Problem-Solving Strategies

(UPS-Check)

A student once asked her math teacher what was the best way to solve a particular problem. The teacher answered, “The way that works best for you.” Many strategies can be used to solve math problems. When you feel that there is only one or two, you severely limit your options and reduce the chances of finding the correct answer. Following are some helpful problem-solving strategies. We call this the UPS-Check.

When you have difficulties, change your point of view. Look at the problem from different angles.Make notes of your attempted solutions in the margin. This will help you to keep track of your steps.Periodically review what you’ve done. Above all, be patient and persistent.

Understand the Problem

  • Read the problem carefully, two, three, or as many times as it takes.
  • Decide what the question is asking. What do you need to find?
  • Find the important information. What do you know?
  • Eliminate any unnecessary information.
  • Supply any missing facts.

Plan How to Solve the Problem– What can I do to solve the problem?

  • Use trial and error (sometimes called guess and check).
  • Write an equation or use a formula.
  • Use estimation.
  • Use logical reasoning.
  • Design a table or chart to organize data.
  • Sketch or draw a picture or graph.
  • Make comparisons.
  • Use a Venn diagram.
  • Make an organized list.
  • Find a pattern.
  • Work backwards.
  • Act out the problem.
  • Solve a simpler problem. Substitute easier numbers. Replacing fractions with whole numbers often makes it easier to see which operation to use.

Solve the Problem and Show All of Your Work

  • Show how you carried out your plan by showing all of your work.
  • Be able to explain how you arrived at your solution.

Check Your Solution for Accuracy

  • Did you answer the question?
  • Make sure you used all the important information.
  • Check your calculations.
  • Does your answer make sense? (No one pays $2,500.00 for a parking ticket; move the decimal point and $25.00 becomes a logical answer.)
  • If the problem calls for an explanation, does your explanation make sense?
  • Does your answer meet all conditions set out in the problem?