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Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning. Grade 4 Module 4. Partners for Mathematics Learning. 2 Geometry  What comes to mind when you hear the word “geometry”?  For fourth grade students, what is geometry?. Partners for Mathematics Learning. 3. Geometry is…

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning Grade4 Module4 Partners forMathematicsLearning

  2. 2 Geometry Whatcomestomindwhenyouheartheword “geometry”? Forfourthgradestudents,whatisgeometry? Partners forMathematicsLearning

  3. 3 Geometryis… Thestudyofthephysicalworldinwhich welivethroughmathematicalrelationships Thestudyofspaceandspatial relationships Ameanstounderstanding,describing,and analyzingstructuresinourworld Partners forMathematicsLearning

  4. 4 Geometry Whyisgeometryimportant? Howcanitbeusedtodeepen mathematicalunderstanding? Partners forMathematicsLearning

  5. 5 GeometryBigIdeas ShapesandProperties Studyofthepropertiesofshapesinbothtwoandthree dimensions,aswellastherelationshipsbuiltonproperties Transformation Studyoftranslations,reflections,androtationsandthe studyofsymmetries Location Refersprimarilytocoordinategeometryorotherwaysof specifyinghowobjectsarelocatedintheplaneorinspace Visualization Recognitionofshapesintheenvironment,developing relationshipsbetween2-and3-dimensionalobjects;the abilitytodraw/recognizeobjectsfromdifferentperspectives Partners forMathematicsLearning

  6. 6 BigIdeasinGeometry Shapesorgroupsofshapescanbe classifiedbytheirproperties Two-dimensionalshapesarecombinedto makethree-dimensionalshapes Area,perimeter,andvolumesare examplesofmeasurableattributesin geometry Partners forMathematicsLearning

  7. 7 BigIdeasinGeometry Shapescanbedescribedin termsoftheirlocationandviewedfrom differentperspectives;geometricfigures canbemovedinaplanewithoutchanging theirsizeorshape Coordinatesystemscanbeusedto describelocationsprecisely Partners forMathematicsLearning

  8. 8 Shapes&Properties Refining Concepts Exploring Attributes ofShapes Classifying Shapes Developing Vocabulary Partners forMathematicsLearning

  9. 9 PerimeterandArea TrueorFalse Twoshapeswiththesameperimeter musthavethesamearea Twoshapeswiththesamearea musthavethesameperimeter Partners forMathematicsLearning

  10. 10 Area Whichislarger? Partners forMathematicsLearning

  11. 11 PerimeterandArea Whatpercentoffourthgradersandwhat percentofeighthgradersdoyouthink respondedcorrectlytotheNAEPproblem below? Findtheareaofacarpetthatis9feet longand6feetwide Partners forMathematicsLearning

  12. 12 PerimeterandArea Whydochildrenhavedifficultywith perimeterandarea? P=4S P=2L+2W P=L+L+W+W A=LW Partners forMathematicsLearning

  13. 13 PerimeterandArea Defineperimeterandarea Listsituationsinwhichyouneed tofindeach Partners forMathematicsLearning

  14. 14 PerimeterorArea? Somechildrenwereplayingbaseballand accidentallybrokeaneighbor’swindow Ofcourse,theyhadtoreplacethewindow whichwas24incheswideand42inchesin height Dotheyneedperimeter,area, both,orsomethingelsewhen theygotobuytheglassto replacethebrokenwindow? Partners forMathematicsLearning

  15. 15 AREA Areaisthemeasureofthespace insidearegionorhowmuchis neededtocoveraregion Partners forMathematicsLearning

  16. 16 Area Studentsmustfirstunderstandthe attributeofareabeforemeasuring Partners forMathematicsLearning

  17. 17 Area Piagetianexperimentsindicatethat8-or 9-yearoldsdonotunderstandthat rearrangingareasintodifferentshapes doesnotaffecttheamountofarea Partners forMathematicsLearning

  18. 18 AREA Usethestringtoformanirregularshape Determinetheamountofpenshancies neededtofillyourshape Asyouwork,recordthestrategiesyou used Partners forMathematicsLearning

  19. 19 Area Usethepapertomakeanirregularshape Tradeshapeswithanothergroup Findtheareausingthesquaretiles Partners forMathematicsLearning

  20. 20 Area Usethesquaretileand/ortherulerto decidewhichrectangleineachpairis larger Bereadytosharehowyouknow Partners forMathematicsLearning

  21. 21 MeasuringArea Makealistofobjectsintheroomthatwe couldmeasureanddeterminelength Whatunitswouldbeappropriate? Makealistofsomeoftherectanglesthat arevisibleintheclassroom Whichoneswouldyoumeasureusingsquare tiles? Partners forMathematicsLearning

  22. 22 AreaofLargerRegions Usethepaperandtoolsprovidedtomake asquarefoot Lookcarefullyatyoursquarefoot Howmanysquareinchesarethereina squarefoot?Howdoyouknow? Howmanysquarefeetarethereina squareyard?Howdoyouknow? Howmanysquareinchesinasquareyard? Partners forMathematicsLearning

