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George Polya’s Four Steps in Problem Solving

By: Taylor Schultz MATH 3911. George Polya’s Four Steps in Problem Solving. 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.

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George Polya’s Four Steps in Problem Solving

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  1. By: Taylor Schultz MATH 3911 George Polya’s Four Steps in Problem Solving

  2. 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.

  3. Polya’s Four Steps • 1. Understand the problem. • 2. Devise a plan. • 3. Carry out the plan. • 4. Look back.

  4. The Problem To Solve • Find the square root of 1,444 without using a calculator. • √1,444

  5. 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)

  6. 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.

  7. 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)

  8. 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)

  9. 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!

  10. 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)

  11. 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.

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