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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.

Typically, the Pythagorean theorem is studied right after square roots or in a geometry course. This happens usually in middle school, not in elementary grades.

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).

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

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

Lesson plan

  1. Ask each student to draw a RIGHT triangle on paper. Students need to use a tool (such as a triangular ruler or a corner of some object) such as to make sure their triangles have a right angle. Ask them to measure all the sides in each triangle.
  2. 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 some of the triangles they drew.

    If they know about variables, then you can present the theorem using variables. If they know about squaring, use the proper symbol for that.
  3. Ask the students to verify this relationship for their own triangles. Of course, since measuring by nature is always somewhat inexact, they will only get close to getting a true equation.
  4. Don't forget to show the students the spcial triangle with sides 3, 4, and 5 units:

    In the image, the sides of the right triangle are 3, 4, and 5 units long. The sides have been "squared". When you add up all the little squares on the two legs, you can see that the sum of the squares on the legs equals the total number of squares drawn on the hypotenuse.
  5. Next, you could show the students a right triangle with some made-up measurements for the two sides. How long is the third side? My guess is students will tell you to simply measure it - why bother calculating if you can measure?

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

    Let's say the two legs are 20 feet and 6 feet. We get:
    (longest side) · (longest side) = 20 · 20  +  6 · 6
    (longest side) · (longest side) = 436

    Ask them to use a calculator to take the square root of 436 — and they have found the length of the longest side of the triangle in feet.

This may not be a very elegant lesson, but like I mentioned, I feel the Pythagorean Theorem shouldn't even be taught in elementary grades. It is going to be somewhat difficult to do so. Also keep in mind, you might want to only teach how to use the theorem to solve the hypothenuse of a right triangle, and leave the other situations for later grades.

See also:

Web resources for the Pythagorean Theorem

Math Lessons menu