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Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning Grade One Module 4. Partners for Mathematics Learning. 2. What is Geometry? “geo” - means earth “metry” – means measure “Measurement of the earth”. Partners for Mathematics Learning. 3. We know that…  Children develop spatial

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning GradeOne Module4 Partners forMathematicsLearning

  2. 2 WhatisGeometry? “geo”-meansearth “metry”–meansmeasure “Measurementoftheearth” Partners forMathematicsLearning

  3. 3 Weknowthat… Childrendevelopspatial awarenessandreasoning overtimeasaresultof whattheyexperience Veryearlytheylearnto recognizebasicshapes evenwhentheydonot alwaysattachan appropriateterm Partners forMathematicsLearning

  4. 4 EssentialStandards Classifyaccordingtogeometricattributes2-D shapesasparallelograms,rhombuses, trapezoids,andhexagonsand3-Dshapesas prismsandpyramids Comparegeometricfiguresintermsoftheir perspectives,orientations,attributes,and properties Representdifferentperspectivesand orientations,describeafigure’sgeometric attributesandproperties,anddeterminehow figuresarealikeanddifferent Partners forMathematicsLearning

  5. 5 WhatDoWeRemember? Turntohandout1andtakeafewminutes tocompletethechart Thinkabout:Whatwillstudentsneedto knowandbeableto doforthesestandards? Whatnewvocabulary dostudentsneedto learnthisyear? Partners forMathematicsLearning

  6. 6 Polygon Closedplanefigureboundedbythreeor morelinesegmentsthatmeetonlyattheir endpoints polygons NOTpolygons 2-Dfigures Canbeclassifiedbythenumberofsides Partners forMathematicsLearning

  7. 7 Quadrilateral Polygonwithfoursides Whyarethesefiguresnotquadrilaterals? Partners forMathematicsLearning

  8. 8 Parallelogram Quadrilateralwithoppositesidesparallel andequalinlength Oppositeanglesarecongruent parallelograms Partners forMathematicsLearning

  9. 9 Rectangle Closedfigurewithfourlinesegments,2 pairsofparallellines,andfourrightangles (“squarecorners”) rectangles NOTrectangles Studentsneedtoseerectanglesthatare rotated-notparalleltoedgeofpaper Partners forMathematicsLearning

  10. 10 Rhombus(RhombusesorRhombii) Havefoursidesallhavethesamelength Closedfigurewithoppositesidesparallel Diagonalsareperpendicular NOTrhombus Partners forMathematicsLearning rhombus

  11. 11 Square Hasfoursides(linesegments)allofthe samelengthaswellasfourrightangles Everysquareisarectangle Closedfigure squares Partners forMathematicsLearning

  12. 12 SquaresAreRhombusesAre… quadrilaterals rectangles squares rhombuses polygons Partners forMathematicsLearning

  13. 13 Trapezoid Closedfigure,madeoffourlinesegments, exactlytwoofwhichareparallel(onepair ofparallelsides) Redpatternblockisanexample trapezoid NOTtrapezoid Partners forMathematicsLearning

  14. 14 Hexagon Polygonwithsixsides Theyellowpatternblock(liketheredone below)isahexagon hexagons nothexagons Partners forMathematicsLearning

  15. 15 AvoidingMisconceptions If isahexagon Is ahexagon? Partners forMathematicsLearning

  16. 16 Two-Dimensional(2-D)Shapes Alsocalledplanefigures Shapesthatcanbecompletelyseenin oneplane(shownonaflatsurface) Circlesareplanefiguresbutarenot polygons Partners forMathematicsLearning

  17. 17 Shapes,Sides,Corners,Congruent?     Whatisthisshape? Howmanysides? Howmanyvertices? HowcanIcutthisshapetogettwo smallerrectangles? Arethetworectanglescongruent? Arethereotherwaystocutthisshapeto have2rectangles? Partners forMathematicsLearning

