The Wheel of Theodorus

In this week's #msmathchat the topic of irrational numbers came up. I talked about an assignment that I used to give my grade 8 students called the Wheel of Theodorous. I adapted this from an assignment that Leslie Lewis wrote about in an article in the April 2007 Mathematics Teaching in the Middle School.

This project highlighted the connection between math and art and gave my students a chance to blow me away with their creativity. Julie Reulbach encouraged me to blog about this assignment, so here goes.

This assignment was introduced to my students after they had been doing some work exploring irrational numbers and square roots. It was also a great way to review and practice the Pythagorean Theorem. The assignment outline can be found here: https://www.dropbox.com/s/fty0rgxmqccfsa9/The%20Wheel%20of%20Theodorus.doc.

Essentially, all students started with a right angle triangle that had legs that were each 1 unit (most used cm). They then had to show how to find the measurement of the hypotenuse. In this case it was sqrt 2. This then became the base for the next triangle and they made a rotation of 90 degrees and made the adjacent leg 1 unit. Once again, they had to find the measurement of the hypotenuse. In this case it was sqrt 3. When repeated again, the next hypoteuse was sqrt 4, which they had to write as 2. This allowed them to see the difference between perfect squares and non perfect squares and reinforced which numbers were irrational and which numbers were rational. They kept repeating this process, labelling all sides. They ended up creating a sprial, or the Wheel of Theodorus. They then had to make this into some sort of creative art work. Here is a link to more specific instructions in case that didn't make sense. I had the students hand in this worksheet along with their completed piece of art work: https://www.dropbox.com/s/9smr0e3gsmb986b/Wheel%20of%20Theodorus%20Work%20Sheet.doc?m

Here are some pictures of my students' work. I was blown away by their creativity.