[3ACTS] Finals Week

Which of these drinks has the strongest caffeine concentration? Can you rank them from strongest to weakest? I couldn’t. What information would you need to know to find out?

Two options here:

One, have students talk about the information they’d need and how they’d get it. (Two questions central to mathematical modeling.) Then just give them that information.

Two, have students talk about the information they’d need and how they’d get it. Give them the names of the drinks and have them research the information themselves.

I’m not too uptight about the difference. Option two has the students practicing their Google-fu. Option one costs less time.

Here are the goods. I’m pretty sure caffeine doesn’t work the way I illustrate it in the third act, so you may want to skip that clip.

I also included the cost of each drink in case you’d like to ask students to calculate the “bang per buck” ratio as a follow-up, a cool improper fraction that reads “milligrams per ounce per dollar.”

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. Regarding act three, wouldn’t the amount of caffeine be the measure for how much “awake time” you’d get, not the concentration? Same thing with the “bang per buck” measure, I would think the more interesting ratio would be milligrams per dollar.

  2. Hey Dan!

    I’m a student attending the University of South Alabama! I really like this mini-project, because it’s so relevant in this day and age! Even as a college student, I’m curious. In addition, it seems like a very dynamic project with endless variations (ie you could do just soft drinks or go a healthier route with tea). So many variables, so little time, right?

    Love the posts, and I hope to read more from you!


  3. Love the 3acts, Dan. Compared to traditional pedagogy, I see them as the difference between following a carefully laid trail of breadcrumbs vs. exploring a mysterious forest.

    This latest 3act reminded me of an NCTM article on the metabolic decay of caffeine and alcohol. It was titled “How Long Does It Take a Person to Sober Up?” by Winston & Zunker. Might make a good extension problem for some high school students.

    One last note: I recall a problem-based assessment about exponential decay where a hypothetical student was taking Adderall to cram for the SAT but had a drug test for an athletic team the following week. The problem was to determine whether the drug’s concentration would be below detectable thresholds in time.