,*APT] #D3 ,SPATIAL       #D4A
       ,>RANGE;TS & ,NUMB] ,L9ES
         ,US$ 9 ,GRADES ;,K-#F

    ,NEW ,SYMBOLS ,9TRODUC$
.=7777 .<DOTS #B-#C-#E-#F1 DOTS
  #B-#C-#E-#F1 DOTS #B-#C-#E-#F1 DOTS
  #B-#C-#E-#F.> ,C>RI$ NUMB] 9DICATOR
  "<L5G? V>IES2 NO PR9T EQUIVAL5T">
.=3333 .<DOTS #B-#E1 DOTS #B-#E1 DOTS
  #B-#E1 DOTS #B-#E.> ,SEP>A;N L9E US$ 9
  SPATIALLY ALIGN$ ADDI;N1 SUBTRAC;N1 &
  MULTIPLICA;N1 & DIVI.N PROBLEMS Z WELL
  Z 9 3JUNC;N ) ! DIVID$ 9TO SIGN
.=O .<DOTS #A-#C-#E.> ,DIVI.N SIGN OR
  DIVID$ 9TO

      ,NUMB] L9E SYMBOLS
.=[ .<DOTS #B-#D-#F.> ,LEFT-PO9T+ >R[H1D
.=3 .<DOTS #B-#E.> ,L9E "<AXIS L9E">
.=R .<DOTS #A-#B-#C-#E.> ,COORD9ATE
  SCALE M>K "<TICK M>K">
.=O .<DOTS #A-#C-#E.> ,"R-PO9T+ >R[H1D
.== .<DOTS #A-#B-#C-#D-#E-#F.> ,SOLID OR
  FILL$-9 CIRCLE ABV ! NUMB] L9E      #A
               ,*APT] #D           A#D4A
  "<PO9T">

    ,NEW ,,BANA ,T]MS
_4 ^1,SPATIAL ^1>RANGE;T3 ,A MA? PROBLEM
  T IS WRITT5 V]TICALLY "<"O NUMB] OV] !
  O!R"> IS CALL$ A SPATIAL >RANGE;T4

    ,KEY ,PO9TS
_4 ,9 A V]TICALLY ALIGN$ PROBLEM
  "<SPATIAL >RANGE;T">1 ! ^1ADDI;N OR
  ^1SUBTRAC;N ^1SIGN GOES "O CELL TO !
  LEFT ( ! WIDE/ NUMB] 9 ! PROBLEM4
_4 ,A ^1SEP>A;N ^1L9E IS US$ 9 A
  V]TICALLY ALIGN$ PROBLEM4 ,X IS "O
  CELL L;G] ON ! LEFT & "O CELL L;G] ON
  ! "R ?AN ! WIDE/ "P ( ! PROBLEM4
------------------------------------#D4B
_4 ,:5 BRAILL+ A V]TICALLY ALIGN$
  PROBLEM1 MAKE A ^1W9D[ >.D ! PROBLEM4
  ,? M1NS Y L1VE A BLANK L9E ABV & 2L !
  PROBLEM & #A-#B BLANK CELLS TO ! LEFT
  & "R ( ! PROBLEM4
_4 ,:5 V]TICALLY ALIGN$ PROBLEMS >E
  PLAC$ NEXT TO EA* O!R ^79 A R[^'1   #B
               ,*APT] #D           A#D4B
  "! M/ 2 #A BLANK CELL "<AL? Y MAY USE
  #B BLANK CELLS"> 2T ! SEP>A;N L9ES ( !
  PROBLEMS4
_4 ,:5 BRAILL+ ^1M"OY AM.TS 9 A
  V]TICALLY ALIGN$ PROBLEM1 ALIGN !
  DECIMAL PO9TS4 ,FOLL[ ! PR9T = PLACE;T
  ( ! ADDI;N OR SUBTRAC;N SIGN 9 RELA;N
  TO ! DOLL> SIGN4
_4 ,9 A V]TICALLY ALIGN$ PROBLEM1 !
  ^1MULTIPLICA;N ^1SIGN IS PLAC$ 9 !
  CELL IMMLY TO ! LEFT ( ! MULTIPLI] "<!
  BOTTOM NUMB] ( ! PROBLEM">4
_4 ,:5 V]TICALLY ALIGN$ PROBLEMS >E
  ^1NUMB]$1 "! M/ 2 "O CELL 2T ! 5D ( !
  NUMB] & ! 2G9N+ ( ! SEP>A;N L9E4
_4 ^1,DIVI.N ^1PROBLEMS >E 3SID]$
  SPATIAL :5 M ?AN ! DIVISOR & DIVID5D
  >E %[N4
_4 ,9 A SPATIALLY ALIGN$ DIVI.N PROBLEM1
  PLACE ! ^1DIVI.N ^1SIGN 2T ! DIVISOR &
  DIVID5D4 ,! ^1SEP>A;N ^1L9E 2G9S ABV !
  DIVI.N SIGN & EXT5DS "O CELL TO ! "R (
  ! PROBLEM4
_4 ,! ^7C>RI$ NUMB] 9DICATOR^' DOES   #C
               ,*APT] #D           B#D4B
  N H A PR9T EQUIVAL5T4 ,9 A V]TICALLY
  ALIGN$ PROBLEM1 X IS PLAC$ ABV ! TOP
  NUMB] 9 ! PROBLEM & IS ! SAME L5G? Z !
  SEP>A;N L9E4
_4 ^1,NUMB] ^1L9ES C 2 CR1T$ 9 BRL )
  ,NEME? ,CODE SYMBOLS US+ A BRLWRIT]4
  ,L1VE A BLANK L9E ABV & 2L A NUMB]
  L9E4
_4 ,ON NUMB] L9ES1 ^1NUM]IC ^19DICATORS
  >E N US$4 ,NUMB]S M/ 2 EQUALLY SPAC$
  AL;G ! AXIS4

    ,SPATIAL ,>RANGE;TS = ,ADDI;N &
    ,SUBTRAC;N ( ,:OLE ,NUMB]S
  ,/UD5TS >E USUALLY 9TRODUC$ TO
V]TICALLY ALIGN$ ADDI;N & SUBTRAC;N
PROBLEMS 9 K9D]G>T5 OR F/ GRADE4 ,? =MAT
IS V HELP;L :5 /UD5TS CALCULATE OR
COMPUTE ! ANSW]4 ,9 ,NEME? ,CODE1
V]TICALLY ALIGN$ PROBLEMS >E AL CALL$
^1SPATIAL ^1>RANGE;TS4
  ,NUM]IC 9DICATORS >E N US$ 9 SPATIAL
>RANGE;TS1 & S+LE L9E SPAC+ IS US$ "?\T
! PROBLEM1 EV5 = "Y /UD5TS "<,RULE    #D
               ,*APT] #D           C#D4B
,,II1 ^S#AA;B">4
------------------------------------#D4C
  ,! L9E "U ! SECOND ADD5D IS CALL$ A
^1SEP>A;N ^1L9E4 ,X IS CR1T$ 9 ,NEME?
,CODE ) A L9E ( DOTS #B-#E4
  .=3333
  ,! SEP>A;N L9E EXT5DS "O CELL TO !
LEFT & "O CELL TO ! "R ( ! WIDE/
>RANGE;T 9 ! PROBLEM "<,RULE ,,XXIV1
^S#AGH;C">4
  ,9 ! V]TICALLY ALIGN$ PROBLEM1 ! PLUS
SIGN IS PLAC$ "O CELL TO ! LEFT ( !
WIDE/ NUMB] ABV ! SEP>A;N L9E "<,RULE
,,XXIV1 ^S#AGH;C">4
  ,EXAMPLE #D4A 3TA9S AN ADDI;N PROBLEM
WRITT5 V]TICALLY1 T IS GO+ D[N ! PAGE
9/1D ( HORIZONTALLY ACR A S+LE L9E4 ,!
F/ ADD5D IS DIRECTLY ABV ! SECOND ADD5D
9 ! PROBLEM4




