Problem Solving in Mathematics

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Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures to work through them, and knowing what those procedures are and when to apply them is key to their solution. To identify procedures, you have to be familiar with the problem's situation—is it one of addition, subtraction, multiplication, or division? Then you can collect the appropriate information needed to solve the problem, identify a strategy or set of strategies, and then apply those strategies appropriately.


Small Book, Big Ideas

Mathematician George Pólya’s book “How to Solve It,” written in 1957, is a great guide to have on hand. The ideas below are similar to those expressed in Pólya’s book and should help you untangle even the most complicated math problem.

As with any task, the more you practice math problem-solving, the better you will get. And the more consistent you are in your approach and procedures, the greater your chance of success. Here is a four-step plan that will help you get there:

Look for Clue Words

Think of yourself as a math detective. The first thing to do when you encounter a math problem is to look for clue words. This is one of the most important skills you can develop. If you begin to solve problems by looking for clue words, you will find that those words often indicate an operation.

Common clue words for addition problems:

  • Sum
  • Total
  • In all
  • Perimeter

Common clue words for subtraction problems:

  • Difference
  • How much more
  • Exceed

Common clue words for multiplication problems:

  • Product
  • Total
  • Area
  • Times

Common clue words for division problems:

  • Share
  • Distribute
  • Quotient
  • Average

Although clue words will vary a bit from problem to problem, you'll soon learn to recognize which words mean what in order to perform the correct operation.

Read the Problem Carefully

This, of course, means looking for clue words as outlined above. Once you’ve identified your clue words, underline them. This will let you know what kind of problem you’re dealing with. Then do the following:

  • 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 in that instance?
  • What facts are you given about this problem?
  • What facts do you still need to find out about this problem?

Develop a Game Plan to Solve Your Problem

Based on what you discovered by reading the problem carefully and identifying similar problems you’ve encountered before, you can then:

  • Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking.
  • If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work.

Reflect on Your Work

This part is critical. If it seems like you’ve solved the problem, ask yourself the following:

  • Does your solution seem probable?
  • Does it answer the initial question?
  • Did you answer using the language in the question?
  • Did you answer using the same units?

If you feel confident that the answer is “yes” to all questions, consider your problem solved.


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Your Citation
Russell, Deb. "Problem Solving in Mathematics." ThoughtCo, Feb. 13, 2018, Russell, Deb. (2018, February 13). Problem Solving in Mathematics. Retrieved from Russell, Deb. "Problem Solving in Mathematics." ThoughtCo. (accessed February 18, 2018).