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Pólya’s Four Problem-Solving Steps

Step 1—Understand the problem.

  • Read the problem as stated, several times if necessary.
  • Be sure you understand the meaning of each term used.
  • Restate the problem in your own words. Discuss the problem with others if you can.
  • Identify clearly the information that you need to solve the problem.
  • Find the information you need from the given data.

Step 2—Develop a mathematical model of the problem.

  • Draw a picture to visualize the problem situation. It usually helps.
  • Introduce a variable to represent the quantity you seek. (In some cases there may be more than one.)
  • Use the statement of the problem to find an equation or inequality that relates the variables you seek to quantities that you know.

Step 3—Solve the mathematical model and support or confirm the solution.

  • Solve algebraically using traditional algebraic methods and support graphically or support numerically using a graphing utility.
  • Solve graphically or numerically using a graphing utility and confirm algebraically using traditional algebraic methods.
  • Solve graphically or numerically because there is no other way possible.

Step 4—Interpret the solution in the problem setting.

  • Translate your mathematical result into the problem setting and decide whether the result makes sense.