,GEOMETRY & ,TACTILE ,GRAPHICS = ,/UD5TS 9 ,GRADES #C TO #H ,LESSON #C3 ,MAT]IALS & ,/RATEGIES = ,GEOMETRY ,9/RUC;N ,"P #B ,,PROJECT ,,9SPIRE ,UNIV]S;Y ( ,S\? ,C>OL9A ,UP/ATE ,SLIDE #AE3 ,L9E> ,M1SURE;T _4 #CRD GRADE SKILL " _4 #DTH GRADE SKILL " _4 #ETH GRADE SKILL " _4 ,ASK ! G5]AL $UCA;N T1*] ;$= ,/&>D OR METRIC8 ;$= ,:AT L5G? "D">8 _4 ,SKILL ( L9+ UP :AT TO #A M1SURE S "! IS A CLE> 8#J PO9T04 _4 ,,APH Y>D /ICK ,- LOOK AT ! 8#J0 ON ! PR9T SIDE VS4 ! BRL SIDE6 _4 ,TACTILE CALIP] F MULTIPLE S\RCES " @.<,PICTURE #A3 ,A R$ RECTANGUL> PRISM IS NEXT TO A TACTILE CALIP]4 ,! LEFT $GE ( ! TACTILE CALIP] IS ALIGN$ ) ! BOTTOM $GE ( ! RECTANGUL> PRISM4 ,! SLID] ON ! TACTILE CALIP] HAS BE5 PU%$ Z F> LEFT AG/ ! "R SIDE ( ! RECTANGUL> PRISM Z X C G4 ,PICTURE #B3 ,A /UD5T USES A PR9T-BRL RUL] TO M1SURE ! SIDE ( A BOX4@.> #B ,SLIDE #AF3 ,L9E> ,M1SURE;T ,TOOLS ,/&>D _4 ,Y>D/ICK " _4 _% #18'' _: FLEXIBLE RUL] " _4 #A FOOT RUL] " _4 ,TACTILE M1SUR+ TAPE " _4 ,TACTILE ,CALIP] " ,METRIC _4 ,MET]/ICK " _4 _% #30 CM _: FLEXIBLE RUL] " _4 ,TACTILE M1SUR+ TAPE " _4 ,TACTILE ,CALIP] " ,COMB9$ ,/&>D_/,METRIC _4 #A FOOT BRL RUL] " _4 ,TOSS-,AWAY ,RUL] _% (7 IN_/17 CM) _: " _4 ,TALK+ TAPE M1SURE #C ,SLIDE #AG3 ,COORD9ATE ,GRAPHS _4 #ETH GRADE SKILL "<#AST QUADRANT ONLY"> ;$= ,COMPON5TS3 AXES1 ORIG91 COORD9ATES1 ORD]$ PAIRS ;$= ,BASIC GRAPH+ " _4 #FTH GRADE SKILL ;$= ,POLYGONS 9 A COORD9ATE PLANE ;$= ,4T.E 2T PO9TS ) SAME ;X OR SAME ;Y-COORD9ATE _4 ,USE3 ;$= ,GRAPHIC ,AID = ,MA!MATICS ;$= ,TACTILE GRAPH PAP] ;$= ,PU% P9S1 BRASS FA/5]S1 TACTILE /ICK]S1 ETC4 TO REPRES5T PO9TS @.<,PICTURE3 ,A /UD5T'S H&S EXPLORE TACTILE GRAPH PAP] ON : L9ES & PO9TS >E %[N4@.> #D ,SLIDE #AH3 ,SCALE ,DRAW+S _4 #GTH GRADE SKILL _4 ,SOLV+ PROBLEMS 9VOLV+ SCALE DRAW+S ( GEOMETRIC FIGURES _4 ,COMPUT+ ACTUAL L5G?S & >EA BAS$ ON SCALE _4 ,USE3 ;$= ,GRAPHIC ,AID = ,MA!MATICS ;$= ,TACTILE GRAPH PAP] ;$= ,PU% P9S1 BRASS FA/5]S1 TACTILE /ICK]S1 ETC4 TO REPRES5T PO9TS @.