  12. 12 JoinProblems Join:ResultUnknown Sarahad28pencils.Georgegaveher13more. HowmanypencilsdoesSarahavealtogether? Join:ChangeUnknown Sarahad28pencils.Georgegavehersome more.NowSarahas41pencils.Howmanydid Georgegiveher? Join:StartUnknown Sandrahadsomepencils.Georgegaveher13 more.NowSandrahas41pencils.Howmany pencilsdidSandrahavetobeginwith?

  13. 13 SeparateProblems Separate:ResultUnknown Sarahad41pencils.Shegave13pencilsto George.HowmanypencilsdoesSarahavenow? Separate:ChangeUnknown Sarahad41pencils.ShegavesometoGeorge. Nowshehas28pencils.Howmanydidshegive toGeorge? Separate:StartUnknown Sarahadsomepencils.Shegave13toGeorge. NowSarahas28pencilsleft.Howmanypencils didSarahavetobeginwith? Partners forMathematicsLearning

  14. 14 ProblemSolving “Problemsolvingisaprocessgrounded inreasoning.” RandallCharles Teachersneed Tounderstandthe problemtypes Tobeintentionalin choosingnumbers withinproblems Partners forMathematicsLearning

  15. 15 ProblemSolving “Problemsolvingisaprocessgrounded inreasoning.” RandallCharles Studentsneedto Identifythequantitiesin aproblem Usereasoningtoidentify therelationship betweenthem Partners forMathematicsLearning

  16. 16 ResearchFindings Studentshaveimprovedproblem-solving performanceswhenthey Representmathematicalwordproblems Usediagramstorepresentwordproblems Teacheremphasizestherepresentationof problemstructures ? Partners forMathematicsLearning

  17. 17 BarDiagramsforJoinProblems Kimhas23antiquedolls.Herfathergives her18more.Nowhowmanyantiquedolls doesshehave? Danhassaved$57.Howmuchmore moneydoesheneedinordertohave$85? Partners forMathematicsLearning

  18. 18 DiagramsforSeparateProblems Tomashas94jellybeans.Heeats56of theminoneweekend.Howmanyjelly beansareleft? Maryhas35pencils.Shegivesometo herclassmates.Nowshehas17.How manydidshegiveherclassmates? Partners forMathematicsLearning

  19. 19 Part-Part-WholeProblems Part-Part-Whole:WholeUnknown Sydneyhas24penniesand14nickels. Howmanycoinsdoesshehave? Part-Part-Whole:PartUnknown Sydneyhas38coins.Twenty-fourof hercoinsarepennies,andtherestare nickels.Howmanynickelsdoes Sydneyhave? Partners forMathematicsLearning

  20. 20 BarDiagrams:Part-PartWhole 24+14=? 24+?=38 Partners forMathematicsLearning

  21. 21 CompareProblems Compare:DifferenceUnknown Georgehas24pencilsand Sarahas14pencils.Howmany morepencilsdoesGeorge havethanSara? Compare:LargerorSmallerUnknown Georgehas10morepencilsthanSara.Sarahas 14pencils.HowmanypencilsdoesGeorgehave? Georgehas10morepencilsthanSara.George has24pencils.HowmanypencilsdoesSara have? Partners forMathematicsLearning

  22. 22 Differentiation Thedentisthad(11,43,120) toothbrushes.Shegavesometo herpatients.Thenshehad(7,18,83)left. Howmanytoothbrushesdidthedentist givetoherpatients? Thedentisthad_____toothbrushes.She gavesometoherpatients.Thenshehad _____left.Howmanytoothbrushesdid thedentistgivetoherpatients? (11,7) (120,83) (43,18) Partners forMathematicsLearning

  23. 23 WritingStoryProblems Inyourgroupdiscussyourassignedstory problemtype Writeproblemstomatchthestoryproblem type Includesomeproblemswithdifferentiation options Discusswhybeingawareofthesedifferent typesisimportant Partners forMathematicsLearning

  24. 24 Multi-stepProblems Lauraboughtapencilfor$0.20andan eraserfor$0.15.Shepaidtheclerk$0.50. Howmuchchangeshouldshereceive? Ihave36cookies.Myclasshas15boys and10girls.DoIhaveenoughcookiesso everyonegetsonecookie?Howdoyou know? Partners forMathematicsLearning

  25. 25 InProblemSolvingClassrooms   StudentsLearn Concepts Computationalskills StudentsShareStrategies Communicatetheirthinking Learnfromeachother Provideawindowintoastudent’sthinking Partners forMathematicsLearning

  26. 26 KeyWords:AMisleadingStrategy Thereare25studentsinourclass altogether.Thereare15girls.Howmany areboys? Mymomismakingcookiesformyparty. Therewillbe7peopleatmyparty, includingme.Eachpersonwillhave3 cookies.HowmanycookiesshouldMom makealtogether? Partners forMathematicsLearning

  27. 27 SolutionStrategies DirectModeling CountingALLtodeterminetheamount CountingOn CountingONtodeterminetheamount Recall/NumberFacts Usinganefficientstrategytodetermine theamount—usingfactsandnumber sensetosolveproblems Partners forMathematicsLearning

  28. 28 Students’Strategies Ihad46dollars.Mymomgavemesomemore money.NowIhave83dollars.Howmuch moneydidmymomgiveme?83 46+____=83 Partners forMathematicsLearning

  29. 29 NumberTalks ComputationStrategies NumberRelationships MentalStrategies 36-10 43-30 36-20 36-24 43-33 43-39 Subtract Partners forMathematicsLearning

  30. 30 NotJustStoryProblems ExplainingStrategies MentalMath Reasoning Open-endedTasks QuickImages ChoralCounting NumberTalks        Partners forMathematicsLearning

  31. 31 Teacher’sRole Inaproblem-based classroomtheteacher… Listenstostudents’strategies Asksquestions Makessuredifferentstrategiesareshared Hasstudentssolveproblemsinmore thanoneway Hasstudentsdiscusshowstrategiesarealike andhowtheyaredifferent Presentsrichandinterestingproblems Partners forMathematicsLearning

  32. 32 Math&Literature Partners forMathematicsLearning

  33. 33 MathematicsandLiterature Partners forMathematicsLearning

  34. 365 Penguins. 34 Whatdoyoudowith60penguins? Partners forMathematicsLearning

  35. 35 StudentWork Studentsworkedinpairstofindwaysto organize60penguins Theyhad60cubes Theyrecordedtheirsolutions LookatCole’s,Emma’sandMiles’work Whatdotheyunderstand? Whatdoyouwanttoaskthem? Partners forMathematicsLearning

  36. 36 Organize Them! 365 Penguins Partners forMathematicsLearning

  37. 37 ExtendingtheMathematics     3-digitnumbers Costoffood Calendar Predictions Partners forMathematicsLearning

  38. 38 Penguins&Measurement Connections Research Writing Art Measurement ProblemSolving Partners forMathematicsLearning

  39. 39 PenguinsonParade Partners forMathematicsLearning

  40. 40 ComputerResources Partners forMathematicsLearning

  41. 41 LiteratureConnections     Readabook Planamathlesson Lookatthehandouttoguideyourthinking Shareyourplanwiththegroup Partners forMathematicsLearning

  42. 42 ReflectingonOurWork Basedontoday’swork,Iwanttorethink howIamteaching… Oneideathatisnewtometodayis… SomethingIwouldlikefurther conversationsaboutis… Partners forMathematicsLearning

  43. 43 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

  44. 44 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

  45. 45 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

  46. 46 PARTNERS forMathematicsLearning ProblemSolving WordProblems Communication Connections Partners forMathematicsLearning

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