                                      #E
               ,*APT] #D           A#D4C

      ,EXAMPLE #D4A _%

  6
 +2
3333

_:
  ,:5 PROBLEMS >E WRITT5 V]TICALLY 9
PR9T1 !Y >E WRITT5 V]TICALLY 9 ,NEME?
,CODE4 ,X IS ESS5TIAL T "Y /UD5TS LE>N
H[ TO R1D & WRITE SPATIALLY ALIGN$
PROBLEMS Z !Y W SEE SPATIALLY ALIGN$
PROBLEMS 9 _! TEXTBOOKS & /&>DIZ$
ASSESS;TS4
  ,2F WRIT+ A SPATIALLY ALIGN$ PROBLEM
ON A BRLWRIT]1 X IS IMPORTANT TO DET]M9E
9 : BRL CELL EA* L9E ( ! PROBLEM W 2G94
  ,EXAMPLE #D4B 3TA9S TWO SUBTRAC;N
PROBLEMS 9 SPATIAL =MAT4 ,NOTICE T3

_4 ,SIMIL> TO ! PLUS SIGN1 ! M9US SIGN
  IS PLAC$ "O CELL TO ! LEFT ( ! WIDE/
  NUMB] 9 ! PROBLEM & DIRECTLY ABV    #F
               ,*APT] #D           B#D4C
  ! SEP>A;N L9E "<,RULE ,,XXIV1
  ^S#AGH;C">4
_4 ,9 ! F/ PROBLEM1 ! SECOND L9E ( !
  PROBLEM IS ! WIDE/ L9E 9 ! >RANGE;T4
  ,X TAKES TWO BRL CELLS TO WRITE ! M9US
  SIGN & ! DIGIT #C4
------------------------------------#D4D
_4 ,9 ! SECOND PROBLEM1 ! SECOND L9E ( !
  PROBLEM IS AL ! WIDE/ "P ( ! >RANGE;T4
  ,X TAKES TWO BRL CELLS TO WRITE ! M9US
  SIGN & ! DIGIT #A4
_4 ,9 BO? PROBLEMS ! SEP>A;N L9E IS #D
  CELLS L;G4 ,X 2G9S 9 CELL #A4
_4 ,9 ! SECOND PROBLEM1 ! ANSW] IS
  9CLUD$ 2C X IS 9CLUD$ 9 PR9T4

      ,EXAMPLE #D4B _%

  4
 -3
3333


                                      #G
               ,*APT] #D           A#D4D
  7
 -1
3333
  6

_:

      ,PRACTICE #D4A
  .7,9T]L9E ! SPATIALLY ALIGN$
PROBLEMS4.' _%

  8
 -4
3333

  9
 +1
3333





                                      #H
               ,*APT] #D            #D4E
  6
 -5
3333

  7
 -6
3333

  8
 +2
3333

  1
 +3
3333

_:

  .7,USE YR BRLWRIT] TO WRITE !
SPATIALLY ALIGN$ PROBLEMS4.'
      @.<,PROBLEMS >E SPELL$ \ TO ALL[ =
    PRACTICE4@.>
EI<T M9US ?REE
TWO M9US "O                           #I
               ,*APT] #D           A#D4E
F\R PLUS F\R
N9E PLUS FIVE
?REE M9US TWO
SEV5 PLUS SIX
------------------------------------#D4F
  ,BY ! "T /UD5TS F9I% F\R? GRADE1 !Y %D
2 ABLE TO E6ICI5TLY ADD & SUBTRACT
MULTI-DIGIT :OLE NUMB]S "<,COMMON ,CORE
,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ">4
,EXAMPLE #D4C 3TA9S AN ADDI;N PROBLEM )
A TWO-DIGIT ADD5D4 ,NOTICE T3

_4 ,! PLUS SIGN IS PLAC$ "O CELL TO !
  LEFT ( ! WIDE/ NUMB] 9 ! PROBLEM1 #AJ4
_4 ,! F/ L9E ( ! PROBLEM 2G9S 9 CELL #C1
  & ! SECOND L9E ( ! PROBLEM 2G9S 9 CELL
  #B4
_4 ,! SEP>A;N L9E 2G9S 9 CELL #A4





                                     #AJ
               ,*APT] #D           A#D4F

      ,EXAMPLE #D4C _%

  10
 + 5
33333

_:
  ,EXAMPLE #D4D 3TA9S FIVE MULTI-DIGIT
ADDI;N & SUBTRAC;N PROBLEMS4 ,NOTICE T3

_4 ,! NUMB]S 9 EA* PROBLEM >E ALIGN$ AC
  TO _! PLACE VALUE4
_4 ,:5 A COMMA IS 9CLUD$ )9 A NUMB] 9
  PR9T1 A MA!MATICAL COMMA IS 9CLUD$ )9
  ! NUMB] 9 BRL4
_4 ,"! IS A BLANK L9E ABV & 2L EA*
  PROBLEM4





                                     #AA
               ,*APT] #D           B#D4F

      ,EXAMPLE #D4D _%
  47
  20
 +13
33333

------------------------------------#D4G

  46
 +18
33333

  295
 - 63
333333

  2,000
 -   62
33333333



                                     #AB
               ,*APT] #D           A#D4G

  89,105
 + 3,289
333333333

_:
  ,= ADDI;N & SUBTRAC;N PROBLEMS WRITT5
9 SPATIAL =MAT1 ! ANSW] IS WRITT5 2L !
SEP>A;N L9E4 ,! DIGITS 9 ! ANSW] M/ 2
ALIGN$ ) ! DIGITS 9 ! NUMB]S ABV !
SEP>A;N L9E4
  ,EXAMPLE #D4E 3TA9S TWO EXAMPLES 9 : !
ANSW] IS 9CLUD$ ) ! PROBLEM4
------------------------------------#D4H

      ,EXAMPLE #D4E _%

  814
 - 25
333333
  789


                                     #AC
               ,*APT] #D           A#D4H

  7
  9
 +2
3333
 18

_:

      ,PRACTICE #D4B
  .7,9T]L9E ! SPATIALLY ALIGN$
PROBLEMS4.' _%

  27
 - 8
33333

  193
 - 54
333333
  139


                                     #AD
               ,*APT] #D            #D4I

  8,000
 -  450
33333333

  3,756,780
 +   12,237
333333333333

  28
 +13
33333
  41

_:
  .7,USE YR BRLWRIT] TO WRITE ! PROBLEMS
9 SPATIAL =MAT4.'
      @.<,PROBLEMS >E SPELL$ \ TO ALL[ =
    PRACTICE4 ,! ^W 8PLUS0 IS REP1T$ 2T
    ALL ADD5DS4 ,9 PR9T1 A PLUS SIGN IS
    F.D ONLY 2S ! F9AL ADD5D4@.>
SEV5TE5 PLUS F\R PLUS N9E
FIFTY-SIX PLUS TW5TY-"O
TWO ?\S& ?REE HUNDR$ SEV5TY SIX      #AE
               ,*APT] #D           A#D4I
  M9US SIXTY-?REE
"O HUNDR$ ?\S& M9US TW5TY ?\S&

  ,:5 V]TICALLY ALIGN$ PROBLEMS >E PLAC$
SIDE-BY-SIDE 9 PR9T1 "! M/ 2 AT L1/ "O
BLANK CELL 2T ! SEP>A;N L9ES 9 BRL
"<,RULE ,,XXV1 ^S#AHE;C">4 ,= "S /UD5TS1
X IS EASI] TO R1D ! PROBLEMS :5 "! >E
TWO BLANK CELLS 2T ! SEP>A;N L9ES4 ,"!
%D ALW 2 A BLANK L9E ABV & 2L SPATIALLY
ALIGN$ PROBLEMS "<,RULE ,,XXV1 ^S#AHE">4

