Step 1:Understand the
Problem
¨Do you understand all the
words?
¨Can you restate the problem
in your own words?
¨Do you know what is
given?
¨Do you know what the goal
is?
¨Is there enough
information?
¨Is there extraneous
information?
¨Is this problem similar to
another problem you have solved?
Step 2:Devise a
Plan
Can one (or more) of the following strategies (heuristics) be used? (A strategy is defined as an artful
means to an end.)
1.Guess and test. 
12.Work backwards 
2.Use a variable. 
13.Use cases. 
3.Draw a picture. 
14.Solve an equation. 
4.Look for a pattern. 
15.Look for a formula. 
5.Make a list. 
16.Do a simulation. 
6.Solve a simpler problem. 
17.Use a model. 
7.Draw a diagram. 
18.Use dimensional analysis. 
8.Use direct reasoning. 
19.Identify subgoals. 
9.Use indirect reasoning. 
20.Use coordinates. 
10.Use properties of numbers. 
21.Use symmetry. 
11. Solve an equivalent problem. 
.
¨Implement the strategy or
strategies that you have chosen until the problem is solved or until a new
course of action is suggested.
¨Give yourself a reasonable
amount of time in which to solve the problem.If your are not successful, seekhints from others or put the problem aside for
a while.(You may have a flash of insight
when you least expect it!)
¨Do not be afraid to start
over.Often, a fresh start and a new
strategy will lead to success.
¨Is your solution
correct?Does your answer satisfy the
statement of the problem?
¨Can you see an easier
solution?
¨Can you see how you can
extend your solution to a more general case?
Usually, a problem is stated in words, either orally or written.Then, to solve the problem, one translates the words into an equivalent problem using mathematical symbols, solves this equivalent problem, and then interprets the answer.This process is summarized in Figure 1.1.
