Partners for Mathematics Learning

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