  ^1,T1*+ ^1,TIP3 ,SPATIALLY ALIGN$
  PROBLEMS H A 8W9D[0 >.D !M4 ,? M1NS "!
  IS A BLANK L9E ABV & 2L ! PROBLEM4
-----------------------------------#D4AJ
  ,IF M ?AN "O SPATIALLY ALIGN$ PROBLEM
  IS ON ! SAME L9E1 "! M/ 2 AT L1/ "O
  BLANK CELL 2T ! PROBLEMS4

  ,EXAMPLE #D4F 9CLUDES A R[ ( ?REE
SPATIALLY ALIGN$ PROBLEMS TRANSCRIB$ 9
TWO DI6]5T WAYS4 ,! F/ TRANSCRIP;N
9CLUDES "O BLANK CELL 2T ! SEP>A;N   #AF
               ,*APT] #D          A#D4AJ
L9ES4 ,! SECOND TRANSCRIP;N 9CLUDES TWO
BLANK CELLS 2T ! SEP>A;N L9ES4

      ,EXAMPLE #D4F _%

  4    10    12
 -2   - 3   - 6
3333 33333 33333

  4    10    12
 -2   - 3   - 6
3333 33333 33333

_:

      ,PRACTICE #D4C
  .7,9T]L9E ! SPATIALLY ALIGN$
PROBLEMS4.' _%

  18    6    5
 - 3   -4   +9
33333 3333 3333

                                     #AG
               ,*APT] #D          B#D4AJ

  788    68    12
 + 14   - 3   +15
333333 33333 33333

_:
  .7,USE YR BRLWRIT] TO WRITE ! PROBLEMS
9 SPATIAL =MAT4 ,L1VE "O BLANK L9E 2T !
PROBLEMS4 ,Y MAY ELECT TO USE #A OR #B
BLANK CELLS 2T SEP>A;N L9ES4.'
      @.<,! FOLL[+ SIX PROBLEMS >E BROK5
    9TO #B SETS ( #C PROBLEMS4 ,! #C
    PROBLEMS APPE> SIDE BY SIDE ON !
    SAME L9E 9 PR9T4@.>
@.<,SET #A@.>
N9ETE5 M9US SEV5
SEV5TY-EI<T M9US ?REE
EI<T M9US SIX
-----------------------------------#D4AA
@.<,SET #B@.>
TWO HUNDR$ EI<TY-N9E M9US FIVE
?IRTY-N9E M9US SIXTE5
=TY-SIX M9US Z]O
                                     #AH
               ,*APT] #D          A#D4AA

    ,SPATIAL ,>RANGE;TS ,:5 ! ,PROBLEMS
    >E ,NUMB]$
  ,MA? "W%EETS & TE/S PROBLEMS >E (T5
NUMB]$4 ,Y M/ TAKE C>E :5 NUMB]+ A
SPATIALLY ALIGN$ PROBLEM 2C Y M/ L1VE A
8W9D[0 >.D ! PROBLEM4 ,9 ADDI;N TO !
BLANK L9E 2F & AF EA* PROBLEM & A BLANK
CELL 2T ! PROBLEMS1 "! M/ 2 "O BLANK
CELL 2T ! 5D ( EA* PROBLEM NUMB] & ! />T
( ! SEP>A;N L9E "<,RULE ,,XXV1
^S#AHE;C">4
  ,X MAY 2 EASI] = "S /UD5TS TO R1D
NUMB]$ SPATIALLY ALIGN$ PROBLEMS IF Y
L1VE TWO BLANK CELLS 2T ! PROBLEMS4 ,9
,EXAMPLE #D4G NOTICE "! >E TWO BLANK
CELLS 2T ! PROBLEMS4

      ,EXAMPLE #D4G _%

#35_4   32   #36_4   94
       +20          - 8
      33333        33333
                                     #AI
               ,*APT] #D          B#D4AA

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

_:

      ,PRACTICE #D4D
    ,9T]L9E ! SPATIALLY ALIGN$ PROBLEMS4
_%

#1_4   36   #2_4   21
      -29         +88
     33333       33333

#3_4   807   #4_4   4,847
      + 64         -  795
     333333       33333333

_:
-----------------------------------#D4AB
    ,USE YR BRLWRIT] TO WRITE ! PROBLEMS
  9 SPATIAL =MAT4 ,L1VE "O BLANK L9E 2T
  ! R[S ( PROBLEMS4 ,"! %D AL 2 "O   #BJ
               ,*APT] #D          A#D4AB
  BLANK CELL 2T ! PROBLEM NUMB] & ! />T
  ( EA* SEP>A;N L9E4 ,9 ADDI;N1 Y MAY
  ELECT TO USE #A OR #B BLANK CELLS 2T
  EA* SEP>A;N L9E & ! NEXT PROBLEM
  NUMB]4
      @.<,PROBLEMS >E SPELL$ \ TO ALL[ =
    PRACTICE4 ,! ^W 8PLUS0 IS REP1T$ 2T
    ALL ADD5DS4 ,9 PR9T1 A PLUS SIGN IS
    F.D ONLY 2S ! F9AL ADD5D4@.>
      @.<,! FOLL[+ F\R PROBLEMS >E BROK5
    9TO #B SETS ( #B PROBLEMS4 ,! #B
    PROBLEMS APPE> SIDE BY SIDE ON !
    SAME L9E 9 PR9T4@.>
@.<,SET #A@.>
N9ETY-"O PLUS F\R PLUS ?IRTE5
"O HUNDR$ TWELVE PLUS ?IRTY-FIVE PLUS
  ?IRTY-SIX
@.<,SET #B@.>
EI<T ?\S& N9E-HUNDR$ PLUS ?IRTY-FIVE
?REE HUNDR$ N9ETY-SEV5 M9US =TY

    ,SPATIALLY ,ALIGN$ ,PROBLEMS T
    ,9CLUDE ,M"OY
  ,/UD5TS W 3T9UE TO R1D & WRITE     #BA
               ,*APT] #D          B#D4AB
MA? PROBLEMS T >E V]TICALLY ALIGN$ "?\T
! ELE;T>Y GRADES4 ,9 REVIEW1 V]TICALLY
ALIGN$ PROBLEMS >E CALL$ SPATIAL
>RANGE;TS 9 ! ,NEME? ,CODE4 ,NUM]IC
9DICATORS >E N US$ 9 SPATIAL >RANGE;TS1
& S+LE L9E SPAC+ IS US$ "?\T ! PROBLEM
"<,RULE ,,II1 ^S#AA;B">4
  ,9 ADDI;N TO SPATIAL >RANGE;TS T
9CLUDE ADDI;N & SUBTRAC;N ( :OLE NUMB]S1
/UD5TS NE$ TO LE>N H[ TO R1D & WRITE
SPATIAL >RANGE;TS T 9CLUDE DECIMALS1
M"OY1 FRAC;NS1 & MIX$ NUMB]S4 ,FRAC;NS &
MIX$ NUMB]S >E 9TRODUC$ 9 ,*APT] #E4
  ,EXAMPLE #D4H 9CLUDES ?REE V]TICAL
ADDI;N PROBLEMS4 ,! F/ ADD5D IS WRITT5
DIRECTLY ABV ! SECOND ADD5D 9 EA*
PROBLEM4 ,? 9CLUDES ! DECIMAL PO9T4
  ,FUR!RMORE1 ! PLUS SIGN IS PLAC$ "O
CELL TO ! LEFT ( ! WIDE/ NUMB] ABV !
SEP>A;N L9E 9 ! >RANGE;T "<,RULE ,,XXIV1
^S#AGH;C">4
  ,EXAMPLE #D4H 3TA9S ?REE PROBLEMS T >E
SIDE-BY-SIDE 9 PR9T4 ,!Y >E AL
SIDE-BY-SIDE 9 BRL S9CE !Y W ALL     #BB
               ,*APT] #D          C#D4AB
FIT ON A L9E4 ,:5 ! SAME NUMB] (
PROBLEMS C 2 A3OMMODAT$ ON A S+LE BRL
L9E1 X IS (T5 HELP;L TO D S4 ,? W "S"TS
MAKE X EASI] & QK] = ! /UD5T "PICIPAT+ 9
A G5]AL $UCA;N MA? CLASS TO LOCATE A
SPECIFI$ PROBLEM4
  ,9 ALL ?REE PROBLEMS ! DECIMAL PO9TS
>E ALIGN$ 9 PR9T & "!=E >E ALIGN$ 9 BRL4
-----------------------------------#D4AC

