1.Understand the problem.

2.Develop a plan.

3.Carry out the plan.

4.Look back.

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1. Can you state the problem in your own words?

2. What are you trying to find or do?3. What are the unknowns?4. What information do you obtain

from the problem?5. What information, if any, is

missing or not needed?http://www.drkhamsi.com/classe/polya.html

1. Look for a pattern.2. Examine related problems and

determine if the same technique can be used.

3. Make a table, or diagram.4. Write an Equation.5. Use guess and check.6. Work backward.7. Identify a subgoal. http://www.drkhamsi.com/classe/polya.html

1.Apply the strategy from step 2 and perform any necessary computations or actions needed.

2.Check each step of the plan as you continue.

3.Keep an accurate record of your work.

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1. Check the results in the original problem.

2. Interpret the solution in terms of the original problem. Does the answer make sense? Is it reasonable?

3. Determine whether there is another method to solve this problem. http://www.drkhamsi.com/classe/polya.html

• At the end of a soccer game, each player on the team “gave five” to each player on the opposing team and to each other. How many “fives” were given? (Assume there are 11 players on each team.)

• Each player “gives five” to another player not themselves so 22-1 players “give 5”.

• To solve this problem I am going to do 21 – 1= n and then 21 + 1 = 22(21) which gives me 22 sums.

• I could also use the formula S= n(n+1)

2

21 + 20 + 19 + 18 +…..+ 1

1 + 2 + 3 + 4 +…..+ 21

22(21)

2

21(21+1)

2

21( 22)

2

462

2

= 231

Method

1 :

Method 2:

= 231

• Ask yourself, “does my answer make sense?”

• This answer makes sense because if each player was to “give five” to another player but themselves there would be 231 “fives given.”

Click on the right answers to solve the problem correctly!

• There are a total of 9 coins, some of them pennies, some of them nickels, and some of them dimes. If you collect all the pennies and nickels, there are 7 coins. If you collect all the nickels and dimes, there are 5 coins. How many of the 9 coins are pennies, how many are nickels, and how many are dimes?

• According to Polya, what is the first step to solving this problem?

1. Devise a plan?2. Read the problem?3. Understand the problem?4. Draw a picture?

There are 9 coins in total, if you collect all the pennies and nickels, there are 7 coins. If you collect all the nickels and dimes, there are 5 coins. How many of the coins are nickels? How many are dimes? How many are pennies?

According to Polya what do we do next?1. Look Back?2. Devise a plan?3. Carry out a plan?4. Re-read the problem?

• I am going to let P= the number of pennies, N= the number of nickels, and D= the number of dimes

• The problem tells us that P + N + D = 9

P + N = 7

N + D = 5

*What do we do next?1. Look back?

2. Re-read our explanation?

3. Carry out the plan?

4. Devise a second plan?

What's the plan?

• P + N + D = 9

P + N = 7

N + D = 5

• P = 7 – N

D = 5 – N

• Substitute:

– (7 - N) + N + (5 – N)= 9

– -N + 12 = 9

– 12 – 9 = N

– N = 3

• What does P equal?1. 4

2. 3

3. 5

4. 6

This is how you

do it!

• What does D equal?

1. 2

2. 8

3. 1

4. 4

• According to Polya what is the final problem solving step?

1. Do the problem a different way

2. Look Back

3. Draw a diagram to explain

4. Understand the problem

What do we

do next?

• There are 3 nickels, 4 pennies, and 2 dimes. Since 3 + 4 + 2 = 9 this checks with the initial information of there being 9 total coins. Also, there are 3 + 4 = 7 pennies and nickels, and there are 3 + 2 = 4 nickels and dimes, so these also check!

Please click slide to get worksheet!

Congratulations you have completed the presentation! Now that you are

finished please print out and complete the worksheet from the link below!

Sources

• Beckmann, Sybilla. Mathematics for Elementary Teachers. New York: Pearson Addison Wesly, 2005.

• "The Four-Step Problem-Solving Process." Polya's Remarks. 16 Oct. 2006. 16 Oct. 2006 <http://www.drkhamsi.com/classe/polya.html>.