George Polya’s Four Steps in Problem Solving

By: Taylor SchultzMATH 3911

George Polya

George Polya was a teacher and mathematician.

Lived from 1887-1985

Published a book in 1945: How To Solve It, explaining that people could learn to become better problem solvers.

Polya’s Four Steps

1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Look back.

The Problem To Solve

Find the square root of 1,444 without using a calculator.

√1,444

Understanding the Problem When first looking at a problem, you must first

read the problem carefully and see if you understand it.

Ask yourself, what do you know, and what do you want to figure out?

We know that: A number b is a square root of a number a if b2 = a.

In order to find a square root of a, you need a # that, when squared, equals a.

We want to figure out: What number squared would equal 1,444.

(b2 = 1,444)

Devising a Plan

For this second step, you need to develop a strategy for using what you know.

Consider how the problem relates to concepts you know or other problems you have solved.

You can solve this problem by using a guess-and-check (trial and error) approach, or by using an algebraic square root method.

Devising a Plan Continued..

So, how do we find the square root? IT’S EASY!

Just ask what times itself is the number in the root symbol?

Examples: √9 is 3 because 3 times 3 is 9 ( 3×3=9) √16 is 4 because 4 times 4 is 16

( 4×4=16) √49 is 7 because 7 times 7 is 49

(7×7=49)

Devising a Plan: Guessing and Checking

This strategy requires you to start by making a guess and then checking how far off your answer is.

Then, you revise your guess and try again!

So, we want to know what the b is in b2 = 1,444.

Plan: Find what b is to equal 1,444. (b×b=1,444)

Carrying Out the Plan

This is the step where you carry out the steps of your plan.

We have came up with the guessing and checking method, so let’s put it to use!

Carrying Out the Plan: Guessing and Checking Process

You could start by multiplying any of the two same numbers together.

Let’s try: 20×20, which equals 400. This answer is obviously way lower than 1,444, so I’ll revise

my guess and try again. This time I’ll try: 30×30, which equals 900.

This answer is still too low, but I am getting closer. This time I’ll try 34×34, which equals 1,156.

I am still not quite there, but I am getting closer. I have now started to narrow down my guesses, so

this time I’ll try 38×38, which equals 1,444! Through guessing and checking, I have now figured out

that b=38 (382=1,444)

Looking Back

Finally, in this last step you look back reviewing and checking your results.

Have you answered the original question? Yes, we have answered that the √1,444=38.

Is there a way to check your answer to see if it is reasonable? Yes, by multiplying 38×38 to equal 1,444. Also, if you have a calculator, you can plug in the

√1,444 giving you 38. You can use this knowledge to solve related

problems in the future.