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0RINCIPLES OF !LGEBRA
!2% 9/5 2%!$9 0!'% S D S D S D p S D
NO
SUBTRACTION OPPOSITE OPERATION
QUOTIENT
SUM
DIVISION
PRODUCT
S D S D S D p S D NO
0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER ALGEBRAIC X NOT ALGEBRAIC
S D S D
S D S D
0OSSIBLE ANSWER 3UBSTITUTE THE GIVEN VALUE FOR
THE VARIABLE 4HEN FIND THE VALUE OF THE RESULTING
NUMERICAL EXPRESSION
0OSSIBLE ANSWER 4HE YVALUE IS NOT GIVEN
%XERCISES
%VALUATE X FOR X %VALUATE A FOR A %VALUATE S N D FOR N S D S D S D S D S D
YES
%VALUATE X Y FOR X AND Y S D S D S D S D
YES
%VALUATE P Q FOR P AND Q S D S D S D p S D NO
?? 9OU WILL NEED CUPS OF FLOUR
S D S D p NO
?? 9OU WILL NEED CUPS OF FLOUR
?? ???
9OU WILL NEED ?? CUPS OF FLOUR
S D S D S D p S D NO
S D S D
YES
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
?? ??
9OU WILL NEED ?? CUPS OF FLOUR
%VALUATE X FOR X %VALUATE G FOR G %VALUATE X FOR X %VALUATE Y FOR Y %VALUATE T FOR T %VALUATE Y FOR Y %VALUATE S K D FOR K S D %VALUATE S Z D FOR Z S D
%VALUATE X Y FOR X AND Y %VALUATE Z Y FOR Z AND Y %VALUATE M N FOR M AND N ?? CUPS PINTS
?? CUPS PINTS
?? CUPS PINTS
?? CUPS PINTS
%VALUATE YZ FOR Y AND Z %VALUATE Y X FOR Y AND X %VALUATE Z Y FOR Z AND Y %VALUATE D FOR D %VALUATE S Y X D FOR Y AND X S D
%VALUATE X FOR X %VALUATE S Y D FOR Y S D
%VALUATE N FOR N %VALUATE T FOR T %VALUATE S Z D FOR Z S D %VALUATE A FOR A %VALUATE S Y D FOR Y S D %VALUATE B FOR B %VALUATE S T D FOR T S D %VALUATE M FOR M #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
%VALUATE Y S T D FOR Y AND T S D TEAMS 4HERE ARE PLAYERS PER TEAM
TEAMS S D
4HERE ARE PLAYERS PER TEAM
4HERE ARE FOUR MORE PLAYERS PER TEAM
WHEN TEAMS ARE INCLUDED COMPARED
TO TEAMS
" MORE
%VALUATE X Y Z FOR X Y AND Z %VALUATE X Z Y FOR X Z AND
Y 0OSSIBLE ANSWER 4HE STUDENT IS CORRECT )N THE FIRST
EXPRESSION X AND WOULD BE MULTIPLIED FIRST UNDER
THE ORDER OF OPERATIONS )N THE SECOND EXPRESSION
X AND WOULD BE MULTIPLIED FIRST BECAUSE IS THE
COEFFICIENT OF THE VARIABLE X
%VALUATE Y S X T D FOR Y X AND
T S D
9ES WHEN X BOTH EXPRESSIONS HAVE A VALUE OF $ %VALUATE X FOR X %VALUATE S Z T D FOR Z AND T S D S D & )T WILL COST A CUSTOMER TO BUY DOZEN MUFFINS
AND LOAVES OF BREAD
%VALUATE TXZ FOR T X AND Z S D S D S D
%VALUATE X FOR X %VALUATE Z XY FOR Z X AND Y S D S D S D
%VALUATE 0 S R D FOR 0 AND R S D
4HE AMOUNT OF WOULD BE DUE FOR A LOAN OF
WITH AN INTEREST RATE OF %VALUATE ?? S W D FOR W ?? S D
??
