PROBLEM SOLVING STRATEGIES

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PROBLEM SOLVING STRATEGIES
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PROBLEM SOLVING PLAN

• Determine what the problem is asking.
• Decide which strategy will help solve the
  problem.
• Solve.
• Check solution to see that it answers the
  question.

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The following strategies will help you solve any
type word problem you may be given. Refer to the
examples any time you need help. Look for
similarities in problems to help you choose the
correct strategy. Remember that some problems
may require you to use more than one of these
strategies and many problems may be successfully
solved in more than one way.
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GUESS, CHECK and REVISE
Lincoln Middle School needs new smoke alarms.
The school has 415 to spend. Alarms with escape
lights cost 18, and alarms with a false-alarm
silencer cost 11. The school wants 4 times as
many escape-light alarms as silencer alarms. How
many of each kind can the school purchase?
What facts are needed to solve the problem?
Cost of alarms 18 and 11 Amount to be spent
415 Fact 4 times as many escape-light alarms as
silencer alarms
Try.
Buy 12 escape-light alarms and 3 silencer alarms.
Continue
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Check.
12 x 18 216 3 x 11 33 Add
249 249 is a lot less than the 415 that the
school has to spend. Revise with different
combinations until you solve the problem.
Try.
Buy 20 escape-light alarms and 5 silencer alarms.
20 x 18 360 5 x 11 55 Add
415
Check to see if your answer agrees with the
information in the problem.
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WRITE AN EQUATION
The cost for a car and driver on a car ferry is
15. Each additional passenger is 2. If Brett
pays a toll of 21, how many additional
passengers does he have?
What information are you given?
Cost of car and driver 15. Cost for each
passenger 2.
What are you asked to find?
The number of additional passengers.
Continue
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You are given a relationship between numbers, so
an equation will help solve the problem.
Assign variable. p passenger
2 for each passenger, so
15 2p toll, toll 21, so
15 2p 21 Solve equation
for p. 15 2p
21 Subtract 15. 15 15 2p 21 15
2p 6 Divide by 2.
2p 6 2 2
p 3 There are
three passengers. Check. 15 2 x 3 21
15 6 21 21
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WORK BACKWARDS
The store manager recorded 80 greeting cards sold
on Friday. The day before she had sold one-half
that number. On Wednesday, she sold 25 more than
on Thursday. On Monday and Tuesday she sold a
total of twice what she sold on Wednesday. How
many cards did she sell during the five days.
What does the problem ask you to find?
You need to find the total number of cards sold
in 5 days.
Work backwards. Cards sold on Friday
80 Cards sold on
Thursday 80 2 40 Cards
sold on Wednesday 40 25
65 Cards sold on Monday and Tuesday 2 x 65
130
Continue
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Add.
80 40 65 130 315 She sold 315
cards. Check. Write the number of cards sold as
a mathematical expression. 80 (80 2) (40
25) (2 x 65) 315 Solve by using order of
operations. 80 40 65 130 315
315 315
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MAKE A GRAPH
Stuart is from Australia, where speed limits are
measured in kilometers per hour. While visiting
the United States, Stuart drives along a road
with a speed limit of 50 miles per hour (mph).
Stuart would like to know the equivalent speed in
kilometers per hour (kph). He remembers that 15
mph 25 kph, and 30 mph 50 kph.
You can make a line graph to approximate 50 miles
per hour in kilometers per hour.
Continue
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Plot the points (15,25) and (30,50) on a
coordinate plane and connect them with a line.
Check. In reading the graph, you can see that
50mph is about 83kmp.
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MAKE AN ORGANIZED LIST
A stadium sells buttons, pins, and pennants. The
prices are 1.25 for a button, .54 for a pin,
and 4.39 for a pennant. Audrey wants to buy an
equal number of each. What is the greatest
number she can buy without spending more than
20.00?
An organized list helps to solve the problem.
Continue
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Audrey can buy 3 of each without spending more
than 20.00. You can estimate to check whether
your answer is reasonable.4 2 13 is less
than 20.
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DRAW A DIAGRAM
Steve found that each time a ball bounces, it
returns to one half its previous height. If he
drops the ball from 40 feet, how many feet will
it have traveled when it hits the ground the
fourth time?
The problem asks for the total distance the ball
will travel up and down by the time it hits the
ground the fourth time. Draw a diagram to
represent the traveling ball.
Continue
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Add to solve. 40 20 20 10 10 5 5
110 feetCheck. Count the number of times the
ball hits the ground check that each bounce is
one half the height of the previous bounce.
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MAKE A TABLE AND LOOK FOR A PATTERN
Stony Hollow School District has a softball
playoff each spring for its 8 schools. Each
school plays one game against every other school.
The winner is the school with the greatest
number of victories. How many playoff games are
played in all?
You need to find the total number of playoff
games. Each school plays any other school just 1
time. Draw a diagram and look for a pattern.
Continue
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28 games must be played.Check.Does the pattern
make sense? Yes. Each school added to the table
plays each of the other schools once. So, the
number of games added is 1 less than the total
number of schools.
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SOLVE A SIMPLER PROBLEM
A mystery game has 3 rooms. Each room has 3
desks. Each desk has 3 drawers, and each drawer
has 3 dollars. If you are able to collect all
the money, how many dollars would this be?
If you cannot solve the entire problem at once,
make it easier by finding the amount of money in
just 1 room first.
Multiply. 3 (desks) x 3 (drawers) x 3 (dollars)
27 in one room Next. There are 3 rooms, so 3 x
27 81 There are 81 in all three rooms.
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SIMULATE A PROBLEM
You have six different-color pairs of loose socks
in a drawer. You reach into the drawer without
looking and take out two socks. What is the
probability you will pick a matched pair?
What are the possible results of picking two
socks?
You could pick two socks of the same color or two
socks of different colors. You want to find the
approximate probability of picking two socks of
the same color.
Continue
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Solve.After repeating the simulation many times,
divide the number of times the colors were the
same by the total number of simulations you did
to find the approximate or experimental
probability of getting a matched pair.
You can simulate the problem by making a spinner
like the one at the right. Each number stands
for one of the six colors. Spin the spinner
twice to find the colors of two socks. Record
your results.
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USE LOGICAL REASONING
Dan, Sandy, Rita, and Joe mixed up their class
schedules. Each student has math class during a
different period, and the schedules show math in
period A, B, C, or D. Dan knows he eats lunch in
period C. Sandy sees Dan arrive for math class
just as she is leaving. Rita goes to math after
eating lunch with Dan. Which schedule belongs to
each student?
There are four different schedules for four
students. The goal is to match each student with
a schedule.
Continue
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Look back and check.Reread the problem. Make
sure your solution matches all the facts given.

• Make a table. Label the schedules A, B, C, and D
  for the periods where math appears. Use the
  clues to determine the schedules.
• Dan eats lunch during period C. Write no in
  the box for Dan and schedule C.
• Rita goes to math after lunch with Dan. Put
  yes in the box for Rita and schedule D.
• To have math before Dan, Sandy must have class in
  period A and Dan would have math in period B.
• Joe must have math in period C.

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USE A FORMULA
The following formulas are those that you should
become familiar with as you will be using them
often throughout middle school.
A lw A bh
a² b² c² A ½bh A ½(a b)h
I prt
(simple interest) A p r²
d rt
(constant motion) P 2l 2w C 2p r V lwh A
2lw 2lh 2wh (surface area)
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REMEMBER!!!
WHEN SOLVING SOME PROBLEMS, YOU MAY NEED TO USE
MORE THAN ONE OF THESE STRATEGIES.