Problem Solving in Mathematics

High school student reviewing algebra equations digital tablet
Hero Images/Getty Images

Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures and knowing what and when to apply them. To identify procedures, you have to be familiar with the problem situation and be able to collect the appropriate information, identify a strategy or strategies and use the strategy appropriately. G. Polya wrote a book titled 'How To Solve It' in 1957.

Many of the ideas that worked then, continue to work for us now. The steps below are very similar to those expressed in Polya's book.

Problem solving requires practice! The more your practice, the better you get.
Practice, practice, practice.

Problem Solving Plan in 4 Steps:

1. Clues:

  • Read the problem carefully.
  • Underline clue words.
  • Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
  • What did you need to do?
  • What facts are you given?
  • What do you need to find out?

2. Game Plan:

  • Define your game plan.
  • Have you seen a problem like this before?
  • Identify what you did.
  • Define your strategies to solve this problem.
  • Try out your strategies. (Using formulas, simplifying, use sketches, guess and check, look for a pattern, etc.)
  • If your strategy doesn't work, it may lead you to an 'aha' moment and to a strategy that does work.

3. Solve:

  • Use your strategies to solve the problem

    4. Reflect:

    • This part is critical. Look over your solution.
    • Does it seem probable?
    • Did you answer the question?
    • Are you sure?
    • Did you answer using the language in the question?
    • Same units?

    Clue Words:

    When deciding on methods or procedures to use to solve problems, the first thing you will do is look for clues which is one of the most important skills in solving problems in mathematics.

    If you begin to solve problems by looking for clue words, you will find that these 'words' often indicate an operation.

    For instance:
    Clue Words for Addition

    • sum
    • total
    • in all
    • perimeter

    Clue Words for Subtraction

    • difference
    • how much more
    • exceed

    Clue Words for Multiplication

    • product
    • total
    • area
    • times

    Clue Words for Division

    • share
    • distribute
    • quotient
    • average

    Although clue words vary a bit, you'll find that there will be consistency with them to guide you to the correct operation.