My co-worker Regina and I took a stab at our first three-act math lesson. Well, we took a stab at writing a lesson to provide some motivation for learning about measuring liquid volume, and it sort of morphed into a three-act lesson along the way. However we got there, it was fun to write, and the teachers we shared it with at a PD session in March really enjoyed it. Here’s hoping I get the chance to develop another three-act lesson sooner rather than later!

Writing this lesson came hot on the heels of spending a day with Dan Meyer at the recent Texas Association of Supervisors of Mathematics meeting. He offered some advice for designing engaging learning experiences that I couldn’t wait to try out:

- Start a fight
- Turn the math dial down
- Create a headache

If you’re intrigued by his advice – and I hope you are – I recommend checking out his recent talk at NCTM. You’re only going to get about 45 minutes with his ideas about engagement instead of the 6 or so hours I got, but I guarantee it is still time well spent.

# A Gallon of Ice

## Standards

- Texas: 3.7D and 3.7E
- CCSS: 3.MD.2

## Act 1

Watch the video.

- What do you notice? What do you wonder?
- How long do you think it will take for all of the ice to melt? Estimate – Write an estimate that is too low, an estimate that is too high, and your just right estimate.
- How much water will be in the jug after all the ice melts?

I recommend bringing in an empty milk jug so students can draw small mark and their initials on the side of the jug to show their estimate. **Start a fight!** The students will want to know if their answer is correct. I did this with teachers during a PD session, and they had quite a range of answers. At this point, **the math dial is turned down low**, so we did not talk about units of measurement, just an estimate of how high the water will fill the jug once the ice is melted.

## Act 2

Watch the video.

- How long did it take the ice to melt? (Sadly, it finished melting while I was sleeping, so the most precise answer we can give is longer than 11 hours but less than 20 hours, since I checked the jug again at 7:00am.)
- Whose estimate was closest to the actual height of the water in the jug? (Resolve the controversy!)
- How much water is in the jug? Estimate – Write an estimate that is too low, an estimate that is too high, and your just right estimate.

This is where you start to **slowly turn up the math dial**. Question 3 is a great question to find out what your students already know about units of volume. They might very well be stumped depending on their prior experiences. You might have them imagine other packages and containers that have liquids in them and think if there are any words they know that describe how much liquid is inside. It’s totally fine for the estimates to be sort of weak here.

The whole purpose of this question is to **create a bit of a headache** – get the class to a point where you (or your students!) can say, “I think we need to know a bit more about measuring liquids so we can come up with estimates we’ll feel confident about,” and then take a break from this three-act lesson to do some explorations of measuring liquid volume. After doing that, which might take a day or two, show the Act 2 video again and then give the students a chance to add on or revise their estimates.

Here are some estimates made by 3rd grade teachers at our PD session:

I can tell the teachers were hooked when they reacted in shock when they found out I wasn’t going to reveal the answer right away. Just like with students, we took a detour away from this lesson. We wanted to spend a bit of time sharing ideas for how students can explore measurements of liquid volume. But they wanted to know the answer! One of them was really worried and wanted to make sure we would tell them before they left the PD session.

I couldn’t have been happier.

## Act 3

All is revealed! Now that your students have some personal experiences with measuring liquids using various units and you’ve given them a chance to add on or revise their estimates, it’s time to find out the actual volume!

And of course I spilled some water! When I was first filling the jug, I had to cut a flap in the top to make the opening wider for ice cubes to fit. Unfortunately, I forgot about it when I was doing my first pour and water did not come out like I was expecting. Thankfully it was only a small amount.

There’s so much going on in this video! You’ve got quarts, and half gallons, and cups, and fractions of cups. All great stuff to talk about! But I purposefully tallied the number of cups throughout the video so that students could at least come up with 8 2/3 cups. However, this is a great opportunity to talk about how we can read measurements differently depending on our units. For example:

- 8 2/3 cups
- 1/2 gallon and 2/3 cup
- 69 1/2 ounces
- 2 quarts and 2/3 cup

This is different from making conversions; it’s more about the choices available when reading a measurement off a tool. You don’t have to go here, but I think it is important for students to know that they do have choices in how they read a measurement given the options provided by the tool. Learning that flexibility here is only going to help them when they start encountering questions related to measurement conversions down the road.

And that’s a wrap! If you try out this lesson in your own classroom, I’d love to hear about it in the comments.

Danielle OehlerI will have to try this one out!

bstockusPost authorPlease do! Let me know how it goes.

Dan MeyerThanks for the reflections here, Brian. I’m really curious how we can make this problem and others like it more accessible for other teachers. 101questions was my best stab – a place for sharing that tries to find a balance between freedom and constraint. There’s so much richness in your narrative that’s hard to capture anywhere else, though.

bstockusPost authorYou raise a good point. Having 3 Acts (and other similar resources) scattered to the wind on the internet is not particularly user friendly to teachers seeking out lessons. To be honest, I didn’t even think about submitting to 101questions, even though I know it exists. There’s a lot of energy spent in sharing what’s out there, but I don’t feel like there’s as much put toward getting folks to contribute to resources/sites that already exist. Which leaves me using the path of least resistance – posting on my blog. Or maybe I’m wrong and lots of people encourage folks to contribute and I’ve just had blinders on and not noticed, which could very well be the case.

All that to say, you make a good point and it’s something I want to think about. It very much relates to my job as a curriculum coordinator where I help curate the wide world of curriculum resources in and out of our district for my teachers.

Deborah (@debswyers)I love the idea of recording estimates on the milk jug, (and so did my students when we did this)! They wanted to fill the jug up with ice and test it out for themselves. Great opportunity to create curiosity!