      ,EXAMPLE #D4H _%

  6.1     3.78     19.253
 +2.1    + .45    + 4.68
333333  3333333  333333333

_:
  ,EXAMPLE #D4I 3TA9S TWO SUBTRAC;N
PROBLEMS 9 SPATIAL =MAT4 ,! ANSW] IS
9CLUD$ 9 ! SECOND PROBLEM 2C X IS 9CLUD$
9 PR9T4 ,! PROBLEMS >E NUMB]$ 9 PR9T1 S
!Y >E NUMB]$ 9 BRL4 ,! DECIMAL PO9TS >E
ALIGN$4 ,L1VE "O BLANK CELL 2T ! PROBLEM
NUMB] & ! />T ( ! SEP>A;N L9E        #BC
               ,*APT] #D          A#D4AC
"<,RULE ,,XXV1 ^S#AHE;B">4

      ,EXAMPLE #D4I _%

#1_4   14.7   #2_4   8.06
      -  .3         -2.5
     3333333       3333333
                     5.56

_:
  ,9 A SPATIALLY ALIGN$ PROBLEM1 ! PLUS
OR M9US SIGN %D NORMALLY 2 PLAC$ "O CELL
TO ! LEFT ( ! WIDE/ NUMB] ABV ! SEP>A;N
L9E 9 ! >RANGE;T "<,RULE ,,XXIV1
,S#AGH;B">4 ,H["E1 :5 A DOLL> SIGN IS AL
9CLUD$1 ! PLACE;T ( ! PLUS OR M9US SIGN
MAY FOLL[ PR9T "<,RULE ,,XXIV1
,S#AGH;B">4
  ,SEE ,EXAMPLE #D4AJ 2L = ?REE EXAMPLES
3TA9+ A DOLL> SIGN4 ,9 ! F/ PROBLEM1 !
M9US SIGN IS PLAC$ TO ! LEFT ( ! DOLL>
SIGN 9 PR9T & BRL4
  ,9 ! SECOND PROBLEM1 ! M9US SIGN IS
PLAC$ DIRECTLY 2L ! DOLL> SIGN 9     #BD
               ,*APT] #D          B#D4AC
PR9T & BRL4 ,NOTICE ! M9US SIGN IS PLAC$
2L ! SECOND CELL ( ! DOLL> SIGN4 ,9 BO?
( ^! PROBLEMS ! ANSW] IS 9CLUD$ 9 PR9T1
S ! ANSW] IS 9CLUD$ 9 BRL4
  ,9 ! ?IRD PROBLEM1 ! PLUS SIGN IS
PLAC$ TO ! LEFT ( ! DOLL> SIGN 9 PR9T &
BRL4
-----------------------------------#D4AD

      ,EXAMPLE #D4AJ _%

#1_4   @S3.75
      -  1.30
     333333333
       @S2.40

#2_4  @S700
       - 50
     3333333
      @S650



                                     #BE
               ,*APT] #D          A#D4AD

#3_4   @S25.99
         46.50
      +  31.98
     3333333333

_:

      ,PRACTICE #D4E
    .7,9T]L9E ! SPATIALLY ALIGN$
  PROBLEMS4.' _%
#1_4   @S50
      +  20
     3333333

-----------------------------------#D4AE

#2_4   @S2.12
      -   .23
     333333333

#3_4  @S7.98
       -5.73
     33333333                        #BF
               ,*APT] #D          A#D4AE

#4_4   @S  .46
         17.03
      +   2.99
     3333333333

_:
    ,USE YR BRLWRIT] TO WRITE ! PROBLEMS
  9 SPATIAL =MAT4 ,L1VE "O BLANK L9E 2T
  ! PROBLEMS4
      @.<,! FOLL[+ PROBLEMS >E WRITT5 \
    TO ALL[ = PRACTICE4 ,": DOLL>
    SYMBOLS >E US$1 ! ^W 8DOLL>S0 W
    FOLL[ ! NUMB]4 ,": A DOLL> AM.T
    9CLUDES A DECIMAL1 S* Z @S#C4EJ1 !
    AM.T IS WRITT5 Z 8DOLL>S & C5TS01
    "<E4G4 ?REE DOLL>S & FIFTY C5TS">4
    ,": DOLL> SIGNS >E PRES5T1 !Y APPE>
    ONLY NEXT TO ! F/ ADD5D 9 PR9T4
    ,ADD5DS )\T DOLL> SIGNS >E N
    ID5TIFI$ Z DOLL> AM.TS 9 !
    DESCRIP;NS 2L4@.>
#A4 =TY-N9E DOLL>S & SIXTY-?REE C5TS
  M9US ?IRTY-SIX PO9T N9ETY-"O       #BG
               ,*APT] #D          B#D4AE
  @.<,M9US TO ! LEFT ( DOLL> SIGN@.>
#B4 EI<T PO9T SIX PLUS ?REE PO9T F\R
#C4 SEV5 HUNDR$ FIFTY-"O DOLL>S M9US
  EI<TY @.<,M9US DIRECTLY "U DOLL>
  SIGN@.>
#D4 SIXTY-SEV5 DOLL>S & N9ETY-SIX C5TS
  PLUS ?REE PO9T "O TWO @.<,PLUS TO !
  LEFT ( DOLL> SIGN@.>

    ,SPATIAL ,>RANGE;TS = ,MULTIPLICA;N
    ,PROBLEMS
  ,/UD5TS >E 9TRODUC$ TO V]TICALLY
ALIGN$ MULTIPLICA;N PROBLEMS 9 ?IRD
GRADE "<,COMMON ,CORE ,/ATE ,/&>DS
,9ITIATIVE1 #BJAJ">4 ,:5 ! PROBLEMS >E
V]TICALLY ALIGN$ 9 PR9T1 !Y %D 2
V]TICALLY ALIGN$ 9 BRL4
  ,! FOLL[+ RULES = SPATIAL ADDI;N &
SUBTRAC;N PROBLEMS >E ! SAME = SPATIAL
MULTIPLICA;N PROBLEMS4
-----------------------------------#D4AF

_4 ,:5 V]TICALLY ALIGN$ PROBLEMS >E
  PLAC$ SIDE-BY-SIDE 9 PR9T1 "! M/   #BH
               ,*APT] #D          A#D4AF
  2 AT L1/ "O BLANK CELL 2T ! SEP>A;N
  L9ES 9 BRL "<,RULE ,,XXV1 ^S#AHE;C">4
_4 ,"! %D ALW 2 A BLANK L9E ABV & 2L
  SPATIALLY ALIGN$ PROBLEMS "<,RULE
  ,,XXV1 ^S#AHE">4
_4 ,IF ! SIGN ( OP]A;N IS 9CLUD$ 9 PR9T1
  !N X IS 9CLUD$ 9 BRL4
_4 ,! SEP>A;N L9E EXT5DS "O CELL TO !
  LEFT & "O CELL TO ! "R ( ! OV]ALL WID?
  ( ! >RANGE;T "<,RULE ,,XXIV1
  ^S#AGI;C">4

