Polya's 4 Steps of Problem Solving

1. Understand the problem.
   • Understand the situation.
   • Draw a diagram/picture if needed.
   • What is known? What is unknown?
   • What is the question?
   • How do various quantities in the problem relate?
   • State some predictions/expectations for the answer.
2. Devise a Plan.
   • Think of a strategy that can be used to solve the problem.
3. Carry Out the Plan.
   • Attempt to solve the problem with the chosen strategy.
   • If the strategy does not work, return to step 2 (try another strategy).
4. Look Back.
   • Check your answer, if possible. (Note: this is not always possible.) In particular, solve the problem in a different way, if possible.
   • If checking the answer is not possible, does it make sense? Were your expectations met?
   • Is there a way to simplify your solution?
   • Are there any other (perhaps simpler) approaches?
   • Is there a way to simplify the presentation of your solution? (Note: depending on your audience, "simplify" might mean different things.)
   • If you did not use a diagram/picture, could one help you explain your solution?

Strategies for Problem Solving (for step 2)

• Draw a diagram
• Make a table
• Look for a Pattern
• Examine a simpler problem (e.g. for smaller numbers)
• Examine a special case
• Break the problem into smaller/simplier pieces
• Identify a subgoal
• Examine a related problem
• Recall related theorems
• Guess and check
• More strategies will be introduced in this class!