! RECTANGLE WITH A WIDTH OF INCHES WOULD NEED A
LENGTH OF INCHES IN ORDER TO BE PLEASING TO THE
EYE
!LL ARE ODD
0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER PLUS ADD LESS THAN MINUS TIMES
MULTIPLIED BY DIVIDED BY QUOTIENT OF
A 0OSSIBLE ANSWER M WHERE M IS THE RUN
TIME IN MINUTES
B 4HERE ARE FRAMES IN THE MOVIE %4
0OSSIBLE ANSWER THE SUM OF AND TIMES N PLUS
THE PRODUCT OF AND N
%XERCISES
LESS THAN THE PRODUCT OF AND P
P MORE THAN THE PRODUCT OF AND U
U
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
MORE THAN THE QUOTIENT OF D AND D
??
MINUS THE QUOTIENT U AND U
??
S
0OSSIBLE ANSWER MORE THAN THE PRODUCT OF AND S
G 0OSSIBLE ANSWER THE PRODUCT OF AND G PLUS ??
D
0OSSIBLE ANSWER MORE THAN DIVIDED BY D
W ????
0OSSIBLE ANSWER LESS THAN W DIVIDED BY %VALUATE N FOR N %ACH PERSON WILL NEED TO CONTRIBUTE
%VALUATE N FOR N %ACH PERSON WILL NEED TO CONTRIBUTE
%VALUATE N FOR N %ACH PERSON WILL NEED TO CONTRIBUTE
%VALUATE N FOR N %ACH PERSON WILL NEED TO CONTRIBUTE
???
R
0OSSIBLE ANSWER LESS THAN DIVIDED BY R
Y
???
0OSSIBLE ANSWER MORE THAN Y DIVIDED BY B 0OSSIBLE ANSWER THE PRODUCT OF AND B MINUS %VALUATE N FOR N -ARK WILL EARN IF HE CLEANS POOLS
%VALUATE N FOR N -ARK WILL EARN IF HE CLEANS POOLS
%VALUATE N FOR N -ARK WILL EARN IF HE CLEANS POOLS
%VALUATE N FOR N -ARK WILL EARN IF HE CLEANS POOLS
0OSSIBLE ANSWER 4HE TOTAL COST OF A NEW RADIATOR
IS PLUS LABOR (OW MUCH IS THE TOTAL COST IF THE
COST OF LABOR IS %VALUATE R FOR R 4HE TOTAL COST IS TIMES THE SUM OF AND Y
S Y D
0OSSIBLE ANSWER +ENNINGTON -IDDLE 3CHOOL EARNED
A REWARD LUNCH FOR BEING THE TOP SCHOOL WITH THE
MOST STUDENTS INVOLVED IN THE STATE SPELLING BEE
CONTEST 4HEY PLANNED TO FEED X STUDENTS WHICH
IS EVERY STUDENT THAT ATTENDS THE SCHOOL "UT THEY
FORGOT THAT THE SEVENTH GRADERS WOULD BE ON
A FIELD TRIP THAT DAY (OW MANY STUDENTS WILL BE AT
SCHOOL TO EAT THE REWARD LUNCH
%VALUATE X FOR X HALF THE SUM OF M AND ?? S
M D
?? OF THE SUM OF AND P
?? S P D
DIVIDED BY THE SUM OF AND G
?????
G
MORE THAN THE PRODUCT OF AND Y
Y MORE THAN THE QUOTIENT OF AND N
?N?
MINUS THE PRODUCT OF AND P
P
LESS THAN THE PRODUCT OF AND Y
Y LESS THAN M DIVIDED BY ?M?
TWICE THE QUOTIENT OF M AND M
???
LESS THAN THE PRODUCT OF AND J
J PLUS THE QUOTIENT OF R AND ??R
MORE THAN THE PRODUCT OF AND Q
Q
S D
?? OF THE DIFFERENCE OF P AND ?? S P D
TIMES THE SUM OF ?? AND X
?? X
T
0OSSIBLE ANSWER MINUS THE PRODUCT OF AND T
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S
D
(OLT -C$OUGAL -ATHEMATICS
S X D FOR
X AND S X D S D S D S X D S D S D S X D S D S D S X D S D S D B LESS THAN THE PRODUCT OF AND B
S M D
TIMES THE SUM OF M AND ?????
X
DIVIDED BY THE DIFFERENCE OF AND X
S D
???
