How to Find Pythagorean Triples for Kids
Explaining Pythagorean Triples requires that students have a basic knowledge of the Pythagorean Theorem. The Pythagorean Theorem pertains to right triangles, which have two shorter sides and a longer, slanting side called the hypotenuse. The Theorem helps find a side or the hypotenuse if two of the three pieces of information is known. The formula is a^2 + b^2 = c^2 where "a" and "b" are the shorter sides, "c" is the hypotenuse and "^2" represents squaring the numbers. Pythagorean Triples are sets of values that can be inserted into the Theorem to produce a whole number result.
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Instructions
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Write the Pythagorean Theorem on the board and draw a right triangle with the "a", "b" and "c" sides labeled as such. Write out the numbers "3", "4" and "5" and explain that this is the smallest Pythagorean Triple. Show the work: 3^2 + 4^2 = 5^2 or 9 + 16 = 25.
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Prove that multiplying this triple by any other number also results in a triple. Ask the class for a number between "1" and "5". Pretend for now that they selected "3": 3 * 3 = 9, 4 * 3 = 12 and 5 * 3 = 15. Set up the Theorem and use calculators to prove correct: 9^2 + 12^2 = 15^2 or 81 + 144 = 225.
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Explain that there are an infinite number of Pythagorean Triples but that multiplying a low level set is the easiest way to find other triples. Write the next two lowest sets on the board: "5, 12 and 13" and "7, 24 and 25".
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Tips & Warnings
A Pythagorean Triple will either be three even numbers or two even numbers with one odd number. That's because squaring an even makes an even, squaring an odd makes an odd, adding two evens creates an even and adding an even and odd makes an odd.
