There are lots of contributions by great Mathematicians in the field of science and technology that had changed the lives immensely. Among other mathematicians, George Polya was not a typical mathematician but he is known for his work ‘how to solve a mathematical problem’ amusingly. In 1945, he published the 4-steps for solving problems systematically which quickly become his most prized publication. Today in the 21st century, many research scholars are using his model to support their research publications.

George Polya identifies four basic principles of problem solving are listed below:

  • Step 1: Understand the problem
  • Step 2:  Devise a plan (translate)
  • Step 3:  Carry out the plan
  • Step 4: Look back

Example: 01 Six is added to four times a number, the result comes 50. What is the number?

Let’s apply Polya’s model in mathematical problem:

Step 1: Understand the problem

Make sure that you read the question carefully several times. Think questions, what is missing? What variable represent? Assign variable.

Since we are looking for a number, we suppose as

Let n = a number

Step 2:  Devise a plan (translate)

Since ‘n’ represents the number, four times the number would be 4n and 6 added to that result comes 50.

            6 + 4n = 50

Standard form

            4n + 6 = 50

Step 3:  Carry out the plan (solve it)

6 + 4n = 50

             4n = 44

             n = 11 Answer

n = 11 which is the required number

Step 4: Look back (check and interpret)

At last review the process and check the results

Put ‘11’ in standard equation

6 + 4(11)

= 6 + 44 = 50

50 = 50

It is now verified that problem is solved correctly.

Solving word problem

  • Word problems are thought to the toughest to solve but are not actually difficult
  • Word problem is half done if you understand the problem
  • Better vocabulary is beneficial to understand mathematical terminologies

Steps to solve a word problem

  • Read the problem carefully and figure out what it is asking you to find
  • Assign a variable to the quantity you are trying to find
  • Write down what the variable represents
  • Write an equation for the quantities given in the problem
  • Make in standard form
  • Solve the equation
  • Answer the question
  • Check/verify the solution

“My method to overcome a difficulty is to go round it” George Polya.  

3 Replies to “Polya’s 4-Step Problem-Solving Techniques”

  1. I do George Polya’s Problem-solving at school and I find some really hard and some ok so I came here for help and I know the 4 steps of Problem-Solving by heart.

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