[3ACTS] March Tasks

I designed two tasks this month:

Some process notes:

  1. It’s a lot to ask someone to click those links and look at a lesson plan. The reader has to decipher the structure of the plan and decode its particular jargon. (ie. “What language does the author use to indicate the point of the task and where on the page can I find it?”) All of that may be necessary at some point in the plan but I’m trying to do my material a favor by isolating what about it is a) most perplexing, b) most visual, c) least verbal, and opening with that. If twenty seconds of video make you curious how many yellow Starbursts are in that huge pile of candy, you’ll be more inclined to wade through my structure and jargon than if I opened with that structure and jargon.
  2. Math tasks imitate life. I imagine math teachers overestimate how often they practically use math in their daily life. It’s easy to say that “math is everywhere,” because it’s true, but most of that math is performed by computer chips that are embedded in everything from your car to your toaster. So whenever you find yourself wielding math like a saber to cut through one of life’s hassles, pull out a camera and capture that moment. Pose the problem to your students as you experienced it.
  3. More where those came from. I’m slowly building up a spreadsheet that lists all these tasks. Something more organized and visually appealing is somewhere in the works, but this will have to do for now.
  4. Behind the scenes. I can’t imagine who’d be interested in the notes I wrote up as I designed these tasks but here are PDFs for Starbursts and Chocolate Milk, for Future Dan if nobody else.
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. I also loved Nana’s Chocolate Milk, but was a little disappointed in the sequel’s Act 3. I liked the Act 1 because it was a more challenging question, but only if you can’t double, just like 2 cups of milk won’t fit in the class for the milk problem. However, your video of how you fixed it is a simpler solution, and I thought the sequel should be more challenging. Going for a 3-egg solution would do that. Or how you wrote it up in the notes, using flour AND milk in the eggs, and getting both wrong. I think that’s a GREAT sequel.

  2. Great additions. Though you say you don’t think it is worthwhile seeing your notes, I did enjoy taking a look at those. I constantly struggle with time management, both in and out of the classroom. In the classroom I wonder if the cost of setting up is worth the learning taking place, as you have mentioned in earlier posts. Outside the classroom, I struggle with the time to setup lessons as my other life tugs at my time, pulling me off the computer, out of the classroom. Which is why I find myself relying more and more on your 3acts and your curriculum. Thanks so much!! (But I do wonder about how long it takes you to put together these packages)

  3. a different eric

    March 7, 2012 - 4:15 pm -

    I’ve already done Nana’s milk with my kids… did it yesterday. Had some great discussions about why THEIR fixes weren’t the same as yours. The kids thought it was hilarious when you said Nana would kill you. I got a little jealous… We also couldn’t imagine why anyone would put flour in their eggs!?

    The thing I find amazing about some of these is that I’m always surprised at the disconnect between what I thought 8th graders knew how to do… and what they actually CAN do (and I’ve been doing this for 7 years).

    For instance, I thought the Bolt speed problem would be a quick and easy conversion warmup. Nope.
    I was blown away when I found out through the Stueben Bridge problem, that a lot of my kids didn’t understand the idea that sound travels!

  4. @a different eric, thanks for keeping me looped in on the classroom testing. Always appreciated.

    @James Cleveland, good criticism. All of those are fair points.


    But I do wonder about how long it takes you to put together these packages

    If I were in the classroom full-time, my output would be a lot lower. I can’t bring myself to put any guilt on people who don’t want to or can’t put in the same time when my time is paid for by Pearson.

  5. Good stuff, as ever.

    You can carry the same experiment into some of the high school standards on probability and statistics, comparing the experimental probabilities to theoretical probabilities. The number of yellow-yellows seemed ridiculously high to me at first, but is actually within 2 standard deviations of the mean (assuming all colors are 1/4 likely and are paired randomly).

    I’d actually be interested in seeing someone else do this and what their results are, because some of the pairs listed actually are very high or low — in particular there were more yellow-yellows than yellow-pinks, when you would expect there to be twice as many yellow-pinks.

    From a publishing standpoint, have you thought about the issues around using branded products? Personally I have no problem with it, but publicly it draws negative attention. For example:


    In particular: “the San Francisco Unified School District will buy no curriculum materials that contain identifiable brand names in the content of the curriculum”.

