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May 2013

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How to help students with multiplication tables?

Pythagorean Theorem for elementary grades?

I was asked, 

In my opinion, if kids have not yet been taught the concept of square root, then there is no way you can explain BOTH 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 Pythagorean Theorem is studied soon after having studied square roots... as an application. Or, within geometry course. This happens usually in middle school, not in elementary grades.

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

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

If it is just elementary school kids, maybe one could just have them draw a bunch of right triangles (random). You could have them measure all the sides. Then take some of their measurements and show (without using the squaring symbol) that

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

is true for their example triangles they drew.

You would 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, and not exact. You could try draw a triangle with sides 3, 4, and 5 inches as accurately as possible and show the theorem for those numbers.

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

See also 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.

You can pose a problem on board where you have drawn a right triangle and put down some made up measurements for the two sides... what is the third side? My guess is kids will just tell you to simply measure it... why bother calculating if you can measure?

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

Say you have 20 feet and 6 feet as the two sides...
You can write

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

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