W
TIMES THE QUOTIENT OF AND W
S A D
!GE
!GE
TA E HUMAN YEARS
S D
S D
S D
S D
S D
0!'%3 n
?? S X D OR X?????
0OSSIBLE ANSWER 4HE STUDENT WROTE AN EXPRESSION
FOR hTHE QUOTIENT OF N MINUS AND v 4HE CORRECT
EXPRESSION IS ?N? 0OSSIBLE ANSWER -ULTIPLICATION IS REPEATED ADDITION
SO EITHER OPERATION CAN BE USED TO SOLVE THE
PROBLEM !DDING THE COST TIMES OR MULTIPLYING THE
COST BY WILL GIVE THE CORRECT ANSWER
4HINK AND $ISCUSS
0OSSIBLE ANSWER )TS EASIER TO MULTIPLY BY THAN TO MULTIPLY BY SO USE THE #OMMUTATIVE
0ROPERTY TO REWRITE THE EXPRESSION AS 4HEN SIMPLIFY THE EXPRESSION MENTALLY
S D
%XERCISES
N YES 4WICE AN ODD NUMBER IS ALWAYS AN
EVEN NUMBER AND ADDING TO AN EVEN NUMBER
ALWAYS RESULTS IN AN ODD NUMBER
5SE THE $ISTRIBUTIVE 0ROPERTY
D D %QUIVALENT
TIMES THE DIFFERENCE OF Y AND # S Y D
5SE THE !SSOCIATIVE 0ROPERTY
BB
5SE THE #OMMUTATIVE 0ROPERTY
B B %QUIVALENT
THE PRODUCT OF A NUMBER N AND ( N N
N #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S X D FOR
X AND S X D S D S D S X D S D S D S X D S D S D S X D S D S D 5SE THE )DENTITY 0ROPERTY
X X .OT EQUIVALENT
5SE THE !SSOCIATIVE 0ROPERTY
A A A
%QUIVALENT
A !NTONIO HAS PACKS OF SPORTS CARDS
B %STIMATE !NTONIO HAS SPORTS CARDS
(OLT -C$OUGAL -ATHEMATICS
0OSSIBLE ANSWER p BECAUSE AND B 0OSSIBLE ANSWER BY THE $ISTRIBUTIVE 0ROPERTY 3IMPLIFY MENTALLY
3HE WILL NEED GAME POINTS
0OSSIBLE ANSWER 4HE QUOTIENT OF AND IS AND IS NOT A WHOLE NUMBER
.OT EQUIVALENT M M BY THE !SSOCIATIVE
0ROPERTY AND M M BY THE :ERO
0ROPERTY 4HE EXPRESSIONS M AND M ARE NOT
EQUIVALENT
B C D %QUIVALENT G G BY THE )DENTITY
0ROPERTY AND G G BY THE #OMMUTATIVE
0ROPERTY
P
F G
0OSSIBLE ANSWER X X BY THE
)DENTITY 0ROPERTY AND X X BY THE
#OMMUTATIVE 0ROPERTY 4HEREFORE X X BY THE 4RANSITIVE 0ROPERTY
%QUIVALENT T T BY THE
!SSOCIATIVE 0ROPERTY T T BY
THE )DENTITY 0ROPERTY AND T T BY THE
#OMMUTATIVE 0ROPERTY
)F THERE IS EVEN ONE COUNTEREXAMPLE FOR A
CONJECTURE THE CONJECTURE IS FALSE 4HIS CONJECTURE
IS FALSE BECAUSE THERE ARE MANY EXAMPLES FOR WHICH
THE STATEMENT IS NOT TRUE FOR INSTANCE AND IS NOT LESS THAN .OT EQUIVALENT M M BY THE
$ISTRIBUTIVE 0ROPERTY AND M M
4HE EXPRESSIONS M AND M ARE NOT
EQUIVALENT
A BY THE
#OMMUTATIVE 0ROPERTY AND BY THE !SSOCIATIVE 0ROPERTY 3IMPLIFY
MENTALLY 3HE MOWED LAWNS IN THE SUMMER
B BY THE
$ISTRIBUTIVE 0ROPERTY 3IMPLIFY MENTALLY 3HE SAVED IN HER SAVINGS ACCOUNT
0OSSIBLE ANSWER ! X X X
" X X X
# X X X
" AND # ARE EQUIVALENT
0OSSIBLE !NSWER p BECAUSE AND
D D
#HOICE " D D SO D IS EQUIVALENT TO D 0OSSIBLE ANSWER 4HE SUM OF AND IS 4HE SUM
IS GREATER THAN BUT NOT GREATER THAN )DENTITY 0ROPERTY OF -ULTIPLICATION
0OSSIBLE ANSWER A WHOLE NUMBER
