# Pythagorean Theorem

I’ve taught the Pythagorean theorem to three different classes this year: geometry, algebra and 8th grade. It keeps getting better as I discover more resources.

Here’s how I structured the unit for Algebra 1:

1. We started with this MTBOS-improved activity discovering the Pythagorean theorem followed by a class discussion and notes about useful vocabulary: legs, hypotenuse. (Note: it’s super important that the squares are cut out exactly, otherwise some combinations (like 7-8-10) look like right triangles….I found this out the hard way.)
2. The next lesson started with direct-instruction showing students how to use the Pythagorean theorem to solve for the legs and hypotenuse. (I can’t stress the usefulness of getting students to label all of the sides with a, b, and c straight away….this forces students to pay attention to which side is the hypotenuse.) Students completed a set of varied practice problems. We ended class by discussing how we could use the Pythagorean theorem to see if a triangle was a right triangle.
3. Then students used the Pythagorean theorem to solve word problems.
4. Students completed: Andrew Stadel’s Square Dance on desmos. And we discussed/took notes on rational and irrational numbers. (Next time: Want to find a way for students to understand WHY the square root of a number such as 5 must continue infinitely.)
5. Students learned how to simplify radicals and applied this to the Pythagorean theorem.
6. Next up: Using the Pythagorean theorem on a coordinate plane
7. And MORE applications.

A growing list of  Pythagorean theorem resources:

“Patterns in Prague” – A MARS performance task that incorporates area, perimeter, and the Pythagorean theorem.

“Glasses” – Another MARS task that is mainly about volume problems (cones, spheres, cylinders and compound shapes) BUT requires the use of the Pythagorean theorem to find the height of the cone.

Pythagorean Theorem Triangle Pile Up – A take on the Trig Pile Up. We started in in class (5 minutes alone followed by a pair share) so that everyone understood the approach and students finished it for HW.

Taco Cart – Dan Meyer’s 3 ACT problem

TED ED VIDEO: Proofs of the Pythagorean theorem – Maybe use this to launch a geometry project?  (Also to discuss “How can we PROVE something is true?”)

Lastly, one of my favorites from The Mathematics Assessment Project. It’s somewhat open-ended and requires creativity and persistence:

Exploring patterns in Pythagorean Triples