# For Teachers: Pythagorean Project

My students just completed a project on The Pythagorean Theorem, and I wanted to show some awesome work they did.

This is the project I presented on at TMC 16, but since this was my audience at that talk…

LOVE YOU, TOM!!!

…I feel like the message could still stand to “get out there” a little more into the #MTBoS community 🙂

Here’s a copy of the instructions to the project, and here are screenshots in case you want to just click through and get an idea…

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The goals of this project are…

•  Give students a deeper understanding of the Pythagorean Theorem.  I want them to do more than just “plug in” and solve for missing side lengths.
• Expose students to new technology tools that can help them in their math career going beyond 7th grade.

So with that said, here are some screenshots of good work samples that my students did on this project.  I personally believe that this is really strong work for 7th grade students.

First GeoGebra…

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What I really liked about this Geogebra section was the reflection questions that I asked.  All of these answers show varying levels of understanding — there’s admittedly a little work to do here — but overall they saw the point of this activity and learned something valuable from it.  I’d argue that this is Step 1 to understanding some Dimensional Analysis, and that’s a pretty cool thing.  Check out those reflections here:

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Even cooler was this kid who decided to go nutso with the rectangles he was building in Geogebra.  But it “worked”:

I like it when a project offers the creativity for kids to go off on some wild hair like this.

Some Excel spreadsheets that generated Pythagorean Triples using either the Rule of Plato, Pythagoras, Euclid, Masères, or Fibonacci:

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I’m not a huge fan of Texas Instruments calculators, and my students would all prefer to use Desmos.  But if our school is still requiring them for testing purposes, I need to find ways of putting them to use.  A basic programming task challenges the kids well; together we wrote a program that found the hypotenuse when the user enters the legs.  Students had to write a second Pythagorean program (that tells the leg when hypotenuse/leg are entered), and some of them went not-so-basic with their third program:

How about that one on the right?  From the user inputting the hypotenuse of an isosceles right triangle, she programmed her calculator to find the area of said isosceles right triangle.  Pretty cool stuff.

Anyhow — I learn something every year I assign this project.  Not just about teaching but about the actual Pythagorean Theorem.  Maybe I should have understood it better from the get go, but I figure that at least speaks to the quality of the assignment and the tasks that these middle schoolers are completing.

Comments/critiques/questions/etc.?  Share ’em below!  Thanks for reading!