1. PROBLEM SOLVING

2. Polya’s 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

6. Is the sum of five consecutive numbers a multiple of 5?
____ _____ _____ _____ _____
_x__ _x+1_ _x+2_ _x+3_ _x+4_
= 5x + 10
5x + 10 = 5 ( x + 2)

7. 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
Ans: 42 m by 68 m

8. It takes 64 cubes to fill a cubical box that has no top
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
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
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
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 
= 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 ___ ___ ___ ___ 67

13. Tom and Barb have only nickels and dimes
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
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?