  ,! PRIM>Y DI6];E 2T MULTIPLICA;N
PROBLEMS & ADDI;N & SUBTRAC;N PROBLEMS
IS ! PLACE;T ( ! MULTIPLICA;N SIGN4 ,X
IS PLAC$ "O CELL TO ! LEFT ( !
MULTIPLI]1 REG>D.S ( ! L5G? ( !
MULTIPLIC& "<TOP NUMB]"> & MULTIPLI]
"<BOTTOM NUMB]"> "<,RULE ,,XXIV1
^S#AGI;B">4
  ,:5 A PRODUCT IS 9CLUD$ = A
MULTIPLICA;N PROBLEM ! L5G? ( ! SEP>A;N
L9E IS ADJU/$ TO A3OMMODATE ! PRODUCT4
,! SEP>A;N L9E M/ / EXT5D "O CELL    #BI
               ,*APT] #D          B#D4AF
TO ! LEFT & "O CELL TO ! "R ( ! WIDE/ "P
( ! PROBLEM4
  ,EXAMPLE #D4AA 3TA9S FIVE SPATIALLY
>RANG$ MULTIPLICA;N PROBLEMS4 ,PAY
SPECIAL ATT5;N TO ": ! MULTIPLICA;N SIGN
IS PLAC$ 9 EA* PROBLEM4 ,AL1 NOTICE T "!
>E TWO BLANK CELLS 2T ! SEP>A;N L9ES4 ,9
! F\R? PROBLEM1 NOTICE T ! ANSW] HAS BE5
9CLUD$ 9 PR9T4 ,?US1 ! ANSW] IS 9CLUD$ 9
! BRL4

      ,EXAMPLE #D4AA _%

   3    6824     87
 @*5    @*12    @*9
33333  333333  33333







                                     #CJ
               ,*APT] #D           #D4AG

  4.9    @S25.00
  @*8       @*18
333333  333333333
 39.2

_:

    ,SPATIAL ,>RANGE;TS = ,DIVI.N
    ,PROBLEMS
  ,9 A DIVI.N PROBLEM1 ! ^1DIVID5D IS !
NUMB] T IS 2+ DIVID$1 & ! ^1DIVISOR IS !
NUMB] T ! DIVID5D IS 2+ DIVID$ BY4 ,!
^1QUOTI5T IS ! ANSW] TO ! DIVI.N
PROBLEM4
  ,! FOLL[+ EXAMPLE IS A DIVI.N PROBLEM4
,X IS N 3SID]$ TO 2 9 SPATIAL =MAT Z X
ONLY 9CLUDES ! DIVISOR & DIVID5D1
COMPRIS$ ONLY ( NUM]ALS4 ,"!=E1 A NUM]IC
9DICATOR IS PLAC$ 2F ! DIVISOR "<,RULE
,,XXIV1 ^S#AHJ;C">4

      ,EXAMPLE #D4AB
_% #6O18 _:                          #CA
               ,*APT] #D          A#D4AG

  ,A DIVI.N PROBLEM IS 3SID]$ TO 2 9
SPATIAL =MAT :5 M ?AN ! DIVISOR &
DIVID5D >E %[N "<,RULE ,,XXIV1
^S#AHJ;C">4 ,:5 BRAILL+ PROBLEMS Z A
SPATIAL >RANGE;T1 A BLANK L9E IS LEFT
ABV & 2L ! PROBLEM UN.S ! PROBLEM IS !
LA/ ITEM ON ! PAGE4
  ,NO NUM]IC 9DICATORS >E US$ 9 A
SPATIALLY >RANG$ DIVI.N PROBLEM4
  ,! DIVI.N SIGN IS MADE ) ! DOTS
#A-#C-#E4 ,PLACE ! DIVISOR 9 ! F> LEFT1
FOLL[$ BY ! DIVI.N SIGN1 & !N ! DIVID5D4
  .=O "<CURV$ DIVI.N SIGN">

  333
  O
  "<CURV$ DIVI.N SIGN ON LEFT1 SEP>A;N
L9E ABV">

-----------------------------------#D4AH
,EXAMPLE #D4AC 3TA9S "O DIVI.N PROBLEM 9
SPATIAL =MAT4 ,! DIVID5D IS #AHB1 !
DIVISOR IS #AD1 & ! QUOTI5T IS       #CB
               ,*APT] #D          A#D4AH
#AC4 ,A SEP>A;N L9E IS PLAC$ DIRECTLY
ABV ! CURV$ DIVI.N SIGN2 X EXT5DS "O
CELL TO ! "R ( ! OV]ALL >RANGE;T "<,RULE
,,XXIV1 ^S#AHJ;C">4

      ,EXAMPLE #D4AC _%

    13
  33333
14O182

_:
  ,EXAMPLE #D4AD 3TA9S TWO DIVI.N
PROBLEMS 9 SPATIAL =MAT4 ,! PROBLEMS >E
NUMB]$4 ,! PROBLEM NUMB] M/ 2 PLAC$ ON !
L9E : 3TA9S ! DIVID5D "<,RULE ,,XXV1
^S#AHE;B">4
  ,NOTICE T "! IS "O CELL 2T ! 5D ( !
PROBLEM NUMB] & ! 2G9N+ ( ! PROBLEM4 ,"!
>E TWO CELLS 2T ! 5D ( ! SEP>A;N L9E 9
PROBLEM #A & ! />T ( ! NUM]IC 9DICATOR
US$ TO LABEL PROBLEM #B4

                                     #CC
               ,*APT] #D          B#D4AH

      ,EXAMPLE #D4AD _%

        8            500
      3333         333333
#1_4 8O64   #2_4 10O5000

_:
  ,EXAMPLE #D4AE 3TA9S A SPATIAL L;G
DIVI.N PROBLEM 9 : ! COMPUTA;N IS
9CLUD$4 ,NOTICE T ! F\R SEP>A;N L9ES >E
EA* ! SAME L5G?4 ,9 ADDI;N1 ALL ! DIGITS
>E ALIGN$ BY _! PLACE VALUE4










                                     #CD
               ,*APT] #D           #D4AI

      ,EXAMPLE #D4AE _%

       1062
      333333
#3_4 3O3186
       3
       3
      333333
        18
        18
      333333
          6
          6
      333333
          0

_:

    ^1,T1*+ ^1,TIP3 ,AL? X IS "T 3SUM+1
  X IS IMPORTANT T HE OR %E C P]=M L;G
  DIVI.N ON A BRLWRIT]4 ,? W 2 REVISIT$
  9 HI< S*OOL :5 !Y COMPLETE L;G DIVI.N
  PROBLEMS ) POLYNOMIALS4            #CE
               ,*APT] #D          A#D4AI
    ^1,T1*+ ^1,TIP3 ,ONCE /UD5TS H
  DEMON/RAT$ T !Y C P]=M L;G DIVI.N ON A
  BRLWRIT]1 !Y MAY USE AN ABACUS =
  DIVI.N & !N WRITE \ ! F9AL ANSW] = !
  MA? T1*]4 ,? W 2 M* QK] = ! /UD5T4
    ^1,T1*+ ^1,TIP3 ,A T1*] OR
  P>APR(ES.NAL C USE ! ,MA? ,W9D[ TO
  DEMON/RATE ! L;G DIVI.N PROCESS4
-----------------------------------#D4BJ

      ,PRACTICE #D4F
    ,9T]L9E ! SPATIALLY ALIGN$ PROBLEMS4
_%

#1_4   27   #2_4   35.8
      @*3           @*6
     33333       3333333
       81         214.8

#3_4  @S60.25
         @*13
     333333333

                                     #CF
               ,*APT] #D          A#D4BJ

        30
      33333
#4_4 5O150

       124
      33333
#5_4 2O248
       2
      33333
        4
        4
      33333
         8
         8
      33333
         0

_:




