Page 1 of 14 MCC@WCCUSD (M3) 10/03/12!
Multiplying*Binomials*and*Factoring*Trinomials*
Using*Algebra*Tiles*and*Generic*Rectangles*
!
Multiplying*Binomials*
!
"#$%&$'&(!!)*+,-'$!./0/!!
!
123,(!!44!32%50!
!
6$#,'2$*5(!!7*$55!5,#!89!)*+,-'$!12*,5!8'!$::,55!#8!$!:83;<#,'!98'!,$:=!;$2'!89!5#<&,%#5 0!!1=,!
-,*8>!>,-52#,5!$**8>5!5#<&,%#5!#8!3$%2;<*$#,!#=,!#2*,5!?2'#<$**@(!
=##;(AA5#$990$'+@**0,;5-0:$AB',,&A3$#=CA5#'$%&DA;8*@E;'8&<:#0=#3 !
=##;(AA%*?30<5<0,&<A,%A%$?A:$#,+8'@E+EFE#ED0=#3*!
!
G$'3H<;!I,@!!J(!!FDDK!!JJ(!!7K!!JJJ(!!.L!
2
6x
!!!DL!
2
10x−
!!!FL!
2
8x
K!!!JM(!!.L!/!!!DL!/!!!FL!/!!!!!
!
G$'3H<;(!!N$?,!5#<&,%#5!5=$',!>2#=!$!;$'#%,'!#=,2'!58*<#28%50!!N$?,!;$2'5!:83,!<;!$%&!5=$',!
=8>!#=,@!98<%&!#=,2'!58*<#28%50!!)5O!29!#=,',!$', !$%@!P <, 5#28 %5 !8'!:8'', :#28% 5K!$% & !=$?,!#=,!
:*$55!$;;*$<&,&!#=,2'!,998'#50!!J(!!Q25:<55!8#=,'!>$@5!5#<&,% #5 !3 < *#2; *2, &! -,52&,5!#=,!#'$&2#28%$*!
3,#=8&!$%&!',?2,>!9$:#8'5!$%&!;'8&<:#50!!JJ(!!7=,:O!#8!3$O,!5<',!#=,@!<%&,'5#$%&!=8>!#8!
&25#'2-<#,!$%&!,%:8<'$+,!8#=,'!3,#=8&5!#=,@!<5,&0!!JJJ(!!6$O,!5<',!5#<&,%#5!<% & ,'5 #$% &!= 8> !
#8!3<*#2;*@!2%#,+,'5!$%&!$',!:*,$'!#=$#
2
()()xx x=
0!!JM(!!J#!25!?,'@!23;8'#$ % # !#= $ #!5 #< & , % #5 !
<%&,'5#$%&!#=,!)&&2#2?,!J%?,'5,!R'8;,'#@0!
!
S,558%(!!!
!
.L!!"=8>!5#<&,%#5!#>8!8#=,'!>$@5!#8!58*?,!>$'3H <;!;'8-*,3!TJUK! $ % &!5=8>!$!;',?2,>!89!
#8&$@V5!*,558%!8%!;$+,!40!!)5O!>=$#!#=,!5232*$'2#2,5!$%&!&299,',%:,5!-,#>,,%!3<*#2;*@2%+!>=8*,!
%<3-,'5!$%&!-2%832$*5W!!
!
DL!!N$?,!5#<&,%#5!#$O,!8<#!#=,!$*+,-'$!#2*,5!$%&!3$O,!5<',!,?,'@8%,!=$5!$!;$'#%,'0!!"=8>!#=,!
5#<&,%#5!#=,!&299,',%#!$*+,-'$!#2*,5!8%!;$+,!4K!$%&!#,5#!#=,3!-@!=$?2%+!#=,3!=8*&!<;!#=,!#2*,5!
@8<!:$**!8<#0!
!
FL!!"=8>!#=,!#2*,5!#=$#!3$O,!X,'8!;$2'5!$%&!#,5#!#=,!5#< & ,% #5!-@!=$?2%+!#=,3!=8*&!<;!#=,!
$&&2#2?,!2%?,'5,!89!#=,!#2*,!@8<!:$**!8<#0!
!
YL!!"=8>!#=,!5#<&,%#5!#=,!$*+,-'$!#2*,!&2?2&,'!8%!;$+,!Z!$%&!,[;*$2%!#=$#!#=,!9$:#8'5!+8!8%!#=,!