  18. 18 CuttingCorners Get5indexcardsandmakestraightcuts fromonesidetoanadjacentsidetomake… A.Atriangleandapentagon B.Twoquadrilateralsthataretrapezoids C.Tworectangles D.Twotriangles E.Atriangleandaquadrilateralthatisatrapezoid Howmanysidesandverticesaretherefor eachshape? Partners forMathematicsLearning

  19. 19 Cutting… B.. A. C. D. E. Doyourshapeshavetolookexactlylike thesetobecorrect?Whyorwhynot? Partners forMathematicsLearning

  20. 20 . . . . . . . . . . . . . . . . . . . . . . . . . ShapesonaGeoboard Predicthowmanyexamplesofyourshape (differentsizeandshape)youcanmake onyourgeoboard Decidehowyouwillkeeparecord Makeashape,record,makethenext shape(reuserubberbandssothatonly onefigureatatimeisontheboard) Makeasmanydifferentexamplesasyou canusingyourgeoboard Partners forMathematicsLearning

  21. 21 FashioningFour Useageoboardand rubberbandstocreate four-sidedfigures Howmanydifferent shaped,closedfigures withfoursidescanyou create? Howcouldwesortthese? Partners forMathematicsLearning

  22. 22 PolygonButNotaQuadrilateral?      Areallquadrilateralspolygons? Areallpolygonsquadrilaterals? Allsquaresarerectangles Areallrectanglessquares? Canthesamefigurebeaparallelogram andarectangleandarhombus? Areallpolygonsclosedfigures? Areallplanefigurespolygons? Partners forMathematicsLearning

  23. 23 BigIdeaforGeometry Two-dimensionalshapesarecombinedto makethree-dimensionalshapes Partners forMathematicsLearning

  24. 24 2-Dimensionalto3-Dimensional Polyhedronmeans“manyfaces” Edge--3-Dterm Formedwhere twofaces coincideFace—3-Dterm Aflatsurfaceon Vertex—apointApolyhedron wheretwoormore(Facesarepolygons) edgesmeet Partners forMathematicsLearning

  25. 25 Pyramid Hasabasethatisapolygonandsidesthat aretriangles Hasonepointatthetop,calledanapex triangularpyramid squarepyramid rectangularpyramid Partners forMathematicsLearning

  26. 26 Prisms Thesearethree- dimensionalshapes whosesidesareall formedbypolygons Theyareprisms becauseends(or bases)arecongruent andsidesare parallelograms Partners forMathematicsLearning

  27. 27 Three-DimensionalShapes Partners forMathematicsLearning

  28. 28 BuildingonStrengths “Somestudents'capabilitieswith geometricandspatialconceptsexceed theirnumberskills.Buildingonthese strengthsfostersenthusiasmfor mathematicsandprovidesacontextin whichtodevelopnumberandother mathematicsconcepts.” RazelandEylon1991 forMathematicsLearning

  29. 29 MoreInformation Whatvocabularywill youusewithfirst graderstoteachthis standard? Giveexamplesof vocabularyusedfor: Perspective Orientation Attribute Property Comparegeometricfigures intermsoftheir perspectives,orientations, attributes,andproperties Partners forMathematicsLearning

  30. 30 OralMap Standbesideyourchair Countyourstepsoutloudasyoumove towardtheclassroomdoor Saywhichwayyouareturning Keepcountingoutloudasyoumovetothe door Howdothedirectionschangeifyougo backtoyourseatfromhere? forMathematicsLearning

  31. 31 ThePathHome Placearedandagreencube onoppositesidesofthe geoboard Userubberbandstomakea pathfromonecubetothe other Describethepathorallyand haveyourpartnerrecordon dotpaperwithoutseeingyour geoboard Partners forMathematicsLearning

  32. 32 OvertheWall Openafoldertomakea “wall”betweenyouandyourpartner Person1buildsadesignwithpatternblocks Describehowyourpartnercanmakethe samedesignontheothersideofthewall Takethewalldownandseeiftheshapes arethesame Discuss:Whatadditionaldirectionsmight yougivestudentsastheyfirstdothetask? Partners forMathematicsLearning