                                     #CG
               ,*APT] #D          B#D4BJ

    ,USE YR BRLWRIT] TO WRITE ! PROBLEMS
  9 SPATIAL =MAT4 ,L1VE "O BLANK L9E 2T
  ! R[S ( PROBLEMS4 ,"! %D AL 2 "O BLANK
  CELL 2T ! PROBLEM NUMB] & ! />T ( EA*
  SEP>A;N L9E4
-----------------------------------#D4BA
      @.<,PROBLEMS #A-#D >E BROK5 9TO #B
    SETS ( #B PROBLEMS4 ,! #B PROBLEMS
    APPE> SIDE BY SIDE ON ! SAME L9E 9
    PR9T4 ,! DIVI.N PROBLEMS 2L >E
    SPATIAL1 & ELE;TS ( ! EXPRES.N >E
    DEF9$ 9 P>5!SES = CL>;Y4@.>
@.<,SET #A@.>
#A4 ?REE "<DIVISOR"> N9ETY-SIX
  "<DIVID5D">2 ?IRTY-TWO "<QUOTI5T">
#B4 N9E "<DIVISOR"> "O ?\S& @.<COMMA@.>
  "O HUNDR$ ?IRTY-F\R "<DIVID5D">2 "O
  HUNDR$ TW5TY-SIX "<QUOTI5T">
@.<,SET #B@.>
#C4 EI<T HUNDR$ TW5TY-FIVE "TS ELEV5
  EQUALS N9E ?\S& SEV5TY-FIVE
#D4 SIXTY-F\R "TS TWELVE EQUALS
#E4 FIVE "<DIVISOR"> F\R HUNDR$      #CH
               ,*APT] #D          A#D4BA
  FIFTY-FIVE "<DIVID5D">2 N9ETY-"O
  "<QUOTI5T">2 @.<L;G DIVI.N 2N
  DIVID5D@.> =TY-FIVE @.<ALIGN$ ) HUNDR$
  & T5S PLACE@.> SEP>A;N L9E2 FIVE
  @.<ALIGN$ ) "OS PLACE@.>2 FIVE @.<NEW
  L9E1 ALIGN$ 9 "OS PLACE@.> SEP>A;N
  L9E2 Z]O @.<ALIGN$ 9 "OS PLACE@.>

    ,C>RI$ ,NUMB] ,9DICATOR
  ^1,C>RI$ ^1NUMB]S1 M COMMONLY CALL$
^1RE"ND ^1NUMB]S1 >E "S"TS US$ 9
SPATIALLY >RANG$ ADDI;N PROBLEMS4 ,RE"ND
NUMB]S >E TYPICALLY 9TRODUC$ 9 ,GRADE
#C4
  ,! ^7C>RI$ NUMB] 9DICATOR^' IS CR1T$ 9
,NEME? ,CODE ) A L9E ( DOTS #B-#C-#E-#F4
,X HAS ! SAME L5G? Z ! SEP>A;N L9E
"<,RULE ,,XXIV1 ^S#AGH;D">4 ,"! IS NO
PR9T EQUIVAL5T = A C>RI$ NUMB] 9DICATOR4
  .=7777
  ,C>RI$ NUMB] 9DICATOR
  ,9 ,EXAMPLE #D4AF1 A C>RI$ NUMB]
9DICATOR IS US$ ABV ! F/ ADD5D 9 BO?
PROBLEMS4                            #CI
               ,*APT] #D          B#D4BA

      ,EXAMPLE #D4AF _%

  1
77777
  63
 +29
33333
  92

-----------------------------------#D4BB

  11
777777
  176
 +389
333333
  565

_:

    ^1,T1*+ ^1,TIP3 ,/UD5TS >E USUALLY
  9TRODUC$ TO ! C>RI$ NUMB] 9DICATOR Z
  !Y MAY SEE ? SYMBOL 9 _!           #DJ
               ,*APT] #D          A#D4BB
  TEXTBOOKS1 ESPECIALLY 9 EXAMPLES4 ,!Y
  >E TAU<T H[ TO R1D ? SYMBOL Z WELL Z !
  PURPOSE ( ! 9DICATOR1 B N NECESS>ILY
  H[ TO WRITE X ON A BRLWRIT]4
    ^1,T1*+ ^1,TIP3 ,AL? /UD5TS W USE A
  V>IETY ( TOOLS :5 COMPLET+ MA?
  PROBLEMS1 X IS ESS5TIAL T ! BRLWRIT] 2
  9TRODUC$ Z A CALCULA;N TOOL :5 !Y >E
  9TRODUC$ TO SPATIALLY >RANG$ PROBLEMS
  "<,RESE>* & ,DEVELOP;T ,9/ITUTE1
  #BJJF">4
    ^1,T1*+ ^1,TIP3 ,/UD5TS >E USUALLY
  ALL[$ TO D ! COMPUTA;N ON _! BRLWRIT]
  )\T /RICTLY ADH]+ TO ALL ( ! ,NEME?
  ,CODE RULES & =MATT+ "<,RESE>* &
  ,DEVELOP;T ,9/ITUTE1 #BJJF">4 ,? ALL[S
  !M TO FOCUS ON ! MA? & SPE$ UP !
  PROCESS ( US+ ! BRLWRIT] Z A CALCULA;N
  TOOL4




                                     #DA
               ,*APT] #D           #D4BC

      ,PRACTICE #D4G
  .7,9T]L9E ! PROBLEMS4.' _%

  1
77777
  76
 + 5
33333
  81

  1
77777
  28
 +47
33333
  75

  1
77777
  29
 +49
33333
  78                                 #DB
               ,*APT] #D          A#D4BC

  1
77777
  39
 +48
33333
  87

-----------------------------------#D4BD

  1
77777
  59
 + 2
33333
  61

_:

    ,NUMB] ,L9ES
  ,/UD5TS >E USUALLY 9TRODUC$ TO NUMB]
L9ES CR1T$ ON A BRLWRIT] ) ,NEME? ,CODE
SYMBOLS 9 F\R? GRADE "<,,BANA1 #BJAJ">4
,! FOLL[+ ,NEME? ,CODE SYMBOLS >E    #DC
               ,*APT] #D          A#D4BD
US$ TO CR1TE NUMB] L9ES3

.=[ "<DOTS #B-#D-#F"> LEFT-PO9T+ >R[H1D
.=3 "<DOTS #B-#E"> L9E "<AXIS L9E">
.=R "<DOTS #A-#B-#C-#E"> COORD9ATE SCALE
  M>K
.=O "<DOTS #A-#C-#E"> "R-PO9T+ >R[H1D
.== "<DOTS #A-#B-#C-#D-#E-#F"> SOLID1
  FILL$-91 OR CLOS$ CIRCLE "<PO9T
  9CLUD$">

  ,NUMB] L9ES >E 3SID]$ A SPATIAL
>RANGE;T "<,,BANA1 #BJAJ">4 ,SIMIL> TO
SPATIALLY ALIGN$ PROBLEMS1 NUMB] L9ES >E
PREC$$ & FOLL[$ BY A BLANK L9E4
  ,SCALE M>KS1 "S"TS CALL$ HA% M>KS OR
TICK M>KS1 >E LABEL$ 2L ! NUMB] L9E US+
,NEME? ,CODE NUMB]S )\T NUM]IC
9DICATORS4 ,IF >R[H1DS >E 9CLUD$ 9 !
PR9T NUMB] L9E1 !N 9CLUDE !M ON BRL
NUMB] L9ES4
  ,! AXIS L9E 2T ! SCALE M>KS C V>Y 9
L5G?1 B ONCE ! L5G? 2T ! F/ TWO SCALE
M>KS IS DECID$ ON1 ! SAME L5G? (     #DD
               ,*APT] #D          B#D4BD
AXIS L9E %D 2 US$ 2T ! O!R SCALE M>KS ON
! SAME NUMB] L9E4
  ,EXAMPLE #D4AG 9CLUDES A NUMB] L9E )
SCALE M>KS LABEL$ F #A TO #F4 ,NOTICE T
NUM]IC 9DICATORS >E N US$1 & ! UNITS ON
! NUMB] L9E >E EQUALLY SPAC$4
-----------------------------------#D4BE