  23. 23 Perimeter Whatisperimeter? Whataresomechallengesthatchildren havewithperimeter? Howdoyouhelpchildrenunderstand perimeter? Partners forMathematicsLearning

  24. 24 AreaStaystheSame Use1hexagon,3trapezoids, 3triangles,and3parallelogramstoform adesign Whatistheareaofyourshape? Whatistheperimeterofyourshape? Makeanewshape Whatistheareaofyourshape?Theperimeter? Partners forMathematicsLearning

  25. 25 PerimeterStaystheSame Using40-50feetofstring,formalong,thin rectangle1personwide Filltherectanglewithpeopleandcount themas“units” Reshapetoarectanglewithalargerwidth andcountthenumberofpeopleunits Repeatafewmoretimes,makingthe stringclosertoasquareeachtime Partners forMathematicsLearning

  26. 26 What’stheArea? Workeachproblemindependently Sharehowyougotyouranswers Bereadytocomparethewaysproblems weresolved Partners forMathematicsLearning

  27. 27 SolvingProblems Whatwouldyoudotoprepareyour childrenfortheseproblems? Findtheareaofasquarewithasideof5 inches Findtheperimeterofaregularhexagonwitha sideof4inches Determinetheperimeterofanequilateral trianglewithasideof8centimeters Partners forMathematicsLearning

  28. 28 PerimeterandAreaChallenge Find“MysteryShapes”inyourhandouts Workwithapartnertosolve Sharestrategieswiththegroup Partners forMathematicsLearning

  29. 29 PerimeterandArea TrueorFalse Twoshapeswiththesameperimeter, musthavethesamearea Twoshapeswiththesamearea, musthavethesameperimeter Partners forMathematicsLearning

  30. 30 GeometryGrade4 Understandtwo-dimensionalshapesin termsofsymmetry(linerotational,both, neither)andtheirtransformations (includingreflections,translations,and rotations) Partners forMathematicsLearning

  31. 31 Transformations Whataretransformations? Whatmakesthemchallenging forchildren? Partners forMathematicsLearning

  32. 32 Transformations Benchmarkturnsoffiguresofquarter (90degrees),half(180degrees)three quarter(270degrees)andwhole (360degrees) Partners forMathematicsLearning

  33. 33 Transformations Whatvocabularyisneededforchildrento besuccessfulwithtransformations? Brainstormwaystointroduce transformations Partners forMathematicsLearning

  34. 34 TransformerSays… Placeyourfigureinthebottomrighthand cornerofyoudeskandthenlistencarefully fordirections Partners forMathematicsLearning

  35. 35 FlipforGeometry Foldthepaperinhalflengthwise Cuttophalfinto4equalsectionssotheywillflip upwhenthepaperisheldhorizontally Drawasimpledesignonthetopofleftflap Writedirectionsforareflection,translation,and rotationontheremainingflaps Lifteachflapandthendrawthedesign aslabeled Partners forMathematicsLearning

  36. 36 Symmetry Whatislinesymmetry? Whatistheconnectionbetween transformationsandlinesymmetry? Whatisrotationalsymmetry? Whyissymmetryimportantingeometry? Partners forMathematicsLearning

  37. 37 ABCsofLineSymmetry     Formgroupsapproximatelythesamesize Examinethealphabetletters Recordonyoursheet Bereadytodefendyouranswers Partners forMathematicsLearning

  38. 38 RotationalSymmetry Whatmakesrotationalsymmetry challenging? Whataresomewaysto introducerotationalsymmetry? Partners forMathematicsLearning

  39. 39 AlphabetRotationalSymmetry Testthelettersofthealphabetyourgroup hasbeenassignedtoseewhich,ifany, haverotationalsymmetry Partners forMathematicsLearning

  40. 40 SymmetrywithPatternBlocks Usethepatternblocksprovidedto completethehandout “LineandRotationalSymmetry” Partners forMathematicsLearning

  41. 41 DesignaLogo Workwithyourgrouptodesign logosthatfitthefollowing Alogowithlinesymmetry Alogowithrotationalsymmetry Alogowithbothlineandrotationalsymmetry Alogowithonlyrotationalsymmetry Alogowithonlylinesymmetry Partners forMathematicsLearning

  42. 42 FoldingFun Watchcarefullyasthepaperisfolded andcut Sketchwhatitwilllooklikewhenit isunfolded Shareyoursketchandexplain howyouarrivedatyouranswer Partners forMathematicsLearning

  43. 43 Reflections Reviewtheactivitieswehavedone Inwhatwaysisthefocusonconceptual understanding? Whatistheteacher’srole? Whatisthestudent’srole? WherearetheProcessStandards? (problem-solving,representations,reasoningand proof,connections,andcommunication) Partners forMathematicsLearning

  44. 44 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

  45. 45 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

  46. 46 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

  47. 47 PARTNERS forMathematicsLearning Grade4 Module4 Partners forMathematicsLearning

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