NOT A WHOLE NUMBER
#OMMUTATIVE 0ROPERTY OF !DDITION
$ISTRIBUTIVE 0ROPERTY
H 4HE WHALE NEEDS LITERS OF FORMULA IN A
HOUR PERIOD
!SSOCIATIVE 0ROPERTY OF -ULTIPLICATION
)DENTITY 0ROPERTY OF !DDITION
:ERO 0ROPERTY
0OSSIBLE ANSWER W W BY THE
#OMMUTATIVE 0ROPERTY W W BY THE
$ISTRIBUTIVE 0ROPERTY
W $ISTRIBUTIVE 0ROPERTY
4HE PRODUCT OF AND T MINUS PLUS THE QUOTIENT OF A AND TIMES THE SUM OF X AND 0OSSIBLE ANSWER (UMANS AND BIRDS HAVE TWO LEGS
AND TWO IS NOT A MULTIPLE OF FOUR )NSECTS HAVE SIX
LEGS AND SIX IS NOT A MULTIPLE OF FOUR
PLUS THE PRODUCT OF AND B
0!'%3 n
A BY THE
#OMMUTATIVE 0ROPERTY AND BY THE !SSOCIATIVE 0ROPERTY
3IMPLIFY MENTALLY 3ELINA WILL NEED TICKETS
4HINK AND $ISCUSS
0OSSIBLE ANSWER .EGATIVE NUMBERS CAN BE USED TO
REPRESENT WITHDRAWALS FROM A BANK ACCOUNT
0OSSIBLE ANSWER /N A NUMBER LINE IS TO THE
LEFT OF #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
%XERCISES
0OSSIBLE ANSWER 0OSSIBLE ANSWER 6IJAY 3INGH 0HIL -ICKELSON 4IGER 7OODS
*USTIN ,EONARD
OXYGEN "ECAUSE OXYGEN HAS THE
GREATER BOILING POINT
!NTARCTICA !SIA .ORTH !MERICA %UROPE 3OUTH
!MERICA !FRICA !USTRALIA
0OSSIBLE ANSWER )F A AND B ARE BOTH POSITIVE AND
A B THEN A B
)F A AND B ARE BOTH POSITIVE AND A B THEN
A B
)F A AND B ARE BOTH NEGATIVE AND A B THEN
A B
)F A AND B ARE BOTH NEGATIVE AND A B THEN
A B
)F A IS POSITIVE AND B IS NEGATIVE AND A B OR
A B THEN A B
)F A IS NEGATIVE AND B IS POSITIVE AND A B OR
A B THEN A B
& & -ONDAY 4HURSDAY 7EDNESDAY
4UESDAY
4HE ABSOLUTE VALUE OF A NUMBER IS NEVER NEGATIVE
N TRUE
N TRUE
N TRUE
0OSSIBLE ANSWER &ROM LEAST TO GREATEST THE SCORES
WERE "ERNIE WON THE TOURNAMENT
AND +ELLY CAME IN FIFTH
C #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
" & A S A B D
BC A
S D
S D
MORE THAN THE PRODUCT OF AND A NUMBER T
T P 0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER !DD THE ABSOLUTE VALUES OF THE
INTEGERS 4HEN WRITE A NEGATIVE SIGN IN FRONT OF THE SUM
0OSSIBLE ANSWER 3TART AT AND DRAW AN ARROW TO
THEN DRAW AN ARROW LEFT UNITS 3TART AT AND
DRAW AN ARROW LEFT TO THEN DRAW AN ARROW RIGHT
UNITS "OTH ARROWS END AT SO BOTH SUMS ARE
EQUAL TO (OLT -C$OUGAL -ATHEMATICS
%XERCISES
S D
(-3
D S S D
S D
S D
S D
S D
%VALUATE Z S D FOR Z S D
#ARS DROPPED OFF ARE AND #ARS PICKED UP ARE AND S D S D S D S D S D
S D
4HERE ARE CARS LEFT IN THE MECHANICS SHOP ON
&RIDAY
%VALUATE M FOR M %VALUATE P S D FOR P S D S D #HECKS ARE WORTH AND $EPOSITS ARE WORTH AND S D S D S D S D ,EES BALANCE AT THE END OF THE MONTH IS S D
(-3
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(-3
D
S S D
%VALUATE X FOR X S D
(-3
%VALUATE T FOR T %VALUATE Q FOR Q S D (OLT -C$OUGAL -ATHEMATICS
