I always think it would be instructive and so entertaining to have my students “discover” the Pythagorean Theorem rather than tell them about it. But I am always caught between a pacing schedule and a benchmark, and end up pushing ahead. This year, I took some baby steps towards a more proof-oriented, discovery based approach.

How I taught it:

- Introduced the concept by drawing a 5, 12, 13 right triangle, and then drawing the squares off of each side. The students determined the area of each square: 25, 144, 169. Then we did a 6, 8, 10 right triangle, and did the same thing. I asked the class if they noticed anything interesting about how those areas relate to each other. The students figured out the connection. I then moved to explain that this is the Pythagorean Theorem and it works for all right triangles in the world. Now I revealed the formulas :

** a² + b² = c**^{² } and ** leg² + leg² = hypotenuse² ^{
}**

^{
}

- Next was my Pythagorean Theorem Rap:

Today we’re goin’ wrangle a right triangle,

we’re goin’ seal its fate if we concentrate,

we’re goin’ calculate the side lengths of a right triangle.

We’re going to let loose the hypotenuse,

we’re going to use a tool called Pythagorean’s rule.

It’s fair to share, so prepare to blare:

** leg² + leg ²** equals

**hypotenuse**

**²**** leg ² + leg²** equals

**hypotenuse**

**²**** leg ² + leg**

**²**equals

**hypotenuse**

**²**Now that’s the cool Pythagorean rule!

- Next we apply the theorem to problems, emphasizing how to document your work. I created this little worksheet to get the labeling of the triangles down which I stress is the most important step. Pythagorean graphic organizer.

- This year I also offered extra credit if they created a poster, video, or powerpoint on a Pythagorean Theorem proof. I showed them a couple of examples:

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Here’s pictures of a couple of the many posters turned in by students. Some creative work!