The document outlines Pólya's four step process for problem solving: 1) Understand the problem, 2) Devise a plan, 3) Carry out the plan, and 4) Look back. It provides strategies for each step, such as drawing pictures, simplifying the problem, looking for patterns, and checking each step of the work. The overall goal is to break down complex problems into manageable pieces and verify the reasoning and solution.

1. Problem Solving
WHAT TO DO WHEN YOU DON’T KNOW WHAT TO DO.
REG ROBSON, ST CLAIR COLLEGE, FALL 2020

2. Pólya’s Problem Solving Steps
1. Understanding the Problem
2. Devising a Plan
3. Carrying out the Plan
4. Looking Back
From How to Solve It (1945)

3. Understanding the Problem
 What do we know?
 What is the question asking?
 What do we wish we knew?
 Is it even possible to solve?
 Do we have enough
information?
 Is some of the given
information redundant?

4. Understanding the Problem (cont.)
 Draw a picture.
 Choose a notation to explain
the problem.
 Separate the different given
conditions in the problem.
 Write down the conditions in
the notation you have chosen.

5.  Have you seen the problem before?
Maybe the same problem but in a
different context?
 Do you know a related problem? What
math do you know that could be useful?
 Look at the unknown! What problems
have you worked on that have similar
unknowns?
 Can you use some past results?
Devising a Plan

6. Strategies for Devising a Plan
 Restate the problem. Try
to write the same
problem in a different
context.
 Go back to definitions.
What is the basic idea of
each part of the
problem.

7. Strategies for Devising a Plan (cont.)
 Simplify the problem.
 Use easy numbers.
 Look for patterns.
 Consider the trivial case.
 Consider the general case.

8. This Photo by Unknown Author is licensed
under CC BY-SA
 Is there a part of the problem that you
do know how to solve?
 Try dropping some of the conditions of
the problem. How does that affect the
unknown?
 Does your plan use all the given
conditions? Are all the conditions
required?
Strategies for Devising a Plan (cont.+)

9. Carrying out the Plan
Check each step!
Can you see clearly that
the step is correct?
Can you prove that it is
correct?

10. Looking Back
 Can you check the result?
 Can you check your argument?
 Can you show the result in a
different way?
 Can you use the result, or the
method, for some other
problem?