I must have cylinders on the brain. Maybe because they’re actually one of the few traditional geometric shapes that we actually interact with on a regular basis? Maybe it’s because they’re readily measured?

Anyway, here have a Coke can and one of those mini-Coke cans. Though it’s dependent on you exactly what information you’d like to black out.

You could black out one of the calorie counts and compare it to the fluid ounces.

You could black out one of the fluid ounces counts and compare it to the calorie counts.

You could eliminate the fluid ounces and one of the calorie counts to get at a really nice volume comparison (though, you’ll need additional dimensions – that’s good! Ask the kiddos what other dimensions you’ll need to procure?).

While you’ll need other dimensions, I would actually withhold the dimensions of the base at the beginning. Why? Because students of all ages have a real tough time with scale factor and volume. Like, REAL tough. As in, I tell them straight up “when you increase the dimensions by a factor, the volume increases by that factor cubed” and then they totally forget that by the time I’m done saying it out loud.

So let students solve it using a simple proportion.

4/5=90/x –> x=112.5 calories

Then when you reveal the actual calorie count, we’re all like “wha?”

“Wha???!!”

“WHAAAAAA??!?!??!! Math is wrong! You lied to us!” Or maybe they’ll claim corporate conspiracies to get us all fat. Either way: win-win.

This is the part when you swoop in with some additional dimensions to save the day. Find the volume relations of the two cylinders, the calorie counts, and you’re home free.

********

I also feel like there’s some way we can leverage this into some additional follow-ups/extensions:

I like having calorie counts as the final measuring stick for this task instead of volume.

Like I said, scale factor and volume (and area) were something my students would consistently get wrong. I think it’s indicative of the problem with front-loading instruction. Students don’t need to think deeply about the content because I’ve showed them how to do it in the “Scale Factor Unit” when it’s applicable, of course. Then, three months later, when we’re not in that unit any more, it’s out the window.

I’d suggest you read Frank’s post and watch the embedded Veritasium (@veritasium) video for more on allowing students to swim in their misconceptions a bit to enhance learning in the end.

I am actually trying to take the same video and turning it into something with solving equations. Like your ideas though.