<,PICTURE3 ,A /UD5T IS GRAPH+ TRIANGLES & RECTANGLES ON ! ,,APH ,GRAPHIC ,AID = ,MA!MATICS4 ,9 QUADRANT ,I TWO TRIANGLES >E %[N1 "O IS TWICE Z L>GE Z ! O!R4 ,9 QUADRANT ,,IV ": ! /UD5T IS "W+1 %E HAS CR1T$ A L>GE RECTANGLE ) ANO!R RECTANGLE "O HALF XS SIZE 9SIDE ( X4 ,%E IS EXPLOR+ ! SMALL] RECTANGLE4@.> #E ,SLIDE #AI3 ,TRANS=MA;NS _4 #HTH GRADE SKILL _4 ,3CEPTS ;$= ,REFLEC;NS - FLIP ;$= ,TRANSLA;NS - %IFT ;$= ,ROTA;NS - TURN ;$= ,DILA;NS - MAKE L>G] OR SMALL] _4 ,USE3 ;$= ,GRAPHIC ,AID = ,MA!MATICS ;$= ,TACTILE GRAPH PAP] ;$= ,PU% P9S1 BRASS FA/5]S1 TACTILE /ICK]S1 ETC4 TO REPRES5T PO9TS @.<,PICTURE #A3 ,A /UD5T IS GRAPH+ ON ! ,,APH ,GRAPHIC ,AID = ,MA!MATICS4 ,%E HAS ALR GRAPH$ A %APE 9 QUADRANTS ,,II & ,,III4 ,9 ,QUADRANT ,I %E HAS PLAC$ TWO ?UMBTACKS & IS PLAC+ A ?IRD 9 ,QUADRANT ,,IV4 ,PICTURE #B3 ,WIKKI ,/IX H BE5 US$ TO CR1TE ! ;X & ;Y-AXIS ON A PIECE ( #F BRL PAP]4 ,A GRE5 FELT RECTANGLE IS 9 ,QUADRANT ,I & A SECOND GRE5 FELT RECTANGLE IS 9 ,QUADRANT ,,II4@.> #G ,SLIDE #BJ3 ,PY?AGOR1N ,!OREM _4 #HTH GRADE SKILL _4 ,LEGS " ,- BY ! "R ANGLE _4 ,HYPOT5USE "<;C"> ,- OPPOSITE ! "R ANGLE _4 ,SOLV+ = UN"KN SIDES US+ _% A^2"+B^2 .K C^2 _: _4 ,F9D+ 4T.E 2T TWO PO9TS 9 A COORD9ATE GRID _4 ,USE3 GRAPH PAP] OR ,DRAFTSMAN = DRAW+S _4 ,USE3 BRLWRIT] = SOLV+ PROBLEMS @.<,PICTURE #A3 ,A COMPUT]-G5]AT$ RECTANGLE ) A SYMMETRICAL L9E CUTT+ "? X DIAGONALLY IS %[N4 ,) SIMBRAILLE1 ! L;G SIDE IS LABEL$ _% #8 CM _: & ! %ORT IS LABEL$ _% #4 CM _:4 ,PICTURE #B3 ,A "R TRIANGLE ) SIDES A1 ;B1 & ;C IS %[N ON A #H ,DRAFTSMAN4@.> ,SLIDE #BA3 ,P]IMET] _4 #CRD GRADE SKILL _4 ,/UD5TS NE$ TO LE>N3 ;$= ,TO C.T SQU>ES ON GRAPH PAP] TO DET]M9E P]IMET] ;$= ,TO F9D LABELS = L5G?S ( SIDES ;$= ,TO DET]M9E L5G? ( A MISS+ SIDE _4 ,T1* /UD5TS TO USE ,FEEL ';N ,PEEL NUMB] /ICK]S TO LABEL MISS+ SIDE L5G?S _4 ,USE GRAPH PAP]1 ,DRAFTSMAN1 ,GEOBO>D1 /UD5T'S TEXTBOOK @.<,PICTURE3 ,A SIX-SID$ IRREGUL> %AP$ CLOS$ FIGURE " HEXAGON"> IS DRAWN ON ! SPECIAL FILM US$ ) ! ,,APH ,DRAFTSMAN4 ,F ! LEFT & R1D+ CLOCKWISE1 ! SIDES >E LABEL$ #I1 #AA1 #F1 #G1 #C & #AH RESPECTIVELY4@.