-*$:O!;$'#!89!#=,!&2?2&,'!5=,,#!$%&!#=,!;'8&<:#!>2**!-,!2%!#=,!>=2#,!$',$!89!#=,!5=,,#0!
Page 2 of 14 MCC@WCCUSD (M3) 10/03/12!
4L!!68&,*!3$O2%+!#=,!$''$@!>2#=!#=,!-2%832$*5K
(1)(2)xx++
0!)5O!#=,3!>=$#!25!
,1, 2,12xxx x••••
!$5!#=,@!:',$#,!#=,!;'8&<:#!>2#=!@8< 0!!N$?,!#=,3!2&,%#29@!#=,!9$:#8'5!$%&!
#=,!;'8&<:#0!!!
!
ZL!!N$?,!#=,3!#$O,!8<#!#=,!>8'O5=,,#!8%!;$+,!\!$%&!58*?,!#=,!92'5#!;'8-*,3!<52%+!$*+,-'$!#2*,5!
8%*@0!!68&,*!=8>!#8!&'$>!#=,!9$:#8'5K!#=,!;'8&<:#K!$%&!>' 2# , !2 % ! #=,!$%5>,'0!!1=,@!%,,&!#8!
P<2:O*@!&'$>!#=,!9$:#8'5!$5!>,**!$5!#=,!;'8&<:#!]2#!&8,5%V#!=$?,!#8!92#!2%!#=,!',:#$%+*,!
;,'9,:#*@L0!!N$?,!#=,3!&8!#=,!%,[#!#>8!;'8-*,35!$5!T^8<!1'@5U0!
!
\L!!_8!-$:O!#8!;'8-*,3!`.!$%&!38&,*!=8>!#8!<5,!#=,!+,%,'2:!',:#$%+*,!#8!#= ,!: *$55 0!!N $?, !
#=,3!&'$>!$!*88;!$'8< % &!#= ,!*2O,!#,'3 5K!$& &!#= ,3 !<; K!$%& !;< #!#= ,!5< 3 !$#!#=,!:8 '%, '!89!#=,!
',:#$%+*,!%,[#!#8!$%!Ta !T!52+%0!!N$?,!#=,!5#<&,%#5!5=$',!#=,2'!58*< #28% 5!> 2#=!#= ,!>= 8 *,!:*$55 K!
$%&!=$?,!#=,3!92%25=!#=,!-$:O!;$+,!2%&,;,%&,%#*@0!
!
Factoring*Trinomials*
!
"#$%&$'&(!!)*+,-'$!..0/!
!
123,(!!44!32%50!
!
6$#,'2$*5(!!7*$55!5,#!89!)*+,-'$!12*,5!8'!$::,55!#8!$!:83;<#,'!98'!,$:=!;$2'!89!5#<&,%#50!!1=,!
-,*8>!>,-52#,5!$**8>5!5#<&,%#5!#8!3$%2;<*$#,!#=,!#2*,5!?2'#<$**@(!
=##;(AA5#$990$'+@**0,;5-0:$AB',,&A3$#=CA5#'$%&DA;8*@E;'8&<:#0=#3!
=##;(AA%*?30<5<0,&<A,%A%$?A:$#,+8'@E+EFE#ED0=#3*!
!
G$'3H<;!I,@(!!J(!!.L!FDD!!!DL!.Y!!!FL!DFK!!JJ(!!)K!!JJJ(!!
2
21121xx−−
K!!JM(!!.L!
!!!DL!
(2 3)x +
!
!
G$'3H<;(!!N$?,!5#<&,%#5!5=$',!#=,2'!$%5>,'5!>2#=!$!;$'#%,'!$%&!#=,%!=$?,!;$2'5!5=$',!#=,2'!
58*<#28%5!#8!#=,!>=8*,!:*$550!!J(!!7=,:O!#8!5,,!29!$%@8%,!98<%&!$!P<2:O!>$@!#8!+,#!`D!$%&!`F!]9$:#!
9$32*2,5L0!!JJ(!!7=,:O!98'!<%&,'5#$%&2%+!8 9!3 < *#2;*@2% +!- 2% 832$*5!$%&!:83-2%2%+!*2O,!#,'350!!JJJ(!!