    Inspired by a sixth-grade math book, the entire state of California banned textbooks that used brand names in 1999:


    In that case, just like here, the brand names used weren’t being paid as advertisers, but that didn’t stop people from thinking their kids were being targeted. Perhaps you or Pearson are already taking care of this in some other way, but it’s an issue in the publishing world.

  6. It’s so hard to make math real without using real world examples. It’s easy enough to not show the brand of chocolate milk mix being used with Nana’s Chocolate Milk. What makes the Yellow Starburst (and other problems like it) interesting is that students connect to it because they don’t like a particular flavor of a particular type of candy. It wouldn’t be nearly as effective without the brand connection. I understand not wanting to commercialize school, but there is little/no student buy-in with generic math problems!

    Thanks for sharing these (and everything else!) I was lucky enough to get to see you present in Baltimore in October, and I love the three acts as building blocks for a lesson.

    The spreadsheet is a great idea (we need a pinterest for math teachers to make it “more appealing”…lol). Since you’ve been writing them on the tasks, it might be helpful to have the common core connections on the spreadsheet too?

  7. Bowen:

    From a publishing standpoint, have you thought about the issues around using branded products? Personally I have no problem with it, but publicly it draws negative attention.

    Like you, I don’t give it a lot of thought. It wouldn’t surprise me to see that Starbursts task cut. To clarify my arrangement with Pearson Foundation, the tasks I make are rarely commissioned and they’re never promised a spot in the product. I get a monthly retainer and I get to make tasks that interest me and give them away. PF gets to sell them.

  8. That’s too bad. I really like the Starburst task, and hope it gets through. Maybe they will modify it somehow. Like Nicole said, the brand attachment adds something to the task instead of being a distractor. The tendency in publishing is to be overly safe about these things: someone might be upset at your reference to candy in general, beyond the Starburst. It’s silly.

    The real question is why are yellow Starbursts so terrible? You’d think they would do something about that after all these years.

  9. I just read this last night and couldn’t help but think of you and your work:

    “Nussbaum and Novick suggest a three part instructional sequence designed to encourage students to make desired conceptual changes. They propose the use of an exposing event, which encourages students to use and explore their own conceptions in an effort to understand the event. This is followed by a discrepant event, which serves as an anomaly and produces cognitive conflict. It is hoped that this will lead the students to a state of dissatisfaction with current conceptions. A period of resolution follows, in which the alternative conceptions are made plausible and intelligible to students, and in which students are encouraged to make the desired conceptual shift.” (Romberg, from Schoenfeld’s “Mathematical Thinking and Problem Solving)

    Not sure if you based your work around a similar learning theory but I thought I’d share it.

  10. I’m afraid I was a bit distracted in the Sunbursts (“Opal Fruits” anyone?) clip by the amount of packaging!

  11. Dan – would you consider adding the Common Core content code to your spreadsheet? It would be great, since you’ve already done the alignment, to have a quick overview of which content standards are addressed for each 3 ACTS.

  12. I worked through Falling Rocks and Sugar Packets today with some secondary math coaches as their first introduction to 3-Act Math and they are hooked and already trying to think of scenarios that they could use to create some of their own.

    After looking at the spreadsheet we also thought that adding the CCSS correlations to the spreadsheet would be a huge help for teachers who are looking for the right hook for a lesson or unit.

    I am introducing this to elementary folks on Friday, so I may have some more feedback after that.

  13. I love your blog and ideas! I noticed that you added common core standards addressed when you click on the tasks. Any thoughts on adding a column to the spreadsheet noting CC standards addressed?

  14. My elementary folks loved these even more than my secondary teachers did. However, they were sad that there weren’t very many at an elementary level. Do you know of anyone working on elementary 3-Act Math scenarios?

  15. Matt Taylor-Byrne

    February 26, 2013 - 4:10 am -

    I was really interested to read your notes on this task. I was looking for a scenario on probability and expected to see a tree diagram exploring the sample space. I then sat down and did my own and got outcomes of 115 pkts and 22 pkts for 1 and 2 yellows respectively. I’m now trying to get my head around how your functions work! Very interesting.