Teaching the "WHY" of the Pythagorean Theorem

Every year, there are two things I can reliably predict about my new batch of Geometry kids: (1) They know enough about transformations and (2) They know the Pythagorean Theorem. Now, let's expand on the second. They "know" the Pythagorean Theorem - well kinda. What they really know is that a^2+b^2=c^2. They have no idea where it came from, why it works, who Pythagoras is... none of the good stuff.

So, this year, instead of just reviewing how to plug and chug with the Pythagorean Theorem, I decided I want them to re-discover (and thus re-learn) the Pythagorean Theorem. I set out on a virtual journey to find the perfect Pythagorean Theorem activity - one that shows kids WHAT they are doing when they use the Pythagorean Theorem, not just HOW to do it. I searched high. I searched low. The #MTBoS came to the rescue, as usual. I had happened upon Dan Meyer's Pythagorean Theorem discovery activity during a google search, but Lisa Bejarano's blog posts about it (HERE and HERE) helped me to re-think how it might be successfully implemented in my classroom. Jacqueline (@_Cuddlefish_) also sent along some really awesome links, especially an informal proof of the Pythagorean Theorem based on Perigal's proof of the Pythagorean Theorem (HERE). 

I decided to re-work Dan Meyer's Pythagorean Theorem idea into an INB page that would provide a little more support for my students. It covers both the Pythagorean Theorem and its converse. Here is what I came up with:

Pythagorean Theorem and its Converse INB page (Click for Google Drive Download Link):

FRONT:

INSIDE:

I plan to still use the square blocks included in Dan Meyer's Pythagorean Theorem Discovery (HERE - Week 25), but I'm going to white out the area calculations and have students calculate those themselves.