(Introduction) Polya's Four-Step Approach to Problem Solving.

(Polya's Four Stepts) We will be looking at the four steps.
     1. Understand the problem.
     2. Devise a plan
     3. Carry out the plan
     4. Look back 

(Understand the Problem) Let's look at these in more detail. Understand the problem. It is impossible to solve a problem if you do know what the problem is. What is known? What is unknown? These are important questions to ask yourself: What do the terms mean? If you do not understand the terms, how will you be able to solve the problem? What is the motivation for the problem? Often understanding the motivation can give hints as to strategies that you can use to solve the problem. Do you have enough information? If you do not, you may have to search out for more information or search for ideas from other sources. Are there extra or redundant conditions which you need to ignore?

(Devise a Plan) 2. Devise a plan. Have you seen the problem or a similar problem before? In which case, those techniques could be applied to this problem. Could the problem be restated in another form which would be easily understood?

(Possible Strategies) Some possible strategies, i.e. reach into your bag of tricks. The most important and often skipped method is guess-and-check, trial-and-error, guess-and test. It is wonderful method; use it. Draw a picture. Look for a pattern. Make a list. Solve a simpler problem. Use a variable. Use deductive reasoning. But, most important, try something.

(Carry Out the Plan) 3. Carry out the plan. If the plan does not seem to be working, start over and try another method. Just because a method did not work does not mean you did it wrong. You have actually accomplished something; you have shown that a method does not work. Take a break from the problem and come back to it later. Often resting your mind will help you solve the problem. Discuss the problem with others. In the real world, teams work together to solve problems. Can you see clearly that each step is correct?

(Look Back) 4. Look back. Did you answer the question? Is your result reasonable? Can you show your result is correct? Is there another way of solving the problem? Look for other methods. Can the problem or solution be generalized? Can you give a formula, method, or algorithm that can be used in solving other or similar problems?

(Polya Quote) A quote from George Polya: It is hard to have good ideas if we have little knowledge of the subject, and it is impossible if we have no knowledge. Good ideas are based on past ideas, experience, and recollections. Experience, intuition, and practice play large roles...

(Fun Problems) Try these sample problems and upon completion click on this page (of the video page) to see the solutions.

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