Problem Solving Strategies

1
Problem Solving Strategies

• Caleb Allison
• Julie Miller

2
Problem Solving Strategies

• Knowing various strategies allows you to
  effectively approach different types of problems.
  You may encounter some of these problems in
  coursework and standardized tests, as well as in
  everyday situations.

3
Types of Strategies

• Eliminate possibilities
• Guess check
• Work backwards
• Draw a diagram
• Make a list

4
Eliminate Possibilities

• You may already use this strategy without knowing
  it, like the game 20 Questions. When presented
  with a problem, you look at all the possible
  solutions, and then you begin to eliminate
  unreasonable answers.
• In the words of Sherlock Holmes, Once you have
  eliminated the impossible, then whatever is left,
  no matter how improbable, must be the solution.

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Eliminate Possibilities

• Juana threw five darts at a dartboard. The
  possible scores on the target were 2, 4, 6, 8,
  10. Each dart hit the target. Which of these
  total scores can be quickly identified as not
  possible 38, 23, 58, 30, 42, 31, 26, 6, 14, or
  15?
• 23, 58, 15
• 31, 6, 15
• 23, 58, 31, 6
• 23, 58, 31, 6, 15

a
b
c
d
6
Oops!

• Unfortunately that is not the correct answer.

Go back and try again!
7
Hooray!!!

• Congratulations, you are correct!

Go to the next strategy.
8
Guess Check

• This strategy might seem trivial, yet it can
  organize information in a way that the
  information becomes more useful in your hands.
  Guess Check is not only a strategy, it is also
  an attitude. You must first believe that you can
  solve a problem, even if you dont understand it.

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Guess Check

• A train leaves Roseville heading east at 600
  a.m. at 40 mph. Another eastbound train leaves
  on a parallel track at 700 a.m. at 50 mph. At
  what time will the two trains be the same
  distance away from Roseville?
• 1000 a.m.
• 1100 a.m.
• 1200 p.m.
• 100 p.m.

a
b
c
d
10
Yippee!!!

• You are so smart!

Go to the next strategy.
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Oops!

• Unfortunately that is not the correct answer.

Go back and try again!
12
Work Backwards

• Most other strategies, you work forwards through
  the information in a problem. To successfully
  work backwards, you need to change your focus and
  consider the whole problem in reverse.

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Work Backwards

• The night before their debut in Carnegie Hall,
  half of the ballet company stayed up late
  watching tractor pulls on TV. Excuse me, make
  that half of the company plus one more. There
  were 13 tired dances in all, so how many dancers
  were in the company?
• 13
• 24
• 50
• 26

a
b
c
d
14
Oops!

• Unfortunately that is not the correct answer.

Go back and try again!
15
Woohoo!!!

• Correct again!

Go to the next strategy.
16
Draw a Diagram

• A diagram has many advantages over verbal
  communication. Diagrams organize information
  spatially, allowing you to visualized a problem.
  For example, a diagram can show positional
  relationships far more easily and clearly than a
  verbal description can.

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Draw a Diagram

• A ball rebounds one-half the height from which it
  is dropped. The ball is dropped from a height of
  160 feet and keeps on bouncing. What is height
  the ball rebounds after the fifth bounce?
• 10 feet
• 5 feet
• 20 feet
• 15 feet

a
b
c
d
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Oops!

• Unfortunately that is not the correct answer.

Go back and try again!
19
Wonderful!!!

• Way to keep your eye on the ball!

Go to the next strategy.
20
Make a List

• A list should use a system to organize
  information in a clear and understandable method.
  Another person should be able to understand the
  system and verify the solution without too much
  effort.

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Make a List

• Frisbin is a game that you throw two Frisbees at
  two different sized bins that are set up on the
  ground. If a Frisbee lands in the larges bin the
  player scores 5 points. If it lands in the
  smaller bin the player scores 10 points. How
  many different ways can the player score?
• 6 ways
• 4 ways
• 7 ways
• 5 ways

a
b
c
d
22
Oops!

• Unfortunately that is not the correct answer.

Go back and try again!
23
Yippeekyeyeah!

• Thats exactly right.

Are you ready for a challenge?
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Challenge Problems

• The next two questions you may employ any of the
  six problem solving strategies covered to get a
  solution.

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True Colors

• Mr. Black, Mr. Brown, and Mr. White were having a
  conversation.
• "It's funny," said Mr. Black to the other two
  men, "that we are all wearing different colors,
  but none of us is wearing the color that is the
  same as his name."
• "True," agreed the man who was wearing white.
• Use the information in this conversation to give
  the correct last name of the man wearing each
  color

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True Colors

• Since no one can be wearing the same color as his
  name, Mr. Black can be wearing only brown or
  white.  Since he is talking to a man wearing
  white, that means Mr. Black must be wearing
  brown.  Mr. White can be wearing only black or
  brown, but Mr. Black is wearing brown, so Mr.
  White must be wearing black.
• That means that Mr. Brown is the man wearing
  white.

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Pocket Coins

• Janice has 2.46 worth of coins in her pocket.
  The coins are of four different denominations,
  and she has the same number of each denomination.
  What are the four denominations, and how many of
  each does she have?

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Pocket Coins

• Janice has six pennies, six nickels, six dimes,
  and six quarters. The easiest way to arrive at
  the answer is to notice immediately that, since
  the last number in the amount she has is 6, she
  must have either six pennies or one penny. She
  can't have just one penny, because then she would
  have only one each of three other denominations,
  and that can't add up to 2.46. So she must have
  six of each denomination. She can't have six
  silver dollars, because then she'd have more than
  2.46. And half-dollars are no longer in
  circulation.

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Conclusion

• Now that we have covered these problem solving
  strategies, can you see where you may have
  already implemented them into your daily lives?
  Continuing to use problem solving strategies will
  improve your chances of success.

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Resources

• Herr, T. Johnson, K., (1994) Problem Solving
  Strategies Crossing the River with Dogs and
  Other Mathematical Adventures. Key Curriculum
  Press.