PROBLEM SOLVING

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PROBLEM SOLVING
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Polyas 4 Steps to Problem Solving

• Understand the problem
• Devise a plan. Strategies to use?
• Carry out the plan
• Look back!
• Does your response answer the question?
• Does your response seem correct?

3
Guess and Test

• Clues suggesting Guess and Test strategy
• Limited number of possible answers to check
• Have a good idea what the answer is
• Can systematically try all possibilities
• No other obvious strategy to try

4
Use a Variable

• Variable A letter used in place of numbers.
• Clues suggesting Use a Variable strategy
• Problem suggests an equation
• A proof or a general solution is required
• An unknown quantity is related to know ones
• Problem says things like for any ,
  consecutive, odd, even.

5
Draw a Picture

• Clues suggesting Draw a Picture strategy
• Problem involves a physical situation
• Involves geometric figures or measurements
• To gain a better understanding of the problem
• Visual representation of the problem is possible

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Is the sum of five consecutive numbers a multiple
of 5?
____ _____ _____ _____ _____
_x__ _x1_ _x2_ _x3_ _x4_
5x 10
5x 10 5 ( x 2)
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A rectangular field has a perimeter of 220 meters
and an area of 2,856 square meters. What are its
dimensions?
220 m l w l w
2 l 2 w
l w 110 50 x 60 3000 40 x 70 2800 42 x 68
2856
l w w l
Ans 42 m by 68 m
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It takes 64 cubes to fill a cubical box that has
no top. How many cubes are NOT touching a side
or the bottom?
16 ? ? 16
9
It takes 64 cubes to fill a cubical box that has
no top. How many cubes are NOT touching a side
or the bottom?
16 ? ? 16
10
It takes 64 cubes to fill a cubical box that has
no top. How many cubes are NOT touching a side
or the bottom?
16 ? ? 16
8 ?
8 ?
11
It takes 64 cubes to fill a cubical box that has
no top. How many cubes are NOT touching a side
or the bottom?
16 ? ? 16
8 ?
16 16 8 8 4 52 64 52 12
8 ?
4 ?
12
After the first two terms in the sequence, each
number is the sum of the preceding two terms.
Find the missing numbers. 4 ___ ___ ___
___ 67
13
Tom and Barb have only nickels and dimes. Barb
has 75 cents and Tom has 90 cents. Both have the
same number of coins and Tom has the same number
of dimes as Barb has nickels. How many nickels
does Barb have?
14
The surface of Big Lake is 31 feet above the
surface of Long Lake. Long Lake is half as deep
as Big Lake and the bottom of Long Lake is 8 feet
below the bottom of Big Lake. How deep is each
lake?
15
Will the sum of any n consecutive integers have a
factor of n?