C 4HE 53 BALANCE OF TRADE IS ABOUT
OR ABOUT
BILLION
0OSSIBLE ANSWER 4HE STUDENT MAY HAVE SUBSTITUTED
INSTEAD OF INTO THE EQUATION
0OSSIBLE ANSWER )F YOU ADD TWO NEGATIVE INTEGERS
YOUR ANSWER WILL BE NEGATIVE
!LSO IF YOU ADD A NEGATIVE INTEGER AND A POSITIVE
INTEGER AND THE NEGATIVE INTEGER HAS THE GREATER
ABSOLUTE VALUE THEN YOUR ANSWER WILL BE NEGATIVE
S D
0OSSIBLE ANSWER 7HEN THERE ARE AN EVEN
NUMBER OF TERMS THE SUM IS 7HEN THERE ARE AN ODD NUMBER OF TERMS THE SUM
IS %VALUATE H FOR H # S D
%VALUATE Y FOR Y (-3
%VALUATE X Y FOR X AND Y S D
(-3
%VALUATE S T FOR S AND T %VALUATE C
FOR C %VALUATE K S D FOR K S D
%VALUATE B S D FOR B S D
S D S D
0!'%3 n
%VALUATE R FOR R 4HINK AND $ISCUSS
0OSSIBLE ANSWER 4HE DIFFERENCES ARE NOT THE SAME
BECAUSE S D IS POSITIVE AND IS NEGATIVE
%VALUATE W FOR W S D
0OSSIBLE ANSWER 4HE ANSWER IS NEGATIVE
%XERCISES
%VALUATE N S D FOR N S D
A 4HE TOTAL OF 53 EXPORTS IN WAS
B 4HE TOTAL OF 53 IMPORTS IN WAS
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
S D
S D
S D
%VALUATE H FOR H S D
(OLT -C$OUGAL -ATHEMATICS
%VALUATE M FOR M S D
%VALUATE S S D FOR S S D
%VALUATE K FOR K S D
S D !PPROXIMATELY FEET ABOVE THE STARTING POINT
S D
4HE TEMPERATURE INCREASED &
S D
S D
S D
S D
%VALUATE B FOR B S D
"#% TO #%
S D
4HE 'RECO2OMAN ERA LASTED YEARS
'REAT 0YRAMID TO #LEOPATRA
"#% TO "#%
S D
YEARS
#LEOPATRA TO PRESENT
"#% TO #%
S D
YEARS
'REAT 0YRAMID TO #LEOPATRA ABOUT YEARS
%VALUATE Q FOR Q S D
1UEEN .EFERTERI RULED %GYPT IN "#%
%VALUATE F FOR F S D
S D
4HERE ARE YEARS BETWEEN WHEN #LEOPATRA
TAKES THE THRONE AND .APOLEON INVADES
S D
4HE NEW DEPTH IS METERS BELOW SEA LEVEL OR M
S D S D
S D
S D
S D
S D
S D S D
S D
S D S D
S D
S D
0OSSIBLE ANSWER 4HE NUMBER OF THE YEAR EXPRESSED
IN "#% DECREASES AS TIME GOES FORWARD 4HIS IS
WHAT HAPPENS WITH THE NEGATIVE PART OF THE NUMBER
LINE !S YOU MOVE TO THE RIGHT AND GET CLOSER TO ZERO
THE ABSOLUTE VALUE OF THE NUMBERS DECREASES
0OSSIBLE ANSWER 4HE CALCULATIONS THAT INVOLVE A #%
AND "#% YEAR WOULD BE ONE LESS THAN ORIGINALLY
CALCULATED "UT ANY CALCULATIONS STRICTLY IN #% OR
"#% WOULD REMAIN THE SAME
" S D %VALUATE X FOR X S D
S D
%VALUATE T FOR T S D
T
%VALUATE M FOR M %VALUATE Y FOR Y S D
%VALUATE M S D FOR M S D
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
%VALUATE M FOR M /CEAN 4IDE
(EIGHT TX E
%VALUATE M FOR M 0!'%3 n
4HINK AND $ISCUSS
0OSSIBLE ANSWER AND S D
0OSSIBLE ANSWER 4HE PRODUCT OF NEGATIVE NUMBERS
IS POSITIVE WHILE THE SUM OF TWO NEGATIVE NUMBERS
IS NEGATIVE
S D
0OSSIBLE ANSWER 4HE SIGN OF THE INTEGERS IS THE
SAME THAT IS EITHER BOTH ARE POSITIVE OR BOTH ARE
NEGATIVE
S D S D
S D
%XERCISES
S D
S D
????
