[It Got Away] Red Rock Coffee

So here’s a feature: the WCYDWT lessons that got away from me. It’s important to me you know that for every WCYDWT lesson I spitshine and post on this blog there are dozens that never got off a list of ideas I keep and several more that got off the list and didn’t pan out. This is my eulogy for the latter group, but don’t mistake these posts as accidents of my curriculum development process. They are the process itself. If I don’t chase these paths all the way to their conclusions, I’m pretty sure I’ll stop seeing them altogether.

For instance, here’s a picture of the menu of my favorite coffee shop, Red Rock Coffee.

Here’s a reconstruction of the menu. (Click for higher resolution.) Notice the description of the last drink. “The most caffeine for your money.”

This is pretty great. You have a ton of data on the board: ounces and shots and price. Have your students write some ideas down about how best to measure “the most caffeine for your money.” Obviously dollars and shots need to figure in there somewhere, but you probably ought to divide the dollars by shots and then by ounces because one shot poured over twelve ounces of milk has a different effect than one shot poured over twenty ounces of milk.

Reagan : Russians :: Me : Coffee Shop Proprietors. “Trust but verify.”

And would you look at those lying liars? You get more shots for less cash poured over fewer ounces with a large Cafe Americano – not with the advertised Red Eye. “Math exposes corrupt marketing” is one my favorite angles on mathematical investigation.

It Got Away

Except my wife pointed out to me that the Red Eye isn’t a shot poured over water (like the Americano) or milk (like the latte). It’s poured over coffee. It’s caffeine poured over more caffeine. Which sunk my battleship.

Just watch your step, Red Rock Coffee.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. This unit still works.

    In fact, I’d be surprised if nobody asks what else is in the red eye while you’re doing your questioning thing. If nobody asks, continue on and be as less-helpful as possible.

    If math is supposed to teach you logical thinking and problem solving, I don’t see why this wouldn’t work – it’s still a whole lot more helpful than the stuff in the textbooks :)

    Does the fact that a shot = 2/3 oz add any complexity to the problem? I’m not a math teacher and it’s late in the day for me… haha.

  2. And I’m betting their menu is a misprint anyway. There’s probably 3 shots in a medium. Why have 2 in both S and M, then jump to 4 in a L? Just speaking as an avid coffee hound.

  3. I don’t get why you’d divide by ounces, anyway. Why does a shot of caffeine + 12 ounces of milk have a different effect than a shot of caffeine + 20 ounces of milk, if you drink the whole thing either way? The calculation you did doesn’t make sense to me.

    Then again, I don’t drink coffee, so what do I know about any of this? Nothing.

  4. With my geometry students, I compare the difference in price for 12″, 14″ and 16″ pizza to find the cost of pizza per square inch.

    For extra fun, compare th prices if you throw out the crust.

  5. I also think there is madness in your method, even before your wife’s comment. Forget your wife, let’s assume caffeine is only contained in the shots. You are skeptical of the claim that Red Eye has “the most caffeine for your money”. You should be able to assess that as is, without needing to transform the table.

    This is because each column in the original price table compares the 4 drinks by a common measure (column 1 is per 2 shots per 12 oz for all 4 drinks, column 2 is per 2 shorts per 16 oz, and column 3 is per 4 shots per 20 oz). So you can already conclude that Red Eye is not the cheapest so their claim is false.

    You should be able to see that the rank of drinks from cheapest to most expensive in all 3 columns is the same before and after you transform the table.

  6. This definitely still works, and the part that ‘got away’ seems to make the problem that much juicier.

    The follow up question now becomes: How strong does a Red Rock employee have to brew their coffee for their claim to be true? (or something to that nature)

    New questions to anticipate:

    What units should we solve this problem in?
    How many mg of caffeine in a shot of espresso?
    How many ounces in a shot of espresso?

    To quote a previous WCYDWT: You’re thinking. You’re Googling. You’re calculating.

  7. Thank you for sharing this part of your process. Nice to know (well, be told again), that every idea you have just doesn’t magically come forth as a complete WCYDWT.

  8. My mind went the same place as Amulya’s… I think that’s a nice question.

    I don’t like “price per shot per ounce” –it’s not claiming to be the most concentrated caffeine for you money, just the most caffeine for your money.

    (Surely they sell espresso shots, and surely those would win on Dan’s terms.)

  9. Forget the analysis of the cost per shot and all that. Take the class down on successive days and do some imbibing. How many servings of each does it take to get some real caffeine jitters going? This is something that can be quantified, results can be studied with 5 number summaries, scatter plots, whatever you like.
    It might be necessary to devise a “jitter scale.”
    I worked for a principal who had the strongest jitter juice I have ever encountered in my career, and she always offered coffee before a “sit down and discuss.” I’m embarrassed to recall how many sessions it took before I learned to decline the coffee.