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How to teach elementary children about the Pythagorean Theorem

I was asked, 

I'm currently a student at MCC. I'm taking a course that is for Elementary Math Teachers. We are supposed to do a lesson plan so that we can teach elementary children how to use the Pythagorean theorem. I need to learn how to break down the Pythagorean theorem for an elementary child. I got stuck at the square rooting part.

In my opinion, if children have not yet been taught the concept of square root, then there is no way you can explain BOTH the Pythagorean theorem AND the concept of square root in one lesson. Besides, before learning about square roots, students need to know about squaring numbers (exponents).

Typically the Pythagorean theorem is studied soon after having studied square roots... as an application. Or, within a geometry course. This happens usually in middle school, not in elementary grades.

The only way I can see around this is if you don't even try to explain what square roots are just tell the students to get them from the calculator. That way you can concentrate on getting through the idea that

  • The Pythagorean theorem lets you find the third side of a right triangle if you already know the two sides.

If it's only elementary school children, you could ask them to draw a bunch of RIGHT triangles. Have them measure all the sides. Then take some of their measurements and show (without using the squaring symbol) that

(side 1) · (side 1) + (side 2) · (side 2) = (longest side) · (longest side)

is true for the example triangles they drew.

Have them measure their triangles in inches or centimeters, show some examples on board, and let them verify the relationship for their own triangles after that. Of course, with measuring errors you will only get close, not exact. Use also a triangle with sides 3, 4, and 5 inches and show the theorem for those numbers.

If they know about variables, then you can present the theorem with variables. If they know about squaring, use the proper symbol for that.

See the image below. In it, the sides of the right triangle are 3, 4, and 5. Squares are drawn on the sides. When you sum up the squares, you can notice that the squares on the legs equal the squares on the hypotenuse.

Pose a problem on board where you have a right triangle with some made-up measurements for the two sides. What is the third side? My guess is children will just tell you to measure it - why bother calculating if you can measure?

So then change the triangle in your picture to be, say, a part of roof and say you're planning to build the roof and need to know BEFORE it's built how long is the long side. You can't measure it yet since it hasn't been built.

Say you have 20 feet and 6 feet as the two sides. Write:

(longest side) · (longest side) = 20 · 20  +  6 · 6
(longest side) · (longest side) = 436

Then tell them to use a calculator to take the square root of 436.

Also, in one lesson you should only teach how to use the theorem to solve the LONGEST side (hypothenuse), and leave the other situations for later lessons or grades.

See also:

Web resources for the Pythagorean Theorem

Math Lessons menu