3 Acts - Viva Las Colas! - Embrace the Drawing Board

3 Acts - Viva Las Colas!

11/19/2011

So apparently I really like pop as you can see here and here. Before we begin I feel I have to let you know my teeth are not rotting, and I do not have a coke addiction, okay clear? So here's what you came for

Act 1 - The Really Big Bottle!

This is the Coca Cola store in Las Vegas Nevada, and when we went in for a drink, we were pleased to read the trivia on our drink tray. This is what we found.

Score!

Act 2 - Measurements

The trivia tray also had some vital information for our cause, here it is. I was trying to figure out the best way to edit these images. I would like to here some critique of my design, to try to find out what looks best, but this is my attempt.

The way I saw solving this was to map some function to the coke bottle, and use our lovely calculus to find the volume by rotating, so I developed a bare bones Geogebra app with sliders and the picture to find a sinusoidal function that would work (an assumption I made, too much for students?). I wonder if this should be an Act 2 artifact or if students should come up with this themselves.

coke.ggb
File Size:	1526 kb
File Type:	ggb

Download File

Act 3 - Reveal

As I am sure you have seen these sorts of answer reveals on trivia trays, they have the answer flipped upside down, and once again, I am not sure of the best way to present this reveal. So here are my two copies of the reveal.

Possible Solutions

As I already stated I used rotation to find the volume, then I had to convert to ounces, and then divide by 8. With GGB I found these equations and these points.

And I allowed wolfram to do the rest

solution_-_coca_cola.pdf
File Size:	244 kb
File Type:	pdf

Download File

In wolfram it converts it to "ounces" but the final answer is really number of 8 ounce coke bottles, and with a number greater than 6 million, I think I can say that we need to have a talk with the math coordinator at Coca Cola Las Vegas. (Assuming I used my math right, could you guys check that for me?)

Sequels

I can think of only a few...

Create a scale picture on GGB (using either a cylinder, or a sphere from the front, or a bottle) to show the true size of 8,000,000 ounces.
If we could fill this coke bottle with 8,000,000 ounces, how full would the bottle be? Did the "math coordinator" account for coke bottles having air?
How much would it cost to fill a coke bottle this large? How much would it cost a consumer to buy that much Coca-Cola?

And without further ado the complete package zip file.

2 Comments

John Berray link

11/20/2011 04:09:27 pm

Hi Timon,
Good job on the Coke post. I too get roughly 6.1 million fluid ounces, using calculus, which is clearly different than Coke's published 8 million ounces. Maybe their number includes filling it to the brim, which would yield more ounces?
Some thoughts on...
ACT 1: unless students are steered into the placemat question, they might also wonder the scale ratio of the big bottle to an actual bottle. The Paris Hotel Eiffel Tower just down the street could dovetail here.

ACT 2: Depending on the level of student, having them create the equations would not be out of reach, but I think even calculus students could see your two equations and still find everything but the answer. I liked playing with the GeoGebra and would rather you give me details as I need them. That will roll out differently in every class I'm sure.
Geometry students could come up with a ball park guess by finding the volume of cylinders they know are too big and too small. Then they could discuss which cylinders would give the closest approximation.

ACT 3: You definitely need to see the bottle filled with Coca Cola. Short of that, the answer on the placemat is okay, but only as an inflammatory piece of info that will outrage the students (assuming our answer is correct). Challenge Coca Cola. Get Coke to respond to your math. Having a verbal or written response from the Coke rep that addresses the difference between your answer and Coke's would be powerful and might have students searching to verify other companies' claims. Students love to prove adults wrong.
SEQUEL: What would the dimensions be of a Coca Cola can that would hold the same volume? (another possibility)

Looking forward to others' comments as well. I'm a 3 Act novice.

Timon Piccini link

11/20/2011 04:32:42 pm

Thanks Jon. I am nowhere near the point that I can spend time to change it (I teach grade eight, this was more I had to do it because I love the math). I like your ideas.

I was thinking along the same lines, how did Coke get it so wrong? I am curious about your answer, because I got 6,000,000 8 ounce cans, meaning it was a gross underestimation of the actual volume. Did you just get mixed up or did one of us go wrong?

I think for me the hook has to be "Can Coca-Cola actually do math?" since we will never get to fill that bottle.

I like your cylinders idea, and I am now wondering if maybe I could talk to my grade eights about this. Have them create a cyldiner that is just to big, and a cyldiner that is just to small. Find the average.