Problem Solving

Objectives

• State Polya's guidelines for solving problems.
• Apply Polya's guidelines to simple problems.

Discussion

• George Polya, 1887-1985, How to Solve It
  1. Understand the problem
     • Carefully read the problem, a number of times
       • Do I understand what I read?
       • What am I asked to find?
       • What information do I have
       • If you don't understand something, get help
     • Draw a picture, label it!
     • List important facts
     • Do you have sufficient information to solve the problem?
  2. Devise a plan to solve the problem
     • Have you seen a problem like this before?
     • Can you write out an equation?
     • Look for patterns (Inductive reasoning)
     • Can you simplify the problem?
     • Can you use smaller numbers to make the problem more understandable
     • Can you put information into a table to help to see a pattern?
     • Can you estimate the solution
       • This helps you know if you have the right solution
       • It also may give you a hint how to solve the problem
  3. Carry out the plan
  4. Check the results.
     • Does your answer make sense?
     • Is your answer reasonable?

Example Problems

• 2 page 29
• 6 page 29
• 8 page 29
• 10
• 12
• 20
• 28
• 30
• 34
• 40

Homework