,GRADES #B TO #E3 ,NEME?
   ,CODE ,SYMBOLS = ,FRAC;NS
     & ,SPATIAL ,PROBLEMS1
       ,9/RUC;NAL ,TOOLS1
    ,MAT]IALS1 & ,TE*NOLOGY

          ,LESSON #B3
      ,SPATIAL ,>RANGE;TS

       ,,PROJECT ,,9SPIRE
    ,UNIV]S;Y ( ,S\? ,C>OL9A
      ,UP/ATE1 ,FALL #BJBJ

    ,SLIDE #B
    ,LESSON #B ,OBJECTIVES
  ,"PICIPANTS W 2 ABLE TO R1D &
WRITE ADDI;N1 SUBTRAC;N1 &
MULTIPLICA;N SPATIALLY ALIGN$
PROBLEMS T 9CLUDE3

_4 MULTI-DIGIT NUMB]S ) & )\T
  COMMAS
_4 DECIMALS
_4 M"OY
_4 SIMPLE FRAC;NS             #A
_4 MIX$ NUMB]S

    ,SLIDE #C
    ,SPATIAL ,>RANGE;TS
    "<,V]TICAL"> ,PROBLEMS =
    ,ADDI;N & ,SUBTRAC;N
_?

  280
 + 15
333333
  295

_:

_4 ,NUMB]S M/ ALIGN 9 SPATIAL
  >RANGE;TS4
_4 ,"! >E NO NUM]IC 9DICATORS 9
  SPATIAL PROBLEMS4
_4 ,! ADDI;N OR SUBTRAC;N SIGN
  GOES "O CELL TO ! LEFT ( !
  WIDE/ NUMB] ABV ! SEP>A;N L9E4
_4 ,! SEP>A;N L9E _? 3333 _: IS
  "O CELL L;G] ON EI SIDE ( !
  WIDE/ "P ( ! PROBLEM4       #B
_4 ,Y M/ H A BLANK L9E ABV & 2L
  A SPATIAL >RANGE;T4

    ,SLIDE #D
    ,ANATOMY ( A ,SPATIAL
    ,PROBLEM
_?

  814
 - 25
333333
  789

_:
      @.<,9 PR9T1 _? 814 _: IS
    LABEL$ "<,M9U5D "<TOP
    NUMB]">2 _? - 25 _: IS
    LABEL$ ,M9US SIGN "O CELL
    LEFT ( WIDE/ NUMB]2
    _? 333333 _: IS LABEL$
    ,SEP>A;N L9E1 "O CELL WID]
    ?AN WIDE/ "P ( PROBLEM2 &
    _? 789 _: IS LABEL$ ,ANSW]
    ALIGN$ ) NUMB]S 9
    PROBLEM4@.>               #C
    ,SLIDE #E
    ,ANATOMY ( A ,SPATIAL
    ,PROBLEM ) ,COMMAS
_?

  56,780
 +12,237
333333333

_:
      @.<,9 PR9T1 _? 56,780 _:
    IS LABEL$ ,ADD5D "<TOP
    NUMB]">2 _? +12,237 _: IS
    LABEL$ ,PLUS SIGN "O CELL
    LEFT ( WIDE/ NUMB]2
    _? 333333333 _: IS LABEL$
    ,SEP>A;N L9E1 "O CELL WID]
    ?AN WIDE/ "P ( PROBLEM2 & AN
    >R[ PO9T+ TO ! V]TICAL
    >RANGE;T ( COMMAS IS LABEL$
    ,COMMAS ALIGN$4@.>



                              #D
    ,SLIDE #F
    ,EXAMPLES ( ,SPATIAL
    ,PROBLEMS
  ,:5 SPATIAL >RANGE;TS >E PLAC$
SIDE-BY-SIDE1 9S]T #A CELL "<OR
#B"> 2T ! 5D ( "O SEP>A;N L9E &
! 2G9N+ ( ! NEXT SEP>A;N L9E4
_?