  33. 33 DifferentPerspectives “FromwhereIamstanding…” “WhenIlookupIsee….” “Lookingdownmakesitlooklike…” Partners forMathematicsLearning

  34. 34 Composeanddecompose geometricfiguresinterms oftheirperspectives, MoreInformation orientations,attributes,and properties Thisstandardhasbeen changed Whatdostudentsneedto knowandbeabletodoto masterthisstandardasit nowexists? Partners forMathematicsLearning

  35. 35 PatternBlockPuzzles     Chooseapuzzle Coverthepuzzlewithpatternblockpieces Howmanypiecesdidyouuse? Didsomeoneelseusemoreorless? Partners forMathematicsLearning

  36. 36 GoodMoves… Howdidyoubegintofillinthe puzzleoutline? Asyouworked,howdidyou decidewheretoplaceyour blocks? Didyourstrategychangeas thepuzzlebecamecloserto beingfull?Ifso,how? Partners forMathematicsLearning

  37. 37 ShapeSorters Smallgroupsofstudentsaregivena collectionofgeometricsolidsandattribute blockpieces Studentsthen Groupthecollectioninseveraldifferentways Sharefindingswithinthesmallgroups Smallgroupssharesortingpossibilities together forMathematicsLearning

  38. 38 TeacherLedDiscussions Askstudentstoexplaintheirsorts Directstudentstosortbyspecificcriteria Havestudentsfindthepolygonsthatare thefacesforthepolyhedra Remember-thisisayear-longactivity! Partners forMathematicsLearning

  39. 39 ModelWaysToRecord Studentscanrecordtheirobservationsand comparisonsofshapes Stamping Tracing Drawing Remember-activitieswithout conversationmaynothelp childrenmakeconnections Partners forMathematicsLearning

  40. 40 Two-PieceShapes Decomposing2-Dshapes Decompose Takingapart Composing2-Dshapes Composing Puttingtogether Partners forMathematicsLearning

  41. 41 Two-PieceShapes Howmanydifferentwayscanyouputthe trianglestogether? Isanyshapebiggerthananother? Partners forMathematicsLearning

  42. 42 BlocksWithFaces      Tracearoundthefacesoneachblock Areanyofthefacesthesame? Areanyofthefacesdifferent? Howmanyfacesdoesyourblockhave? Canyoumatchthefacesyoudrewto facesonotherblocks? Partners forMathematicsLearning

  43. 43 FaceMaps Afacemapofa_____________ Partners forMathematicsLearning

  44. 44 MysteryShapeMaps WhosefaceamI? Partners forMathematicsLearning

  45. 45 MyShapeJournal Writethenameoftheshapeontheline Tellhowyouknowthisisthenameofyour shape DrawapictureORcutapictureofyour shapefromamagazine Whatdoesyourshapelooklike? kite soupcan Partners forMathematicsLearning

  46. 46 QuiltWithMe     Choosefoursquares Cutsomeofthesquaresdiagonally Arrangetheshapestocoverthecard Whatshapesdoyouseeinyourquilt square? Partners forMathematicsLearning

  47. 47 WhatDoYouSee? Makealistoftheshapesand geometricvocabularyillustrated inyoursquare Passyoursquaretothepersononyourright Addtothelistoftermsillustratedandkeep passing Putyoursquarestogethertomakeatable quilt Partners forMathematicsLearning

  48. 48 MathFairBlues 2-and3-dimensional shapesandobjects helpSethandhis friendstobecomea hitattheMathFair Partners forMathematicsLearning

  49. 49 StillCircling… Whatdostudentsneedtoknowandbe abletodotomastertheseEssential Standards? Partners forMathematicsLearning

  50. 50 DPIMathematicsStaff EverlyBroadway,ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmySmith PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublicInstruction. Permissionisgrantedfortheuseofthesematerialsinprofessional developmentinNorthCarolinaPartnersschooldistricts. Partners forMathematicsLearning

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