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 one is fabulous, as are all three of these, indeed. I was intrigued by them all.

    Dan, I especially like your insistence on making guesses, thus defining and hopefully refining a reasonable range for the solution set. I think too often we see estimation as a lower level skill and assume our upper level students have got it down. The Common Core gives it a place in the third grade!

    Nevertheless, the time spent on refining a guess and identifying a reasonable and relatively narrow range gives students valuable insight on identifying the correct focus and therefore directs the learning. How many students stare at us blankly as we try to explain how to choose an appropriate scale/ viewing window when graphing functions? Too many for me.

    Kudos to you. Depending upon where the act 2 discussions lead, I think you can add N-Q.3 and F-IF.5 to your list of standards.

  2. This one, with some modifications, will be a great introduction for my calculus class.

    How many hoses would be required to fill up the cup within two hours ?

    What would be the rate of change of the coffee level in function of the flow ?

    And if we change the cup for a giant Martini glass ?

    Or the spherical water tank of a city ?

    Thanks for the inspiration !

  3. Emily: I think too often we see estimation as a lower level skill and assume our upper level students have got it down.

    I think this is right. In the upper grades we keep estimation in the corner, but then once students have an incorrect answer on an applied problem, we pretend like estimation is our best friend. “Does that answer make sense?” we ask, making too little of an appeal to intuition too late.

    Because what’s the student going to say? If she answers “no, it makes no sense,” she has to re-do her work. There’s serious cost to that answer. Which is why we have to make that appeal to intuition as early as possible.

  4. @Debbie, Timon Piccini tweeted out a picture of the coffee cup, which I linked above. That got me searching for the source of the picture which led me to a bunch of a clips, which I then condensed and edited together.

    I spend a few minutes a day trolling around a few sites for interesting opportunities for math modeling but it’s great when guys like Timon act like an extra set of eyes.

  5. Interestingly, as we were doing this in class, a student on their laptop found articles (like http://today.msnbc.msn.com/id/40007591/ns/today-food/t/wake-smell-worlds-largest-coffee-gallons/#.Tsx8CFYfh6o) claiming the coffee cup was 8 by 8 (rather than the 7 by 7 Dan provided). The 7 by 7 gives the right gallons – perhaps the 8 by 8 was outside dimensions? Or they didn’t fill the cup all the way?

    On another note, the record has since been broken:

  6. It seems as if this record keeps going up…
    The largest cup of coffee contains 13,200 litres (2,903.6 UK gal; 3,487.1 US gal) and was created by De’Longhi (Italy), in London, UK, on 5 November 2012.

    Black coffee was used and the cup measured 2.9 m (9 ft 6 in) tall and 2.65 m (8 ft 8 in) wide.


    Unfortunately, it doesn’t seem as if the Guinness site has historical data to look at the progression of large coffee cups over time.