???
S D S D
S D
S D
S D
S D
S D
S D
S D
S D
S D
S D S D
GAINS ???
S D
????
S D
S D
S D
S D
S D
S D
S D S D
S D
4HE NET CHANGE IS
S D S D
S D
4HE NET CHANGE IS
%ARTH 4IDE
(EIGHT TY E
??
?
?
??
????
????
????
S D
???????
?????
%VALUATE T FOR T S D S D
%VALUATE X FOR X S D S D S D
LOSES S D
X
?
%VALUATE S S D FOR S S D
%VALUATE ??R FOR R ???
FOR T %VALUATE ???
T
????
Y %VALUATE ?????? FOR Y ???????
???
S D
S D
S D
S D S D S D
??????? 4HE AVERAGE DEPTH IS FEET
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
(OLT -C$OUGAL -ATHEMATICS
0OSSIBLE ANSWER "OTH METHODS GIVE THE CORRECT
RESULT !RT IS ADDING NEGATIVE YARDAGE "ELLA IS
SUBTRACTING TOTAL YARDS LOST
%QUIVALENT N S N D BY THE
!SSOCIATIVE 0ROPERTY S N D BY THE
)DENTITY 0ROPERTY AND N N BY THE
#OMMUTATIVE 0ROPERTY
A POSITIVE POSSIBLE ANSWER S D S D S D B NEGATIVE POSSIBLE ANSWER S D S D S D
C NEGATIVE POSSIBLE ANSWER S D S D S D D POSITIVE POSSIBLE ANSWER S D S D S D X X X YARDS MUST BE GAINED
%VALUATE W S D FOR W S D
$ & WAS THE HIGHEST TEMPERATURE
IS DEDUCTED FROM HER MONTHLY PAYCHECK
S D
IS THE CHANGE IN "RENDAS PAYCHECKS AFTER
YEARS
TWICE B LESS B LESS THAN Y
Y S D
S D
S D
S D
S D
S D
S D
4HE DIFFERENCE IN ELEVATION IS FEET
S D
2%!$9 4/ '/ /. 0!'% S D S D
????
???
S D S D S D
S D
0!'%3 n
%VALUATE X Y FOR X AND Y 4HINK AND $ISCUSS
!N EXPRESSION IS A MATHEMATICAL PHRASE AND DOES
NOT CONTAIN AN EQUAL SIGN !N EQUATION INCLUDES TWO
EXPRESSIONS ONE ON EITHER SIDE OF AN EQUAL SIGN
%VALUATE S R T D FOR R AND T S D
S D
0OSSIBLE ANSWER !DD TO EACH SIDE TO ISOLATE Y
4HE NUMERICAL EXPRESSION ON THE RIGHT SIDE OF THE
EQUATION IS THE VALUE OF Y
Y ONESIXTH THE SUM OF R AND ?? S R D
PLUS THE PRODUCT OF AND M
M
%XERCISES
X X OR X p 3O IS NOT THE SOLUTION
X 3O IS THE SOLUTION
.OT EQUIVALENT S T D S D T BY THE
$ISTRIBUTIVE 0ROPERTY AND S D T T
4HE EXPRESSIONS T AND T ARE NOT
EQUIVALENT
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
%VALUATE P FOR P 0OSSIBLE ANSWER )F THE PRODUCT OF TWO INTEGERS IS
NEGATIVE THEN THE INTEGERS HAVE OPPOSITE SIGNS FOR
EXAMPLE S D AND J DECREASED BY J (OLT -C$OUGAL -ATHEMATICS
3O IS NOT THE SOLUTION
X 3O IS THE SOLUTION
X p 3O IS NOT THE SOLUTION
X X OR X p 3O IS NOT THE SOLUTION
X p 3O IS NOT THE SOLUTION
X 3O IS THE SOLUTION
M M ?
