Polya's Four-Step Problem-Solving Process

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  • 0:32 Understanding the Problem
  • 1:47 Devise a Plan
  • 2:32 Carry out the Plan
  • 3:33 Look Back
  • 5:04 Example
  • 6:56 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.

Polya's 4-Step Process

George Polya was a mathematician in the 1940s. He devised a systematic process for solving problems that is now referred to by his name: the Polya 4-Step Problem-Solving Process.

In this lesson, we will discuss each step of the Polya process while working through the solution to a problem. At the end of the lesson, you will have the opportunity to try more examples before taking your quiz.

Understanding the Problem

So, to start, let's think about a party. Sally was having a party. She invited 20 women and 15 men. She made 1 dozen blue cupcakes and 3 dozen red cupcakes. At the end of the party there were only 5 cupcakes left. How many cupcakes were eaten?

The first step of Polya's Process is to Understand the Problem. Some ways to tell if you really understand what is being asked is to:

  • State the problem in your own words.
  • Pinpoint exactly what is being asked.
  • Identify the unknowns.
  • Figure out what the problem tells you is important.
  • Identify any information that is irrelevant to the problem.

In our example, we can understand the problem by realizing that we don't need the information about the gender of the guests or the color of the cupcakes - that is irrelevant. All we really need to know is that we are being asked, 'How many cupcakes are left of the total that were made?' So, we understand the problem.

Devise a Plan

Now that we understand the problem, we have to Devise a Plan to solve the problem. We could:

  • Look for a pattern.
  • Review similar problems.
  • Make a table, diagram or chart.
  • Write an equation.
  • Use guessing and checking.
  • Work backwards.
  • Identify a sub-goal.

In our example, we need a sub-goal of figuring out the actual total number of cupcakes made before we can determine how many were left over.

We could write an equation to show what is unknown and how to find the solution:
(1 dozen + 3 dozen) - 5 = number eaten

Carry Out the Plan

The third step in the process is the next logical step: Carry Out the Plan. When you carry out the plan, you should keep a record of your steps as you implement your strategy from step 2.

Our plan involved the sub-goal of finding out how many cupcakes were made total. After that, we needed to know how many were eaten if only 5 remained after the party. To find out, we wrote an equation that would resolve the sub-goal while working toward the main goal.

So, (1 dozen + 3 dozen) - 5 = number eaten. Obviously, we would need the prior knowledge that 1 dozen equals 12.

1 x 12 = 12, and 3 x 12 = 36, so what we really have is (12 + 36) - 5 = number eaten.

12 + 36 = 48 and 48 - 5 = 43

That means that the number of cupcakes eaten is 43.

Look Back

The final step in the process is very important, but many students skip it, feeling like they have an answer so they can move on now. The final step is to Look Back, which really means to check your work.

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