Problem Solving in Maths using Polya's Model

Polya’s model had been introduced to solve the problem solving. George Polya had identified four steps in the problem solving process:

• Understanding the problem
• Devising a plan
• Carrying out the plan
• Looking back

George Polya 

1. Understanding The Problem

First. you have to understand the problem. What is the unknown? What are the data? What is the condition?  Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory? To easily understanding the question, draw a figure and introduce suitable notation. After that, separate the various parts of the condition.

2. Devising A Plan

Second, find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution; have you seen it before? Or have you seen the same problem in a slightly different form?

After that, try to figure out the strategies related problem? Do the theorem that could be
useful? Try to think of a familiar problem having the same or a similar unknown.

Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible? Could you restate the problem? Could you restate it still differently? Go back to definitions.

3. Carrying Out The Plan

Third. Carry out your plan.  Carrying out your plan of the solution,  checkeach step. Can you see clearly that the step is correct? Can you prove that it is correct?

4. Looking Back

Fourth, examine the solution obtained. Can you check the result? Can you check the argument? Can you derive the solution differently? Can you see it at a glance? Can you use the result, or the method, for some other problem?

EXAMPLE:

QUESTION 1- Guess and check

Jago is a fisherman. If he catches three fish, he will get 2 coins. If he catches 5 fish, he will get 5 coins. Today, he has twenty one fishes on his boat. How much is his wages? 

Step 1: Understand the problem

Jago will get 2 coins for 3 fish.

Jago will get 5 coins for 5 fish.

Today he has 21 fishes.

Count on the wages that he will receive today.

Step 2: Devises a plan 

Solve the problem using Guess and Check.

Step 3: Carry out the plan

21 fish= 

1) 13 + 8

13 / 3 = cannot be solved , 8 / 3 = cannot be solved

2) 14 + 7

14 / 3 = cannot be solved , 7 / 3 = cannot be solved

3) 15 + 6

15 / 5 = 3 , 6 /3 =2 

So the total price of wages:

3 x $5 = $15 

2 x $2 = $4 

Step 4: Check the Answer 

$ 15 + $4= $19 

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