  651     9,027     5,628
 + 80    -   39    -2,407
333333  33333333  33333333

_:

    ,SLIDE #G
    ,ACTIV;Y #B,A
    ,9T]L9E ! SPATIAL PROBLEMS4
_?

  836    375    6,047    5,786
 + 57   -169   -  889   +3,604
333333 333333 33333333 33333333

_:                            #E
    ,SLIDE #H
    ,ACTIV;Y #B,A3 ,ANSW] ,KEY
      @.<,F\R SPATIAL 4PLAYS >E
    %[N SIDE-BY-SIDE ACR ! PAGE
    Z FOLL[S3 ,EI<T HUNDR$
    ?IRTY-SIX PLUS FIFTY-SEV52
    ?REE HUNDR$ SEV5TY-FIVE M9US
    "O HUNDR$ SIXTY-N9E2 SIX
    ?\S& =TY SEV5 M9US EI<T
    HUNDR$ EI<TY-N9E2 FIVE ?\S&
    SEV5 HUNDR$ EI<TY-SIX PLUS
    ?REE ?\S& SIX HUNDR$ F\R4@.>

    ,SLIDE #I
    ,ACTIV;Y #B,B
  ,TRANSCRIBE ! FOLL[+ SPATIAL
ADDI;N & SUBTRAC;N PROBLEMS4
      @.<,?REE SPATIAL 4PLAYS >E
    %[N SIDE-BY-SIDE ACR ! PAGE
    Z FOLL[S3 TWO ?\S& ?IRTY
    M9US N9E HUNDR$ TW5TY2 ?REE
    ?\S& TW5TY-F\R PLUS TWO
    HUNDR$ SIXTY-SEV52
    TW5TY-?REE PLUS =TY-SIX PLUS
    TWELVE4 ,9 PR9T1 ! M9US   #F
    & PLUS SIGNS >E %[N TO !
    LEFT ( ! OV]ALL EQUA;NS4@.>

    ,SLIDE #AJ
    ,ACTIV;Y #B,B3 ,ANSW] ,KEY
_?

  2030     3,024     23
 - 920    +  267     46
3333333  33333333   +12
                   33333

_:











                              #G
    ,SLIDE #AA
    ,NUMB]$ ,PROBLEMS
    ,ADD OR SUBTRACT _%

#35_4   32   #36_4   94
       +20          - 7
      33333        33333

#37_4   403   #38_4   11
       -246          - 8
      333333        33333

_:
      @.<,! ,OP5+ ,NEME? ,CODE
    ,9DICATOR & ,NEME? ,T]M9ATOR
    >E EA* LABEL$4 ,O!R LABELS
    >E3 ,"! M/ 2 "O CELL 2T ! 5D
    ( A PROBLEM NUMB] & ! />T (
    ! SEP>A;N L9E42 ,BLANK L9E
    ABV & 2L A PROBLEM42 & ,USE
    "O OR TWO CELLS 2T ! 5D ( A
    SEP>A;N L9E & />T ( ! NEXT
    PROBLEM NUMB]4@.>

                              #H
    ,SLIDE #AB
    ,SPATIAL ,>RANGE;TS =
    ,MULTIPLICA;N
  .7,J Z ) ADDI;N & SUBTRAC;N3.'

_4 ,NUMB]S M/ ALIGN 9 SPATIAL
  >RANGE;TS4
_4 ,! SEP>A;N L9E _? 3333 _: IS
  "O CELL L;G] ON EI SIDE ( !
  WIDE/ "P ( ! PROBLEM4 ,Y M/ H
  A BLANK L9E ABV & 2L A SPATIAL
  >RANGE;T4

  .1,! .1DI6];E3
  ,! MULTIPLICA;N CROSS GOES "O
CELL TO ! LEFT ( ! MULTIPLI]4








                              #I
    ,SLIDE #AC
    ,ANATOMY ( A ,MULTIPLICA;N
    ,PROBLEM
_?

