Following Up Pythagoras (It Went Great!)

I started off my geometry classes' reintroduction to the Pythagorean Theorem with a simple bell ringer. It was a 3-4-5 triangle, with a missing hypotenuse. With some figuring, they remembered the Pythagorean Theorem and applied it. A student said "The answer is 5." I agreed and asked why. Why was it 5? The response I received was that a^2+b^2=c^2. Yep. That's true - when you have a right triangle. Why does a^2+b^2=c^2? My students decided they didn't know.

So, we proved it. ( I didn't call it that because my kids hate proofs.) I used this awesome 3-4-5 template from Jennie at mathfoldables.blogspot.com (HERE). I didn't use the two layers like she recommends. One worked just fine. We discussed the right triangle formed in the center, its side lengths, finding the area of the squares, and how this all relates to the Pythagorean Theorem. Students really understood and were able to draw connections between what they had colored (see picture below) and the concept behind the Pythagorean Theorem.

It turns out that this introductory coloring activity was a great transition to the Converse of the Pythagorean discovery activity. I modeled completing the INB page for a 3-4-5 triangle. We also completed a 5-7-9 triangle as an example. From there, students were instructed to use any of their squares to form additional triangles and complete the form. This was a great way to spiral in the Triangle Inequality Theorem we'd just learned in the last chapter. Students would ask if x, y, and z would work, and I'd ask them... how could we figure this out? They use those skills and really started to see patterns in their Pythagorean Theorem inequalities and the triangle types.

Tomorrow we'll finish up our tables and discuss takeaways. This was a great activity, and after a tiny bit of productive struggle, the students caught on well.