7=,:O!98'!',#,%#28%!89!#=,!*$5#!*,558%K!',?2,>!29!%,:,55$'@0!!JM(!!",,!29!5#<&,%#5!>,',!$-*,!#8!
#'$%59,'!#=,!9$:#!9$32*2,5!#8!&2?2&2% +!#'2%8 3 2$*5 0!
!
S,558%(!
!
.L!!b[;*$2%!#=$#!>,!>2**!-,!<52%+!#=,!$*+,-'$!#2*,5!#8!9$:#8'!#'2%832$*5!>=2:=!25!#=,!2%?,'5,!89!
@,5#,'&$@V5!*,558%!89!3<*#2;*@2%+!-2%832$*50!!68&,*!58*?2%+!
2
(68)(4)xx x++÷+
!-@!5,##2%+!<;!#=,!
&2?258'!92'5#!#8!+<2&,!#=,3!#8!3$O2%+!#=,!&2?2&,%&!',:#$%+*,!$''$@K!$%&!#=,%!92%&!#=,!P<8#2,%#!
>=2:=!25!
(2)x +
0!!
!
Page 3 of 14 MCC@WCCUSD (M3) 10/03/12!
DL!!N$?,!5#<&,%#5!92%&!#=,!58*<#28 %!#8 !
2
(43)(3)xx x++÷+
<52%+!$*+,-'$!#2*,5!$%&!=$?,!#=,3!
:=,:O!>2#=!#=,2'!;$'#%,'50!!N$?,!$!9,>!5#<&,%#5!5=8>!#=,2'!58*<#28%50!!
!
FL!!N$?,!#=,!5#<&,%#5!#$O,!8<#!#=,!9$:#8'2%+!=$%&8<#!8%!;$+,!.D!0!!68&,*!#=,!92'5#!8%,K!&'$>!
#=,!9$:#8'5!$%&!#=,!;'8&<:#K!$%&!>'2#,!2%!#=,!58*<#28%0!!1=,!%,[#!#>8!;'8-*,35!$',!T^8<!1'@5U0!!
!
YL!!_8!-$:O!#8!;'8-*,3!.!$%&!38&,*!=8>!#8!<5,!#=,!+,%,'2:!',:#$%+*,0!!N$?,!#=,3!;<#!
2
x
2%!#=,!
92'5#!-8[K!Z!2%!#=,!*$5#!-8[K!*88;!-8[,5 !D!$% & !FK!$%&!2%!#=,!:8'%,'!*$-,*!2#!T
5x=
U0!
!
4L!N$?,!#=,3!+'8<;!',5;8%&!8%!=8>!#8!+,#!#=,!9$:#8'50!!S,#!#=,3!O%8>!#=$#!#=,@!3$@!%,,&!#8!
+<,55!$%&!:=,:OK!58!@8<!>2**!+2?,!#=,3!$!=$%&8<#!#8!#'@!&299,',%#!;8552-2*2#2,5!58!#=,@!>8%V#!
=$?,!#8!,'$5,!]5,,!;$+,!.YL0!
!
ZL!!N$?,!#=,!5#<&,%#5!&8!#=,!%,[#!#>8!;'8-*,35!>2#=!#=,2'!;$'#%,'5K!$%&!'$%&83*@!:=88 5,!
5#<&,%#5!#8!5=$',!#=,2'!58*<#28%5!>=,%!385#!$',!&8%,0!!N$?,!#=,!5#<&,%#5!&8!#=,!-$:O!;$+,!
2%&,;,%&,%#*@!5#$'#2% +!> 2#= !#=, !$*+, - '$!#2*,5 !92'5#0!!c8 #,!#= $#!` Y!25 !?,'@!: =$ **,% +2% +0!!_ 2?, !#=, 3 !
$!=2%#!-@!',32%&2%+!#=,3!89!X,'8!;$2'50!!
!
!
!
!
!
*****************************
Page 4 of 14 MCC@WCCUSD (M3) 10/03/12!
**Warm<Up!
!
CST/CAHSEE:*Grade*8***********************
Review:*Grade*4***********************
*
!!
!
!
!
!
!
!
!
!
!
*
*
*
*
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Current:*Grade*8*********************
Other:*Grade*7************************
!
!!
!
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
!
y!
x!
6<*#2;*@!<52%+!#>8!5#'$#,+2,5(!
!
(23)(14)
!
!
!
J5!#=,!,P<$#28%!