  8,207
    @*6
33333333
 49,242

_:

      @.<,9 PR9T1 _? 8,207 _: IS
    LABEL$3 ,M9U5D "<TOP
    NUMB]">4 ,O!R LABELS >E3
    ,MULTIPLICA;N CROSS "O CELL
    LEFT ( ! MULTIPLI] "<BOTTOM
    NUMB]">2 & ,SEP>A;N L9E1 "O
    CELL WID] ?AN WIDE/ "P (
    PROBLEM "<9 ? CASE !
    ANSW]">4@.>



                             #AJ
    ,SLIDE #AD
    ,EXAMPLES ( ,MULTIPLICA;N
    ,PROBLEMS
_?

   5     982      500       63
 @*4     @*3      @*8     @*74
33333  333333  3333333   333333
  20    2946    4,000     4662

_:

    ,SLIDE #AE
    ,SPATIAL ,>RANGE;T =
    ,PROBLEMS T ,9CLUDE
    ,DECIMALS OR ,M"OY
_4 ,! DOLL> SIGN IS _? @S _: & !
  DECIMAL PO9T IS _? . _:4
_4 ,FOLL[ ! PR9T TO DET]M9E IF !
  PLUS OR M9US GOES TO ! LEFT (
  ! DOLL> SIGN _1OR DIRECTLY 2L
  ! DOLL> SIGN4
_4 ,IF PLAC$ 2L ! DOLL> SIGN1
  ALIGN PLUS & M9US SIGN ) !
  SECOND CELL ( ! DOLL>      #AA
  SIGN4
_4 ,DECIMAL PO9TS >E ALIGN$ )
  DECIMAL PO9TS4

    ,SLIDE #AF
    ,EXAMPLES ( ,SPATIAL
    ,PROBLEMS ) ,DOLL> ,SIGNS &
    ,DECIMALS
_?

#5_4   @S4.82  #6_4  @S900
      -  2.10         + 75
     333333333      3333333

#7_4   19.60
      -10.20
     33333333

_:





                             #AB
    ,SLIDE #AG
    ,M ,EXAMPLES ( ,SPATIAL
    ,PROBLEMS ) ,DOLL> ,SIGNS &
    ,DECIMALS
_?

#1_4   1.69   #2_4   6.24
      + .08         - .63
     3333333       3333333
                     5.61

#3_4  @S3,015
          @*2
     333333333
      @S6,030

_:







                             #AC
    ,SLIDE #AH
    ,TWO ,LA/ ,EXAMPLES ,-
    ,SPATIAL ,>RANGE;TS ) ,DOLL>
    ,SIGNS & ,DECIMALS
_?

 @S61.00    5.2
    @*40    @*6
333333333  33333

_:













                             #AD
    ,SLIDE #AI
    ,ACTIV;Y #B,C
    ,9T]L9E ! FOLL[+ DIREC;NS &
  PROBLEMS4

    ,COMPUTE4
_?

#4_4   73   #5_4   83.50
      -17         + 4.75
     33333       33333333

#6_4   @S 9.59   #7_4  3,752
      +  18.26          @*50
     3333333333       3333333

_:







                             #AE
    ,SLIDE #BJ
    ,ACTIV;Y #B,C3 ,ANSW] ,KEY

    ,COMPUTE4
#D4 ,SEV5TY-?REE M9US SEV5TE54
#E4 ,EI<TY-?REE DECIMAL FIFTY
  PLUS F\R DECIMAL SEV5TY-FIVE4
#F4 ,DOLL> SIGN N9E DECIMAL
  FIFTY-N9E PLUS EI<TE5 DECIMAL
  TW5TY-SIX4
#G4 ,?REE ?\S&1 SEV5 HUNDR$
  FIFTY-TWO "TS FIFTY4