      ,EXAMPLE #D4AG _%

[333R3333R3333R3333R3333R3333R333O
    1    2    3    4    5    6

_:
  ,"S"TS NUMB] L9ES 9CLUDE L>G] NUMB]S T
W N FIT ON ! NUMB] L9E4 ,Y C EI OMIT
ALT]NATE LABELS :ILE KEEP+ ! COORD9ATE
M>K]S OR 9CR1SE ! L5G? ( SPACE 2T UNITS4
  ,EXAMPLE #D4AH 9CLUDES TWO NUMB] L9ES
) LABEL$ SCALE M>KS4 ,! F/ NUMB] L9E
9CLUDES ALT]NATE LABELS F #AJJ TO #ADJ1
& ! SECOND NUMB] L9E F #AJJ TO #ABE
9CLUDES AN 9CR1S$ L5G? ( SPACE 2T !
UNITS4 ,BO? V].NS >E CORRECT4        #DE
               ,*APT] #D          A#D4BE

      ,EXAMPLE #D4AH _%

[33R33R33R33R33R33R33R33R33R33O
   100   110   120   130   140

[33R3333R3333R3333R3333R3333R33O
   100  105  110  115  120  125

_:
  ,! CLOS$ CIRCLE IS PLAC$ DIRECTLY ABV
A SPECIFIC LOCA;N ON ! NUMB] L9E 9 ORD]
TO PLOT A PO9T4 ,? CD 2 DIRECTLY ABV A
SCALE M>K OR "S": 9 2T TWO SCALE M>KS4
,EXAMPLE #D4AI 9CLUDES A NUMB] L9E )
PO9TS PLOTT$ AT #ADE1 #AEE1 & #AFE4







                                     #DF
               ,*APT] #D          B#D4BE

      ,EXAMPLE #D4AI _%
-----------------------------------#D4BF

        =         =         =
[33R3333R3333R3333R3333R3333R33O
   140  145  150  155  160  165

_:

      ,PRACTICE #D4H
  ,RECR1TE ! F\R NUMB] L9ES 9 ,EXAMPLES
#D4AF1 #D4AG1 & #D4AH4

             ,*APT] ,SUMM>Y

    ,SPATIAL ,>RANGE;TS
_4 ,:5 PROBLEMS >E WRITT5 V]TICALLY 9
  PR9T1 !Y >E WRITT5 V]TICALLY 9 ,NEME?
  ,CODE4
_4 ,"! %D ALW 2 A BLANK L9E ABV & 2L
  SPATIALLY ALIGN$ PROBLEMS "<,RULE
  ,,XXV1 ^S#AHE">4
_4 ,NUM]IC 9DICATORS >E N US$ 9      #DG
               ,*APT] #D          A#D4BF
  SPATIAL >RANGE;TS1 & S+LE L9E SPAC+ IS
  US$ "?\T ! PROBLEM1 EV5 = "Y /UD5TS
  "<,RULE ,,II1 ^S#AA;B">4
_4 ,! SEP>A;N L9E EXT5DS "O CELL TO !
  LEFT & "O CELL TO ! "R ( ! WIDE/
  >RANGE;T 9 ! PROBLEM "<,RULE ,,XXIV1
  ^S#AGH;C">4
_4 ,:5 TRANSCRIB+ V]TICALLY ALIGN$
  NUMB]$ PROBLEMS1 L1VE A BLANK CELL 2T
  ! PROBLEM NUMB] & ! 2G9N+ ( ! SEP>A;N
  L9E "<,RULE ,,XXV1 ^S#AHE;B">4
_4 ,:5 V]TICALLY ALIGN$ PROBLEMS >E
  PLAC$ SIDE-BY-SIDE 9 PR9T1 "! M/ 2 AT
  L1/ "O BLANK CELL 2T ! SEP>A;N L9ES 9
  BRL "<,RULE ,,XXV1 ^S#AHE;C">4
_4 ,L1VE TWO BLANK CELLS 2T ! 5D ( A
  SEP>A;N L9E & ! FOLL[+ PROBLEM NUMB]
  "<,RULE ,,XXV1 ^S#AHE;C">4
_4 ,! PLUS OR M9US SIGN IS PLAC$ "O CELL
  TO ! LEFT ( ! WIDE/ NUMB] ABV !
  SEP>A;N L9E 9 ! >RANGE;T "<,RULE
  ,,XXIV1 ^S#AGH;C">4
_4 ,! MULTIPLICA;N SIGN IS PLAC$ "O CELL
  TO ! LEFT ( ! MULTIPLI]1 REG>D.S   #DH
               ,*APT] #D          B#D4BF
  ( ! L5G? ( ! MULTIPLIC& & MULTIPLI]
  "<,RULE ,,XXIV1 ^S#AGI;B">4
_4 ,A DIVI.N PROBLEM IS 3SID]$ TO 2 9
  SPATIAL =MAT :5 M ?AN ! DIVISOR &
  DIVID5D >E %[N "<,RULE ,,XXIV1
  ^S#AHJ;C">4
_4 ,PLACE ! DIVI.N SIGN IMMLY 2F !
  DIVID5D "<,RULE ,,XXIV1 ^S#AHJ;B">4
-----------------------------------#D4BG
_4 ,! C>RI$ NUMB] 9DICATOR HAS ! SAME
  L5G? Z ! SEP>A;N L9E "<,RULE ,,XXIV1
  ^S#AGH;D">4

    ,NUMB] ,L9ES
_4 ,/UD5TS >E USUALLY 9TRODUC$ TO NUMB]
  L9ES CR1T$ ON A BRLWRIT] ) ,NEME?
  ,CODE SYMBOLS 9 F\R? GRADE
  "<.1,TACTILE .1,GRAPHICS1 #F4E4A4AB2
  .1,TACTILE .1,GRAPHICS1 #F4E4A4AC">4
_4 ,NUMB] L9ES >E PREC$$ & FOLL[$ BY A
  BLANK L9E "<.1,TACTILE .1,GRAPHICS1
  #F4E4A4B">4
_4 ,IF >R[H1DS >E 9CLUD$ 9 ! PR9T NUMB]
  L9E1 !N 9CLUDE !M ON BRL NUMB]     #DI
               ,*APT] #D          A#D4BG
  L9ES "<.1,TACTILE .1,GRAPHICS1
  #F4E4A4C">4
_4 ,D N USE NUM]IC 9DICATORS ON NUMB]
  L9ES "<.1,TACTILE .1,GRAPHICS1
  #F4E4A4A">4
-----------------------------------#D4BH

    ,*APT] #D3 ,ANSW] ,KEY
    ,ANSW] #D4A
EI<T M9US F\R
N9E PLUS "O
SIX M9US FIVE
SEV5 M9US SIX
EI<T PLUS TWO
"O PLUS ?REE








                                     #EJ
               ,*APT] #D          A#D4BH
_%

  8
 -3
3333

  2
 -1
3333

  4
 +4
3333

_:








                                     #EA
               ,*APT] #D           #D4BI

    ,ANSW] #D4A "<3T9U$"> _%

  9
 +5
3333

  3
 -2
3333

  7
 +6
3333

_:

    ,ANSW] #D4B
TW5TY-SEV5 M9US EI<T
"O HUNDR$ N9ETY-?REE M9US FIFTY-F\R
  EQUALS "O HUNDR$ ?IRTY-N9E
EI<T ?\S& @.<COMMA@.> M9US F\R HUNDR$
  FIFTY
                                     #EB
               ,*APT] #D          A#D4BI
?REE MILLION @.<COMMA@.> SEV5 HUNDR$
  FIFTY-SIX ?\S& @.<COMMA@.> SEV5 HUNDR$
  EI<TY PLUS TWO ?\S& @.<COMMA@.> TWO
  HUNDR$ ?IRTY-SEV5
TW5TY-EI<T PLUS ?IRTE5 EQUALS =TY-"O
_%