?
M M P S D P S D S D
S D ?
?
P
P
Q S D Q S D S D
S D ?
?
Q
Q
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T
T T ?
T
T T ? ?
T T P S D
P S D
S D ?
S D
?
P
P
P X X ?
?
X X X FEET
X X OR X p 3O IS NOT THE SOLUTION
X 3O IS THE SOLUTION
X p 3O IS NOT THE SOLUTION
X X OR X p 3O IS NOT THE SOLUTION
X p #OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
W S D
W S D
S D
S D
?
?
W
W
M M ?
?
M T T ? ?
T Z S D Z S D S D
S D ?
?
Z Z P S D
P S D
S D ??
S D
?
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H S D
S D ?
S D
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X X ?
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T H H ?
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H M S D
M S D
S D ?
S D
?
M
M M ?
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M H H ?
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S D
?
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T
S D
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T S D
T S D
S D
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M M ?
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M X X ?
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X P P ?
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P N S D N S D S D ?
S D
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W
W
S D S D
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W
?
W W ?
?
W
C C ?
C
T T ?
?
T (OLT -C$OUGAL -ATHEMATICS
N N ??
?
N
PEOPLE POSSIBLE ANSWER THE POPULATION
INCREASED FROM TO ABOUT OR BY ABOUT
PEOPLE !N ANSWER OF IS REASONABLE
K
p 3O IS NOT THE SOLUTION
S S S
p 3O IS NOT THE SOLUTION
S
3O IS THE SOLUTION
S
p 3O IS NOT THE SOLUTION
T T ?
?
T #
D D OR D p 3O IS NOT THE SOLUTION
D 3O IS THE SOLUTION
D p 3O IS NOT THE SOLUTION
G G OR G
p 3O IS NOT THE SOLUTION
G
S D
p 3O IS NOT THE SOLUTION
G
3O IS THE SOLUTION
K S D K OR K S D S D 3O IS THE SOLUTION
K S D S D p 3O IS NOT THE SOLUTION
K S D S D p 3O IS NOT THE SOLUTION
D D OR D p 3O IS NOT THE SOLUTION
D p 3O IS NOT THE SOLUTION
D S D 3O IS THE SOLUTION
%LECTRON
#HARGE
)ON
#HARGE
!LUMINUM ION
S !L D
(YDROXIDE ION
S /( D
/XIDE ION
S / D
3ODIUM ION
S .A D
,ET E BE THE ELECTRON CHARGE FOR
!LUMINUM ION S !L D
E E E S D
E E K K OR K
3O IS THE SOLUTION
K
p 3O IS NOT THE SOLUTION
#OPYRIGHT © BY (OLT -C$OUGAL
!LL RIGHTS RESERVED
0ROTON
#HARGE
.AME OF )ON
(YDROXIDE ION S /( D
E E E S D
E E /XIDE ION S / D
E
E
E
E
E
(OLT -C$OUGAL -ATHEMATICS
3ODIUM ION S .A D
Y P Y ????
P ???
????
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Y P
L ????
?K? L
????
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K? K L E E E E E 0OSSIBLE ANSWER 4HE STUDENT EITHER SUBTRACTED FROM OR ADDED TO S D 0OSSIBLE ANSWER 'AINING NEGATIVE YARDAGE IS THE
SAME AS LOSING THAT MANY YARDS
M ???
M H ???
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