3(2 4) 18x −=−
,P<2?$*,%#!#8!
!
6 12 18x −=−
!
!
)L!!^,5K!#=,!,P<$#28%5!$',!,P<2?$*,%#!-@!#=,!
)558:2$#2?,!R'8;,'#@!89!6<*#2;*2:$#28%0!
!
dL!!^,5K!#=,!,P<$#28%5!$',!,P<2?$*,%#!-@!#=,!
7833<#$#2?,!R'8;,'#@!89!6<*#2;*2:$#28%0!
!
7L!!^,5K!#=,!,P<$#28%5!$',!,P<2?$*,%#!-@!#=,!
Q25#'2-<#2?,!R'8;,'#@!89!6<*#2;*2:$#28%!8?,'!
)&&2#28%0!
!
QL!!c8K!#=,!,P<$#28%5!$',!%8#!,P<2?$*,%#!
6<*#2;*@(!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
.L!!
(2 )(3 )xx
!
!
DL!!
(5)(2)xx−
!
!
FL!!
(4)(2)xx−−
!
!
)&&(!
!
.L!!
55−+
!
!
DL!!
22xx−+
!
!
FL!!
22
44xx−+
!
!
Page 5 of 14 MCC@WCCUSD (M3) 10/03/12!
!
!
!
!
!!!!!!!! !
!!!!!
2
252xx=++
!
!
Area*Models*for*Partial*Products*******************************************“Generic*Rectangle”*
!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *
Algebra Tiles
!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Page 6 of 14 MCC@WCCUSD (M3) 10/03/12!
!
!
!
!
!!!!!!!!
•
!
!!!!!!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Page 7 of 14 MCC@WCCUSD (M3) 10/03/12!
6<*#2;*@2%+!d2%832$*5!e52%+!)*+,-'$!12*,5!!!!!!!!!c$3,(EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
!
.L!!
(2)(3)xx++
! ! ! ! ! ! ! .L!!
(2)(3)xx++
!!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! !!!!!!!!! !_,%,'2:!f,:#$%+*,! !
! !
!!!!!!!!!!!!!!!!!!!
!
!
!
!
!
!!
!
DL!!
(3)(3)xx++
! ! ! ! ! ! ! DL!!
(3)(3)xx++
!!!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5!!! ! ! !!!!!!!!!!! !!!!!!!!!! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! ! ! ! ! ! ! ! !
!
!
!
!
!
!
!
FL!!
(3)(2)xx−−
! ! ! ! ! ! ! ! FL!!
(3)(2)xx−−
! ! !
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!
! ! ! ! ! ! ! ! !
!
!
!
!
!
!
!
!
!
!
!
!
!
Page 8 of 14 MCC@WCCUSD (M3) 10/03/12!
!
YL!!
(3)(2)xx+−
! ! ! ! ! ! ! YL!!
(3)(2)xx+−
!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!
! ! ! ! ! ! ! ! ! !
!
!
!
!
!
!
!
4L!!
(2x + 1)(x + 3)
! ! ! ! ! ! ! 4L!!
(2x + 1)(x + 3)
!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! ! ! ! ! ! ! ! ! ! ! ! ! !
!
!
!
!
!
!
!
ZL!!
(2 3)(3 2)xx+−
! ! ! ! ! ! ! ZL!!
(2 3)(3 2)xx+−
!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! ! ! ! ! ! ! ! ! ! ! !
!
!
!
!
! ! !
!
Page 9 of 14 MCC@WCCUSD (M3) 10/03/12!
!
!
)%5>,'!I,@(!!6<*#2;*@2%+!d2%832$*5!$%&!g$:#8'2%+!1'2%832$*5!
!
.L!!
2
(3)(2) 56xx xx++=++
!!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
DL!!
2
(3)(3) 69xx xx++=++
!
!
!!! !
!
!
FL!!
2
(3)(2) 56xx xx−−=−+
!
!
!
!
2
x
!
3x
!
2x
!
3
!
x
!
2+
!
x
!
3+
!
2
x
!
3x
3x
!
9
!
x
!
3+
!
x
!
3+
!
x
!
2−
!
2
x
!
3x−
!
2x−
!
6
!
x
!
3−
!
Page 10 of 14 MCC@WCCUSD (M3) 10/03/12!
YL!!
2
(3)(2) 6xx xx+−=+−
!