  17
   4
 + 9
33333

_:










                                     #EC
               ,*APT] #D           #D4CJ

    ,ANSW] #D4B "<3T9U$"> _%

  56
 +21
33333

  2,376
 -   63
33333333

  100,000
 - 20,000
3333333333

_:







                                     #ED
               ,*APT] #D          A#D4CJ

    ,ANSW] #D4C
      @.<,! FOLL[+ #F PROBLEMS >E
    PRES5T$ 9 #B SETS ( #C4 ,! #C
    PROBLEMS ALL APPE> ON ! SAME L9E 9
    PR9T4@.>
@.<,SET #A@.>
EI<TE5 M9US ?REE
SIX M9US F\R
FIVE PLUS N9E
@.<,SET #B@.>
SEV5 HUNDR$ EI<TY-EI<T PLUS F\R
SIXTY-EI<T M9US ?REE
TWELVE PLUS FIFTE5









                                     #EE
               ,*APT] #D          B#D4CJ
_%

  19    78    8
 - 7   - 3   -6
33333 33333 3333

  289    39    46
 - 5    -16   - 0
333333 33333 33333

_:

    ,ANSW] #D4D
      @.<,! FOLL[+ #D PROBLEMS >E
    PRES5T$ 9 #B SETS ( #B4 ,! #B
    PROBLEMS ALL APPE> ON ! SAME L9E 9
    PR9T4@.>
@.<,SET #A@.>
?IRTY-SIX M9US TW5TY-N9E
TW5TY-"O PLUS EI<TY-EI<T



                                     #EF
               ,*APT] #D           #D4CA

    ,ANSW] #D4D "<3T9U$">
@.<,SET #B@.>
EI<T HUNDR$ SEV5 PLUS SIXTY-F\R
F\R ?\S& @.<COMMA@.> EI<T HUNDR$
  =TY-SEV5 M9US SEV5 HUNDR$ N9ETY-FIVE
_%

#1_4   91   #2_4   112
        4           35
      +13         + 36
     33333       333333

#3_4   4,099   #4_4   397
      +   35         - 40
     33333333       333333

_:





                                     #EG
               ,*APT] #D          A#D4CA

    ,ANSW] #D4E
      @.<,PROBLEMS >E SPELL$ \4 ,! ^W
    8PLUS0 IS REP1T$ 2T ALL ADD5DS4 ,9
    PR9T1 A PLUS SIGN IS F.D ONLY 2S !
    F9AL ADD5D4@.>
      @.<,": DOLL> SYMBOLS >E US$1 ! ^W
    8DOLL>S0 W FOLL[ ! NUMB]4 ,": A
    DOLL> AM.T 9CLUDES A DECIMAL1 S* Z
    @S#C4EJ1 ! AM.T IS WRITT5 Z 8DOLL>S
    & C5TS01 "<E4G4 ?REE DOLL>S & FIFTY
    C5TS">4 ,": DOLL> SIGNS >E PRES5T1
    !Y APPE> ONLY NEXT TO ! F/ ADD5D 9
    PR9T4 ,ADD5DS )\T DOLL> SIGNS >E N
    ID5TIFI$ Z DOLL> AM.TS 9 !
    DESCRIP;NS 2L4@.>
#A4 FIFTY DOLL>S PLUS TW5TY
#B4 TWO DOLL>S & TWELVE C5TS M9US PO9T
  TWO ?REE
#C4 SEV5 DOLL>S & N9ETY-EI<T C5TS M9US
  FIVE PO9T SEV5 ?REE
#D4 PO9T F\R SIX DOLL>S PLUS SEV5TE5
  PO9T Z]O ?REE PLUS TWO PO9T N9E N9E
                                     #EH
               ,*APT] #D          B#D4CA
_%

#1_4   @S49.63
      -  36.91
     3333333333

#2_4   8.6
      +3.4
     333333

_:
-----------------------------------#D4CB

    ,ANSW] #D4E "<3T9U$"> _%

#3_4  @S751
       - 80
     3333333

#4_4   @S67.96
      +   3.12
     3333333333

_:                                   #EI
               ,*APT] #D          A#D4CB

    ,ANSW] #D4F
      @.<,! F/ #B PROBLEMS >E %[N SIDE
    BY SIDE ON ! SAME L9E 9 PR9T4 ,! ^W
    8"TS0 IS US$ = ! MULTIPLICA;N
    CROSS4@.>
#A4 TW5TY-SEV5 "TS ?REE EQUALS EI<TY-"O
#B4 ?IRTY-FIVE PO9T EI<T "TS SIX EQUALS
  TWO HUNDR$ F\RTE5 PO9T EI<T
#C4 SIXTY DOLL>S & TW5TY FIVE C5TS "TS
  ?IRTE5
#D4 FIVE "<DIVISOR"> "O HUNDR$ FIFTY
  "<DIVID5D">2 ?IRTY "<QUOTI5T">
#E4 TWO "<DIVISOR"> TWO HUNDR$ =TY-EI<T
  "<DIVID5D">2 "O HUNDR$ TW5TY-F\R
  "<QUOTI5T">2 @.<L;G DIVI.N 2N
  DIVID5D@.> TWO @.<ALIGN$ ) HUNDR$S
  PLACE@.> SEP>A;N L9E2 F\R @.<ALIGN$ )
  T5S PLACE@.>2 F\R @.<NEW L9E1 ALIGN$ 9
  T5S PLACE@.> SEP>A;N L9E2 EI<T
  @.<ALIGN$ 9 "OS PLACE@.> EI<T @.<NEW
  L9E1 ALIGN$ 9 "OS PLACE@.> SEP>A;N
  L9E2 Z]O
                                     #FJ
               ,*APT] #D          B#D4CB
_%

       32            126
      3333        3333333
#1_4 3O98   #2_4 9O1,134

#3_4   825   #4_4    64
      @*11         @*12
     333333       333333
      9075

_:











                                     #FA
               ,*APT] #D           #D4CC

    ,ANSW] #D4F "<3T9U$"> _%

        91
      33333
#5_4 5O455
       45
      33333
         5
         5
      33333
         0

_:

    ,ANSW] #D4G
      @.<,ALL PROBLEMS 9 ,PRACTICE #D4G
    >E SPATIAL ADDI;N PROBLEMS ) C>RI$
    NUMB]S4@.>
SEV5TY-SIX PLUS FIVE EQUALS EI<TY-"O
  @.<,A #A APPE>S ABV ! T5S PLACE@.>
TW5TY-EI<T PLUS =TY-SEV5 EQUALS
  SEV5TY-FIVE @.<,A #A APPE>S ABV ! T5S
  PLACE@.>                           #FB
               ,*APT] #D          A#D4CC
TW5TY-N9E PLUS =TY-N9E EQUALS SEV5TY-
  EI<T @.<,A #A APPE>S ABV ! T5S
  PLACE@.>
?IRTY-N9E PLUS =TY-EI<T EQUALS
  EI<TY-SEV5 @.<,A #A APPE>S ABV ! T5S
  PLACE@.>
FIFTY-N9E PLUS #B EQUALS SIXTY-"O @.<,A
  #A APPE>S ABV ! T5S PLACE@.>















                                     #FC
               ,*APT] #D           #D4CD

    ,ANSW] #D4H _%

[333R3333R3333R3333R3333R3333R333O
    1    2    3    4    5    6

[33R33R33R33R33R33R33R33R33R33O
   150   160   170   180   190

[33R3333R3333R3333R3333R3333R33O
   150  155  160  165  170  175

   =    =    =
[33R3333R3333R3333R3333R3333R33O
   140  145  150  155  160  165

_:






                                     #FD