What is Polya's Problem Solving Method?

1. UNDERSTANDING THE PROBLEM

* Can you state the problem in your own words?

* What are you trying to find or do?

* What are the unknowns?

* What information do you obtain from the problem?

* What information, if any, is missing or not needed?

2. DEVISING A PLAN

The following list of strategies, although not exhaustive, is very useful.

* Look for a pattern.

* Examine related problems, and determine if the same technique can be applied.

* Examine a simpler or special case of the problem to gain insight into the solution of the original problem.

* Make a table.

* Make a diagram.

* Write an equation.

* Use guess and check.

* Work backward.

* Identify a subgoal.

3. CARRYING OUT THE PLAN

* Implement the strategy or strategies in step 2, and perform any necessary actions or computations.

* Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step.

* Keep an accurate record of your work.

4. LOOKING BACK

* Check the results in the original problem. (In some cases this will require a proof.)

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

* Determine whether there is another method of finding the solution.

* If possible, determine other related or more general problems for which the techniques will work.