Also, reasonable for a rider, and for mathematical illustration is that the shifting the front is mostly to get you into the right range of gears, and shifting the rear is to fine tune your ride. However, I wonder if it might be a better way to teach ratios than gear inches specifically... (you could actually use either one, or possibly both, depending on your needs). You could even go as far as computing wheel circumference and ratios to calculate gear inches for specific tire and gearing selections.

For me, I spend most of my time in the middle chainring, and only use the large ring when riding at higher speed (down hill or with a good tail wind), and the small ring for significant climbs.

You could use this method to help demonstrate how to achieve different ratios/gearings, and the show that there may be more than one way to get a certain ratio/gear inch value. This could also be used to show the value of a Venn diagram.

You should check out Sheldon Brown's gear calculator for different things his calculator produces. This could show a few other ideas of things that are relevant to some riders, and could provide good ideas for math instruction.