CVMS Math League

PROBLEM-SOLVING STRATEGIES

There are many problems within the programs of the American Mathematical Competition (AMC), California Math League contests (ML), and in the Math Olympiad for Elementary and Middle Schools (MOEMS) that may be considered difficult if attacked by setting up a series of equations, but quite simple when attacked with problem-solving strategies such as looking for a pattern, drawing a diagram, making an organized list and so on.

The problem-solving method that will be used in our discussion consists of four basic steps:

FIND OUT
Look at the problem.
Have you seen a similar problem before?
If so, how is this problem similar? How is it different?
What facts do you have?
What do you know that is not stated in the problem?

CHOOSE A STRATEGY
How have you solved similar problems in the past?
What strategies do you know?
Try a strategy that seems as if it will work.
If it doesn't, it may lead you to one that will.

SOLVE IT
Use the strategy you selected and work the problem.

LOOK BACK
Reread the question.
Did you answer the question asked?
Is your answer in the correct units?
Does your answer seem reasonable?

Specific strategies may vary in name. Most, however, fall into these basic categories:

Compute or Simplify (C)
Use a Formula (F)
Make a Model or Diagram (M)
Make a Table, Chart or List (T)
Guess, Check & Revise (G)
Consider a Simpler Case (S)
Eliminate (E)
Look for Patterns (P)

Try to choose one or two the above strategies to solve your problems. You will find
that different strategies are appreciated for different problems. With practice, you
will find the best methods for you to use in solving complex problems.