                             #AF
    ,SLIDE #BA
    ,ACTIV;Y #B,D
    ,TRANSCRIBE ! FOLL[+ SPATIAL
  PROBLEMS4
#D4 ,DOLL> SIGN FIVE HUNDR$ T5
  M9US TW5TY-FIVE EQUALS DOLL>
  SIGN F\R HUNDR$ EI<TY-FIVE4
      @.<,9 PR9T1 ! M9US SIGN IS
    %[N TO ! LEFT ( ! OV]ALL
    EQUA;N4@.>
#E4 ,TWO ?\S& FIVE HUNDR$ SIXTY
  "TS TW5TY4
#F4 ,DOLL> SIGN DECIMAL
  FIFTY-FIVE PLUS TWO DECIMAL T5
  PLUS FIVE DECIMAL TW5TY-FIVE4
      @.<,9 PR9T1 ! PLUS SIGN
    ALIGNS ) ! DOLL> SIGN4@.>







                             #AG
    ,SLIDE #BB
    ,ACTIV;Y #B,D3 ,ANSW] ,KEY
_?

#4_4   @S510   #5_4  2560
      -   25         @*20
     33333333       333333
       @S485

#6_4  @S .55
        2.10
       +5.25
     33333333

_:









                             #AH
    ,SLIDE #BC
    ,SPATIALLY ,ALIGN$ ,PROBLEMS
    ) ,SIMPLE ,FRAC;NS
_4 ,SET UP SPATIALLY ALIGN$
  FRAC;N PROBLEMS ! SAME WAY Y
  SETUP O!R SPATIAL PROBLEMS ,,B
  AL ALIGN3 OP5 FRAC;N 9DICTORS1
  FRAC;N L9ES1 & CLOS+ FRAC;N
  9DICATORS4
_?

#1_4   ?1/2#   #2_4   ?1/7#
      -?3/8#         +?4/7#
     33333333       33333333

_:








                             #AI
    ,SLIDE #BD
    ,SPATIALLY ,ALIGN$ ,PROBLEMS
    ) ,MIX$ ,NUMB]S
_4 ,:OLE NUMB]S1 FRAC;N
  9DICATORS1 & HORIZONTAL FRAC;N
  L9ES >E ALIGN$ V]TICALLY 9 EA*
  PROBLEM4
_4 ,! NUM]IC 9DICATOR IS N TO 2
  US$ 9 FRONT ( ! :OLE NUMB] ( !
  MIX$ NUMB] 9 SPATIALLY >RANG$
  PROBLEMS4

_?

  10_?4/15_#
 + 9_?7/15_#
3333333333333

_:





                             #BJ
    ,SLIDE #BE
    ,EXAMPLES ( ,SPATIAL
    ,PROBLEMS ) ,MIX$ ,NUMB]S &
    ,SIMPLE ,FRAC;NS
_?

  1_?3/5 _#     5_?11/15_#
 +5_?1/10_#    -4_? 2/15_#
333333333333  3333333333333

  2_?1_/8_#
 +  ?3_/4 #
333333333333

_:









                             #BA
    ,SLIDE #BF
    ,ACTIV;Y #B,E
    ,TRANSCRIBE ! FOLL[+
  PROBLEMS3
#C4 ,TW5TY-?REE & ?IRTE5
  OV] TW5TY-"O M9US T5 & FIVE
  OV] TW5TY-"O4
      @.<,9 PR9T1 ! MIX$ FRAC;N
    USES A HORIZONTAL FRAC;N
    L9E4@.>
#D4 ,=TY-N9E & SIX OV] FIFTY
  PLUS EI<T & TW5TY-SEV5
  OV] FIFTY4
      @.<,9 PR9T1 ! MIX$ FRAC;N
    USES A DIAGONAL FRAC;N
    L9E4@.>
#E4 ,"O-SIXTE5? PLUS FIVE-EI<?S4
      @.<,9 PR9T1 ! FRAC;N USES
    A HORIZONTAL FRAC;N L9E4@.>





                             #BB
    ,SLIDE #BG
    ,ACTIV;Y #B,E3 ,ANSW] ,KEY
_?

#3_4   23_?13/21_#
      -10_? 5/21_#
     33333333333333

#4_4   49_? 6_/50_#
      + 8_?27_/50_#
     333333333333333

#5_4   ?1/16#
      +?5/8 #
     333333333

_:







                             #BC