> #I ,SLIDE #BB3 ,>EA _4 #CRD GRADE SKILL " _4 #DTH - #GTH GRADE SKILL " _4 ,TIL+ A FIGURE ) UNIT SQU>ES ,- USE GRAPH PAP] ) /ICK]S1 PO/] PUTTY1 OR ,WIKKI ,/IX TO M>K ! SQU>ES ALR C.T$ _4 ,/UD5TS _1SY/EMATICALLY C.T SQU>ES ON GRID PAP]4 _4 ,US+ =MULAS TO F9D >EA _4 ,DECOMPOS+ %APES ,- USE ,GRAPHIC ,>T ,TAPE1 ,WIKKI ,/IX OR O!R TOOLS TO DIVIDE UP %APES _4 ,USE3 ,TACTILE ,TANGRAMS1 ,GEOBO>DS @.<,PICTURE3 ,A C>D F ! ,TACTILE ,TANGRAMS ,KIT %[+ A "R PO9T+ >R[ IS %[N4 ,A ,WIKKI ,/IX DIVIDES ! TRIANGLE F ! SQU>E POR;N ( ! FIGURE4 ,TWO BLUE FOAM "R TRIANGLES H BE5 PLAC$ 9 ! TRIANGLE POR;N ( ! #AJ >R[4@.> ,SLIDE #BC3 ,CIRCLES _4 #GTH GRADE SKILL _4 ,3CEPTS ;$= ,RADIUS ;$= ,DIAMET] ;$= ,PI ;$= ,CIRCUMF];E ;$= ,>EA _4 ,TO CALCULATE CIRCUMF];E & >EA H ! /UD5T USE A SCI5TIFIC CALCULATOR _4 ,USE3 ,DRAFTSMAN BO>D1 RU2] PAD1 TACTILE COMPASS = MA? & >T @.<,PICTURE3 ,ON A RU2] MAT A PIECE ( BRL PAP] IS PLAC$4 ,! COMPASS = MA? & >T IS 2+ US$ TO DRAW A CIRCLE4 ,) ! LEFT H& ! PO9T IS 2+ HELD4 ,! "R H& IS 2+ US$ TO MOVE ! :EEL4@.> #AA ,SLIDE #BD3 ,3GRU;E _4 #HTH GRADE SKILL _4 ,SAME %APE & SIZE _4 ,R1D+ TACTILE M>K+S ON A GRAPHIC TO TELL :5 SIDES OR ANGLES >E 3GRU5T4 _4 ,US+ L5G? OR M1SURE TO F9D 3GRU;E ;$= ,E/IMA;NS "<,9DEX ,C>D"> ;$= ,EXACT "<,RUL] OR ,PROTRACTOR"> _4 ,USE ,GEOMETRY ,TACTILE ,GRAPHICS ,KIT1 ,DRAFTSMAN1 /ICK]S1 ,WIKKI ,/IX @.<,PICTURE #A3 ,A COMPUT]-G5]AT$ TRIANGLE IS %[N4 ,A V]TICAL L9E " SEP>ATES X 9TO TWO 3GRU5T TRIANGLES4 ,TO 9DICATE T SIMIL>LY M>K$ SIDES & ANGLES >E 3GRU5T ! FOLL[+ M>K+S >E US$4 ,"O TICK M>K IS US$ ON EA* ( ! LEFT & "R SIDES ( ! DIVID$ BASE ( ! L>GE #AB TRIANGLE4 ,TWO TICK M>KS >E US$ ON BO? ! "R & LEFT SIDES ( ! L>GE TRIANGLE4 ,"O >C IS US$ ON EA* ( ! BASE ANGLES ( ! L>GE TRIANGLE4 ,TWO >CS >E US$ ON EA* ( ! LEFT & "R POR;NS ( ! TOP ANGLE ( ! L>GE TRIANGLE4 ,PICTURE #B3 ,AN EQUILAT]AL TRIANGLE IS DRAWN ON ! ,DRAFTSMAN4 ,%ORT PIECES ( GRE5 ,WIKKI ,/IX >E PLAC$ 9 ! MIDDLE ( EA* SIDE4 ,BLUE DOTS >E PLAC$ 9 EA* ( ! 9T]IOR ANGLES4@.