5SE A 0ROBLEM 3OLVING 0LAN
'OAL + 5SE A PROBLEM SOLVING PLAN TO SOLVE PROBLEMS
9OUR .OTES
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5SE THE FOLLOWING FOURSTEP PLAN TO SOLVE A PROBLEM
3TEP Ê ,i>`Ê>˜`Ê1˜`iÀÃÌ>˜`Ê 2EAD THE PROBLEM
CAREFULLY )DENTIFY WHAT YOU WANT TO KNOW AND
WHAT YOU WANT TO FIND OUT
3TEP Ê >ŽiÊ>Ê*>˜Ê
$ECIDE ON AN
APPROACH TO SOLVING THE PROBLEM
3TEP Ê -œÛiÊ̅iÊ*ÀœLi“Ê
#ARRY OUT YOUR PLAN
4RY A NEW APPROACH IF THE FIRST ONE ISNT SUCCESSFUL
3TEP Ê œœŽÊ>VŽÊ
ANSWER IS REASONABLE
%XAMPLE #HECK THAT YOUR
2EAD A PROBLEM AND MAKE A PLAN
9OU HAVE TO BUY ORANGE JUICE AND BAGELS AT THE STORE
! CONTAINER OF JUICE COSTS AND A BAGEL COSTS )F YOU BUY TWO CONTAINERS OF JUICE HOW MANY BAGELS CAN
YOU BUY
3OLUTION
3TEP Ê ,i>`Ê>˜`Ê1˜`iÀÃÌ>˜`Ê Ê 7HAT DO YOU KNOW 9OU
KNOW HOW MUCH MONEY YOU HAVE AND THE PRICE OF
A Ê L>}iÊ AND A CONTAINER OF JUICE
7HAT DO YOU WANT TO FIND OUT 9OU WANT TO FIND OUT THE
NUMBER OF Ê L>}iÃÊ YOU CAN BUY
3TEP Ê >ŽiÊ>Ê*>˜Ê 5SE WHAT YOU KNOW TO WRITE
A Ê ÛiÀL>Ê“œ`iÊ THAT REPRESENTS WHAT YOU WANT
TO FIND OUT 4HEN WRITE AN Ê iµÕ>̈œ˜Ê AND SOLVE IT
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
3OLVE A PROBLEM AND LOOK BACK
%XAMPLE 3OLVE THE PROBLEM IN %XAMPLE BY CARRYING OUT THE
PLAN 4HEN CHECK YOUR ANSWER
3OLUTION
3TEP Ê -œÛiÊ̅iÊ*ÀœLi“Ê 7RITE A VERBAL MODEL 4HEN
WRITE AN EQUATION ,ET B BE THE NUMBER OF BAGELS YOU BUY
0RICE OF
.UMBER
0RICE OF .UMBER
#OST
JUICE
OF
BAGEL
OF
IN DOLLARS
IN DOLLARS CONTAINERS IN DOLLARS BAGELS
Ê £°ÓxÊ
+
Ê ÓÊ
Ê ä°ÇxÊ
+
B
Ê ÇÊ
4HE EQUATION IS Ê Ó°xÊ Ê ä°ÇxÊ B Ê ÇÊ /NE WAY TO SOLVE
THE EQUATION IS TO USE THE STRATEGY GUESS CHECK AND REVISE
'UESS AN EVEN NUMBER THAT IS EASILY MULTIPLIED BY Ê ä°ÇxÊ 4RY Ê Ê Ó°xÊ Ê ä°ÇxÊ B Ê ÇÊ
7RITE EQUATION
Ê Ó°xÊ Ê Ê ä°ÇxÊ Ê ÇÊ
3UBSTITUTE FOR B
Ê
3IMPLIFY Ê `œiÃʘœÌÊ
CHECK
Ê x°xÊ ÊpÊÊ ÇÊ
"ECAUSE Ê x°xʐÊÇÊ TRY AN EVEN NUMBER Ê }Ài>ÌiÀÊ̅>˜Ê 4RY Ê Ê Ó°xÊ Ê ä°ÇxÊ B Ç
7RITE EQUATION
Ê Ó°xÊ Ê ä°ÇxÊ Ç
3UBSTITUTE FOR B
Ê
3IMPLIFY
Ê ÇÊ ÊÊÊ ÇÊ
&OR Ê fÇÊ YOU CAN BUY Ê ÈÊ BAGELS AND Ê ÓÊ CONTAINERS OF
JUICE
3TEP Ê œœŽÊ>VŽÊ %ACH ADDITIONAL BAGEL YOU BUY ADDS
Ê f°ÇxÊ TO THE Ê fÓ°xäÊ YOU PAY FOR THE JUICE -AKE A TABLE
"AGELS
4OTAL #OST
Ó°xä ΰÓx
{
{°Çx
x°x
È°Óx
Ç
4HE TOTAL COST IS Ê fÇÊ WHEN YOU BUY Ê ÈÊ BAGELS AND Ê ÓÊ Ê
CONTAINERS OF JUICE 4HE ANSWER IN STEP IS Ê VœÀÀiVÌÊ ,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
3UPPOSE IN %XAMPLE THAT YOU HAVE AND YOU
DECIDE TO BUY THREE CONTAINERS OF JUICE (OW MANY
BAGELS CAN YOU BUY
££ÊL>}iÃ
&/2-5,! 2%6)%7
4EMPERATURE
# zzz]
&
z z WHERE & zÊ `i}ÀiiÃÊ>…Ài˜…iˆÌÊ
AND # zÊ `i}ÀiiÃÊ
iÃˆÕÃÊ
3IMPLE INTEREST
) z0RT WHERE ) zÊ ˆ˜ÌiÀiÃÌÊ Ê0 zÊ «Àˆ˜Vˆ«>Ê Ê
R zÊ ˆ˜ÌiÀiÃÌÊÀ>ÌiÊ AS A DECIMAL AND T zÊ Ìˆ“iÊ
$ISTANCE TRAVELED
D zRT WHERE D zÊ `ˆÃÌ>˜ViÊÌÀ>Ûii`Ê R zÊ À>ÌiÊ AND T zÊ Ìˆ“iÊ
0ROFIT
0 z) z% WHERE 0 zÊ «ÀœvˆÌÊ ) zÊ ˆ˜Vœ“iÊ AND
% zÊ iÝ«i˜ÃiÃÊ
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
(OMEWORK
)N %XAMPLE THE STORE WHERE YOU BOUGHT THE
JUICE AND BAGELS HAD AN INCOME OF FROM YOUR
PURCHASE 4HE PROFIT THE STORE MADE FROM YOUR
PURCHASE IS &IND THE STORES EXPENSE FOR THE
JUICE AND BAGELS
f{°xä
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE