“All those ways are correct, it’s just what you feel most comfortable with.”

-Student reflecting on different strategies to solve a 3 Act Task

The first time I tried a 3 Act Task was in a school I’d never been in before, in front of a group of unfamiliar students at a grade level I’d never taught. Not to mention, this was before I took the lead student teaching, so I’d only even been at the front of my own class a handful of times.

The concept of a 3 Act Task was totally new to me – I discovered them while searching around for something interesting I could do with these students. I quickly became enamored with the idea and committed to bringing it back to my second graders. I was especially interested in finding tasks with an interesting “Act Three” – where students could see how mathematical modeling might need to be adjusted for the “real world”.

Part one

The first task we tried was “Rows of Oranges” from Kendra Lomax’s blog. At the time, students were working on adding and subtracting within 1000, and this task may fit more into adding and subtracting within 100, however the structure and array represented an interesting way for second graders to also begin thinking about multiplication.

The task shows ten oranges arranged in two rows, and one by one they are peeled, with their slices arranged in columns of five. The video stops with two oranges peeled, and I asked students to notice and wonder with a partner, finally settling on the question, “how many slices are in all the oranges?” I then asked what information students already know to answer the question, and what more they might need. Then I showed them the picture above where the first two oranges are shown to have contained 19 slices, and students got to work thinking about the question.

Most students came up with the idea of 19 slices/2 oranges and had various methods for adding or multiplying to find five groups of 19, such as the student on the left. One student (right) had an interesting idea – that only one of the oranges had 9 slices, and the rest each had 10, therefore there should be 99 slices in all.

One of the most interesting things about the “finale” of this task is that the 10 oranges contained 98 slices – which is not an answer students came up with based on the information they were given. When I asked them what they thought about this – does it make sense? – a student said that it did make sense because maybe two of the oranges were a little smaller and only had 9 slices each instead of 10.

Part two

A couple weeks later, we returned to 3 Act Tasks with a task from Graham Fletcher called “Downsizing Tomatoes“. This time, students are practicing measurement division by figuring out how many small ketchup bottles the large bottle will fill. Almost all students had estimates between 4 and 6 small bottles, based on Act One, where the video pauses and students said they noticed about one and a half small bottles filled, and a little more than half of the large bottle left.

After asking students what information they have/need to answer the question, I showed them the picture above. Their task was to figure out how to use this information to figure out how many small bottles the large bottle can fill.

The student on the left showed they understood the idea of figuring out “how many 64g’s are in 397g’s”. On the right, a student added until they got to 384, writing that this is the “closest I got”.

Another student (above) chose to subtract 64s from 397 using hundreds, tens and ones until they ended up with a number they could not subtract 64 from.

While watching the “reveal”, students noticed that as many of them had calculated, 6 bottles were filled completely. They also noticed a seventh bottle was filled a little bit. We had a conversation about this – how would we represent that amount? Students came up with ideas like “six point one”, “six point two” and “six and a half”, reasoning that the bottle looked either about half full or slightly less than half. It’s especially interesting that students said that 6.1 and 6.2 are less than 6 and a half, without any formal conversations about fractions or decimals in school.

One thing I am wondering about this task in particular – students are using the ketchup’s weight to determine something about the volume. While this does work, I think it would be valuable to think with students about why this works. I wasn’t sure how to incorporate this conversation into our lesson but I’d be interested in doing so in the future.

going forward

• One of the things about most of the 3 Act Tasks I’ve found available online is that they’re often set in White, Western, English, mid/upper class contexts (e.g. the types of food/houses/activities often shown) – which makes sense, because that’s the context most of the people who are creating and sharing these tasks exist in. But what would it look like to create 3 Act Tasks centering other experiences?
  • This is something I’d love to explore more. However I, like everyone, am limited by my own lived experiences, so I am curious what kinds of collaborations could happen to create a more diverse library of 3 Act Tasks.
• Jenna Laib has an amazing blogpost where students created their own 3 Act Tasks. I love this idea and hope to incorporate it into my own teaching.