Show the students this image and ask them what questions they have… I am anticipating answers along the lines of: How much is in each one? Does it go up by the same amount? Is the XL worth the price compared to the small?

Key talking point – I think its really important to dig into the “Does it go up by the same amount” question if it comes up. Do you mean height? Does that matter? Do you mean volume? Are these Cylinders? How do we get around the fact that they’re not??? Also, what is measurable…can we measure the volume? What about the radius? What measurements would be more accurate?

By the end of this all, I hope to get to solving the following problem:

“I love my coffee, and an XL just doesn’t cut it by December. I’d like to have you design a XXL coffee for me.”

Act 2 – The information

Ask the students what information they would like in order to solve the problem. You can provide as much or as little information as you’d like, and you could have them calculate or estimate the rest. This is all of the info I collected. The images are available in the link provided at the start.

Width of the TOP

Width of the BOTTOM

Heights

Prices

Volumes

I think I wouldn’t give the volume measurements. I’d like them to find the volumes, and maybe I’d release this to check their answers.

Act 3 – So what does this look like?

Here, I’d like to see presentations of each group’s product, with mathematical reasoning as to which one is the best. As a group, I’d like to come up with the criteria for what the best one will look like, and then we can decide on the winner.

Some of the mathematical discussion I anticipate will be around variables, so for example if two groups look at cost in these ways:

So which one is better? The top graph compares the size to the cost (S=1, M=2 etc), and the bottom one compares the actual volume to cost. Which one will we use? Do we want to be mathematically fair, or make more money?

So that’s the plan. Let me know how it works, or what you think of it. Cheers.

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