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Useful Problem Solving Strategies for Math

written by: Harlan Bengtson • edited by: Noreen Gunnell • updated: 1/5/2012

Using one of more of the math problem solving strategies presented in this article can aid in solving your math problems. The problem solving techniques discussed here start with a four step procedure. Several useful techniques are given for each of the first two important steps.

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    Four Steps to Success

    There are many possible strategies and techniques you can use to solve math problems. A useful starting point is a four step approach to math problem solving. These four steps can be summarized as follows:

    1. Carefully read the problem. In this careful reading, you should especially seek to clearly identify the question that is to be answered. Also, a good, general understanding of what the problem means should be sought.
    2. Choose a strategy to solve the problem. Some of the possible strategies will be discussed in the rest of this article.
    3. Carry out the problem solving strategy. If the first problem solving technique you try doesn't work, try another.
    4. Check the solution. This check should make sure that you have indeed answered the question that was posed and that the answer makes sense.
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    Step One - Understanding the Problem

    As you carefully read the problem, trying to clearly understand the meaning of the problem and the question that you must answer, here are some techniques to help.

    • Identify given information - Highlighting or underlining facts that are given helps to visualize what is known or given.
    • Identify information asked for - Highlighting the unknowns in a different color helps to keep the known information visually separate from the unknowns to be determined. Ideally this will lead to a clear identification of the question to be answered.
    • Look for keywords or clue words - One example of clue words is those that indicate what type of mathematical operation is needed, as follows:
      • Clue words indicating addition: sum, total, in all, perimeter.
      • Clue words indicating subtraction: difference, how much more, exceed.
      • Clue words for multiplication: product, total, area, times.
      • Clue words for division: share, distribute, quotient, average.
    • Draw a picture - This might also be considered part of solving the problem, but a good sketch showing given information and unknowns can be very helpful in understanding the problem.
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    Step Two - Choose the Right Strategy

    It step one has been done well, it should ease the job of choosing among the strategies presented here for approaching the problem solving step. Here are some of the many possible math problem solving strategies.

    • Look for a pattern - This might be part of understanding the problem or it might be the first part of solving the problem.
    • Make an organized list - This is another means of organizing the information as part of understanding it or beginning the solution.
    • Make a table - In some cases the problem information may be more suitable for putting in a table rather than in a list.
    • Try to remember if you've done a similar problem before - If you have done a similar problem before, try to use the same approach that worked in the past for the solution.
    • Guess the answer - This may seem like a haphazard approach, but if you then check whether your guess was correct, and repeat as many times as necessary until you find the right answer, it works very well. Often information from checking on whether the answer was correct helps lead you to a good next guess.
    • Work backwards - Sometimes making the calculations in the reverse order works better.
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    Steps Three and Four - Solving the Problem and Checking the Solution

    If the first two steps have been done well, then the last two steps should be easy. If the selected problem solving strategy doesn't seem to work when you actually try it, go back to the list and try something else. Your check on the solution should show that you have actually answered the question that was asked in the problem, and to the extent possible, you should check on whether the answer makes common sense.