Here's a chart I made for a math lesson I taught on gear ratios:

Gear Ratios

The gears are off of my beater Bridgestone X0-4.

After the class learned about how the bike gears worked, I used a blank version of this chart and had the students find the values. The resulting epiphany was something to behold! Plus, I got to teach about bikes!

In fact, it was the work I did on this lesson that led me to buy a new bike, buy a bunch of tools and build my wife a bike. I just got back from my lunch break riding around town looking in thrift stores for fixies! This information is what also convinced me that front derailleurs/multiple chainrings are overrated. My next bike, after a fioxed gear, will be a REAL 10 speed!