> #AC ,SLIDE #BE3 #C-,DIM5.NAL ,%APES _4 #FTH GRADE SKILL3 ,REPRES5T+ #C-;,D %APES US+ NETS MADE UP ( RECTANGLES & TRIANGLES _4 #GTH GRADE SKILL3 ,DESCRIB+ #B-;,D FIGURES T RESULT F SLIC+ #C-;,D FIGURES _4 ,USE3 ;$= ,GEOMETRIC ,=MS ;$= ,GEOMETRO ,SETS "GE"> @.<,PICTURE #A3 ,! ,GEOMETRO ,KIT IS %[N4 ,! BOX T 3TA9S ! PIECES IS VISIBLE & DI6]5T PIECES >E LAID \4 ,A P5TAGONAL PRISM HAS BE5 3/RUCT$ ) ! PIECES4 ,PICTURE #B3 ,! NET = A SQU>E PYRAMID IS %[N MADE F ,GEOMETROS4 ,X IS COMPRIS$ ( A SQU>E & #D TRIANGLES4@.> #AD ,SLIDE #BF3 ,SURFACE ,>EA _4 #FTH - #GTH GRADE SKILL _4 ,US+ NETS TO F9D SURFACE >EA ( #C-;,D FIGURES _4 ,US+ =MULAS TO F9D SURFACE >EA _4 ,USE3 ;$= ,GEOMETRIC ,=MS ;$= ,GEOMETRO ,VELCRO ,SOLIDS ;$= ,/ACK,UPS3 ,SPATIAL ,R1SON+ ,US+ ,CUBES @& ,ISOMETRIC ,DRAW+S @.<,PICTURE3 ,TWELVE ,/ACK,UPS CUBES >E 3NECT$ TO MAKE A RECTANGUL> PRISM4 ,! TOP & BOTTOM LAY] HAS A _% #3@*2 _: >RAY ( CUBES4@.> #AE ,SLIDE #BG3 ,VOLUME ( ,PRISMS _4 #ETH - #FTH GRADE SKILL _4 ,US+ UNIT CUBES TO =M A SOLID FIGURE _4 ,F9D+ VOLUME BY C.T+ CUBES _4 ,F9D+ VOLUME ( RECTANGUL> PRISMS BY US+ ! L5G?S ( $GES & ! =MULA ;$= _% ,V .K LWH _: _4 ,ONCE A /UD5T MA/]S VOLUME ) ! CUBES1 !Y C MOVE TO ! C>DS 9 ! ,/ACK,UPS4 _4 ,USE3 ,OMNI,FIX ,CUBES1 ,/ACK,UPS3 ,SPATIAL ,R1SON+ ,US+ ,CUBES @& ,ISOMETRIC ,DRAW+S @.<,PICTURE3 ,TWO ,/ACK,UPS C>DS ) ! CORRESPOND+ #C,;D FIGURE CR1T$ F ! CUBES >E %[N4 ,! TOP %[S A _% #3@*2@*1 _: RECTANGUL> PRISM & ! BOTTOM %[S A _% #1@*1@*1 _: CUBE4@.> #AF ,SLIDE #BH3 ,VOLUME ( ,PRISMS & ,PYRAMIDS _4 #GTH GRADE SKILL _4 ,F9D+ VOLUME ( SOLID FIGURES BY DECOMPOS+ 9TO RECTANGUL> PRISMS _4 ,/>T ) BASIC PRISMS & ADV.E 9TO #C-;,D FIGURES T >E M COMPLEX4 @.<,PICTURE3 ,OMNIFIX CUBES >E %[N4 ,ON ! LEFT A _% #2@*3 _: >RAY & A _% #2@*1 _: >RAY >E %[N SEP>AT$4 ,ON ! "R !Y >E %[N 3NECT$4@.> #AG ,SLIDE #BI3 ,VOLUME ( ,C"OS1 ,CYL9D]S1 & ,SP"HS _4 #HTH GRADE SKILL _4 ,F9D RADIUS 9 C"OS1 CYL9D]S1 & SP"HS _4 ,F9D HEI;Y ) GRAPHICS 9 ! TEXTBOOK _4 ,PREP>E ! /UD5T = ! TYPES ( GRAPHICS !Y'LL SEE 9 TE/+ SITUA;NS #AH