1. How to Solve Problems Alison Kiddle

2. How to Solve It How to Solve It (1945) is a small volume by mathematician George Pólya, suggesting the following steps when solving a mathematical problem: First, you have to understand the problem After understanding, then make a plan Carry out the plan Look back on your work.

3. Understanding the problem Restate the problem in your own words What area of mathematics is this? What exactly am I being asked to do? What do I know? What do I need to find out? What am I uncertain about?

4. Devising a plan Work out the first few steps before leaping in! Have I seen something like it before? Is there a diagram I could draw to help? Is there another way of representing?

5. Carrying out the plan I’m STUCK! How do I get UNSTUCK? Work backwards Subgoals Simpler problem, special cases More general case Act it out Guess and check Has the plan failed? When is it time to abandon the plan and try something else?

6. Looking back Have I answered the question? Does it make sense? Have I fully solved the problem? Is my solution consistent?

7. Control Am I getting stressed? Am I spending too long on this? Is my plan working? Could I move on to something else and come back to this later? Am I focussing on the problem?

8. Solving an unseen problem On the next slide is a problem that I have only seen very briefly. I will attempt to solve it, and talk through my mental process. Try to note down any problem solving techniques you notice me using.

9. The picture shows four squares on the sides of a quadrilateral. Prove that the if the diagonals of the quadrilateral intersect at right-angles then the sum of the areas of one pair of opposite squares equals the sum of the areas of the other two squares.