!
!
!
!
!
4L!!
2
(2 1)( 3) 2 7 3xx xx++=++
!
!
!
!
!
!
ZL!!
2
(2 3)(3 2) 6 5 6xx xx+−=+−
!
!
!
!
!
!
!
2
x
!
3x
!
2x−
!
6−
!
x
!
2−
!
x
!
3+
!
2
6x
!
9x
!
4x−
!
6−
!
3x
!
2−
!
2x
!
3+
!
2
2x
!
1x
!
6x
!
3
!
x
!
3+
!
2x
!
1+
!
Page 11 of 14 MCC@WCCUSD (M3) 10/03/12!
!!!!!!!!!!!!!!!!!!!!!!!!Warm&Up!
!
CST/CAHSEE:**Grade*8**********************
Review:*Grade*4***********************
*
!!
!
!
!
!
!
!
!
!
!
*
*
*
*
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Current:*Algebra*I***********************
Other:*Algebra*I***********************
!
!!
!
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
!
y!
x!
Which of the following expressions is
equal to:
(2)(2)(21)xxx++− +
)!!
2
22xx−
!
!
d!!
2
24xx−
!!
!
7!!
2
2xx+
!!
!
Q!!
2
42xx+
!
!
Multiply*using*a*generic*rectangle*
*
1)**
(23)(14)
*
*
Divide*
*
2)**
322 23÷
*
*
3)**
322 14÷
*
!
Multiply*the*binomials*using*a*generic*
rectangle.**
!
(2 3)( 7)xx+−
!
Divide*
*
1)**
2
(2 11 21) (2 3)xx x−−÷+
*
*
2)**
2
(2 11 21) ( 7)xx x−−÷−
*
!
Page 12 of 14 MCC@WCCUSD (M3) 10/03/12!
g$:#8'2%+!1'2%832$*5!e52%+!)*+,-'$!12*,5!!!!!!!!!c$3,(EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
!
.L!!
2
56xx++
!a!!]!!!!!!!!!!L]!!!!!!!!!!L! ! ! ! .L!!
2
56xx++
!a!!]!!!!!!!!!!L]!!!!!!!!!!L!!!!!!!!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! !!!!!!!!! !_,%,'2:!f,:#$%+*,! !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
!
!
!
!!
!
DL!!
2
69xx++
!a!]!!!!!!!!!!L]!!!!!!!!!!L! ! ! ! DL!!
2
69xx++
!a!]!!!!!!!!!!L]!!!!!!!!!!L!! ! !
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! !!!!!!!!!!! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**
*
!
!
!!!
!
FL!!
2
56xx−+
!a!]!!!!!!!!!!L]!!!!!!!!!!L! ! ! !!!!!!!!!!!!!!FL!!
2
56xx−+
!a!]!!!!!!!!!!L]!!!!!!!!!!L!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!
!!!!!!!! ! ! !
!
!
!
!
!
!
!
!
!
!
!
!
!
Page 13 of 14 MCC@WCCUSD (M3) 10/03/12!
YL!!
2
6xx+−
!a!]!!!!!!!!!!L]!!!!!!!!!!L! ! ! ! YL!!
2
6xx+−
!a!]!!!!!!!!!!L]!!!!!!!!!!!L!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!!!!!
! ! ! ! !!!!!!!!!
!
!
!
!
!
!
!
4L!!
2
273xx++
!a!]!!!!!!!!!!L]!!!!!!!!!!L!! ! ! 4L!!
2
273xx++
!a!]!!!!!!!!!!L]!!!!!!!!!!L!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5!! ! ! ! ! _,%,'2:!f,:#$%+*,!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! ! ! ! ! ! ! ! ! ! ! ! ! ! !!!!!
! ! !!!!!!!!
!
!
!
!
!
!
!
ZL!!
2
656xx+−
!a!]!!!!!!!!!!!L]!!!!!!!!!!!L! ! ! ZL!!
2
656xx+−
!a!]!!!!!!!!!!L]!!!!!!!!!!L!
!
)',$!68&,*!>2#=!)*+,-'$!12*,5! ! ! ! ! _,%,'2:!f,:#$%+*,!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! ! ! ! !!!!!!!! ! ! ! ! ! ! !
!
!
!
!
!
!
Page 14 of 14 MCC@WCCUSD (M3) 10/03/12!
!