I went shopping with my dad last weekend (we were home for a family event) and there were these new "100 calories" Coca Cola Slim packs and I grabbed out my phone and snapped some picture (Dad looked at me funny he is not used to this side of me yet). Anyway I walked down the aisle, and found the new Pepsi slim cans! But they were a different shape, but same price! Boo ya! Math lesson here I come. Anyway I bought those as fast as I can, and this weekend I went to town. I'll present this once more in Mr. Meyer's three acts since I appreciate the narrative...
Act 1 - Any Questions?
Act 2 - The Measurements
Act 3 - The Reveal
- Why do they say 100 calories? Is the pop actually healthier?
- In a pack of six how much more pop do you get with pepsi? Can of 12? Pack of n?
- What is the price per mL of Coke compared to Pepsi?
But where I really want to go is with my original thought. Have pop companies chosen the most environmentally friendly can? Can we maximize the the volume and surface area of both the can and the box? Do we have to sacrifice one for the other? Obviously you could do this in a calculus class by actually doing max min problems, but I figure with just a table of values I can have my grade eight students graph, and introduce them to a relative minimum surface area.
I don't know the answers to these questions either, that's what intrigues me. I feel like either the box could not match the can or vice versa, then we can get into a discussion about which is better for us to use more of cardboard, or aluminum?
Then throw in two litre bottles! Really I could just see this going on forever, what do you guys think? You are my veterans.
P.S. I do need to give a nod to some of my inspiration for this from the "Teaching Mathematics in the Middle School" article here is the reference.
Carmody, Heather Gramberg. Water Bottle Designs and Measures. Dec. 2010/Jan. 2011, 272–77