4.4 Problem Solving Strategies

Activity symbol Activity: Stuck! What Do You Do?

Think back over the occasions when you have used math in real life. Remember a specific situation where you got stuck. What did you try to do to resolve the situation? What strategies have you seen so far?

In your math notebook, make a list of the strategies you can use when approaching a problem.

Hint symbol

Comment

You probably have several strategies from your own mathematical experiences already.

For example, a student nurse made the following comment:

“I’m still not sure about working out the more complicated drug doses, so I check the answer is similar to previous doses and then I discuss the calculation and result with the pharmacist before I proceed with the patient.”

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Answer

Some strategies are summarized below … but feel free to add your own!

  • Check to make sure you understand the problem.
  • Write down what you know—all the information you have, any techniques that might be helpful, and your ideas for tackling the problem.
  • Write down what you want to do or find.
  • Write down any questions you have.
  • Make a note of any ideas that occur to you, such as “I wonder if …” or “Maybe … might work …”
  • Break the problem down into smaller steps that you can tackle one at a time.
  • Have you seen something like this before? Could you use a similar approach?
  • Draw a diagram or use a physical model.
  • Can you solve a simpler problem first? For example, by temporarily replacing awkward numbers by smaller or simpler ones?
  • If it is an abstract problem, would looking at an example with numbers or a real context help?
  • Try out any ideas you’ve had and go through your work carefully writing down all your working—an arithmetic error or other mistake can stop you from moving ahead.
  • Always try to check your final answer for “reasonableness.” For instance, in the last example if your DIY cost was ten times the contractor’s estimate, you’d want to go back over your calculations.
  • Take a break, go for a walk, have a cup of coffee, or run some errands!
  • Discuss the problem with someone else—another student, a family member, or a friend.
  • Don’t panic, and try not to get too frustrated! It’s just math, after all.

4.3.10 Reviewing the Process

4.5 Self-Check