One of the missions of this blog is to take the work of the amazing online community of math teachers known as the MathTwitterBlogoSphere (MTBoS) and to show what modifications are made for students with disabilities. I call it the #MTBoS Mod(ification). You can read the first two editions here and here. This edition is about the lesson structure created by Dan Meyer known as a 3-Act Task.
#MTBoS MOD: 3-Act Edition
The 3-Act math task I chose was created by Graham Fletcher called It All Adds Up. I chose this because in our spring trimester we focus solely on financial literacy. As a teacher of students with disabilities we spend a great deal of time on the adaptive mathematics that is often over-looked or just simply considered a “real world context” in the classes of typically developing students. In the world of special education these tasks are known as Instrumental Activities of Daily Living (IADLs), which are complex skills needed to live independently. IADLs are not to be confused with the Activities of Daily Living, which are basic self-care tasks. At my school we call these skills the Mathematics for the Instrumental Activities of Daily Living.
As a pre-assessment for our “money unit” (as the students call it) I used “It All Adds Up.” The goal was to see how comfortable the students were with identifying coins and counting different combinations of coin denominations. I launched the task with three of my student groups. The task is great for students at different computation levels. At the simplest level the students can solve it by adding coins together to equal $1.00. At a more complex level students can look for patterns that can help them solve the problem more efficiently as well as reflect on the possibility of multiple solutions to the problem. I gave this task to groups of students with a variety of different needs and modes of processing. I’ve broken the three groups into the three stages of the Concrete-Representational-Abstract method of instruction.
Group 1: Concrete Learners
To launch the task I gave them this graphic organizer (PDF). I introduced The Math Forum’s notice and wonder strategy earlier in the year, so the students were prepared for this format. Before we played the video in Act 1, we identified the coins using the visual cues below.
Then I played Graham’s video three times. The first time I just asked them to watch the video. The second time I asked them to notice something they saw in the video. The third time I asked them to write a question they had or wonder about something from the video. If they had trouble coming up with a question, we suggested they ask Graham’s question: What coins did he put in the bank?
This question was also on the Act 2 worksheet (PDF) we supplied the students once they had finished noticing and wondering. If you look at the PDF, you’ll notice we added another scaffold to the Act 2 worksheet. Graham states there are 12 coins in the bank. To make this information more concrete and to aid in their processing, we added 12 coin shaped circles on the worksheet. This allowed the students to use coin manipulatives as they worked on which combination of coins would make Graham’s $1.00.
Group 2: Representational Learners
For this group I also began with the notice and wonder graphic organizer before watching the Act 1 video. They were able to develop their own questions more independently and to use the 12 coin graphic organizer in a more representational way. Instead of just using the actual coins, students in this group were able to use the coins, but then represent the coin values within the constraints of the graphic organizer.
Another way we increased the cognitive demand of the task for this group was to extend Act 3 to a reflection piece (PDF). We asked the students to analyze whether their solution matched what Graham actually did. This allowed for some practice extending their mathematical thinking.
Group 3: Abstract Learners
We launched the task in a different way for our third group of students. As a group of students working to understand mathematics in a more abstract way, we were able to begin with the concrete and then move to more abstract concepts because of the breadth of the task itself.
We began with the notice and wonder graphic organizer and the Act 1 video. One of my favorite quotes after watching the video was, “Wait, what? Play that again!” Once the students noticed that the value was unknown upon watching the Act 1 video, their interest was peaked and the mathematical wheels began to turn more independently than in the first two groups.
The questions this group came up with were very interesting. They asked questions that even surprised me like, “Is there a pattern in the types of coins he put in the bank?” WHAT?!? That is an awesome thing to wonder! Good job, kids!
You’ll also notice that we did not provide this group with the 12 coins graphic organizer for Act 2. The above worksheet was developed from their own “wonderings” and thus did not need the extra scaffolding.
For Act 3 we gave the students a reflection sheet (PDF), but we asked them to make a generalized argument whether this problem has multiple solutions and how they knew that to be true.
Overall, it was a great couple of days where we were able to use the same task with multiple classes. We worked on completely different avenues of the task with students who had different learning and processing needs and required different supports and scaffolds. The beauty of the 3-Act task is that it gives all students a point of access, either a perplexing picture or video, but allows for some students to expand the boundaries of the task to further their level of mathematical thinking.
Here’s what Graham Fletcher has to say about 3-Act tasks and why he creates them…
@bkdidact That’s what’s makes 3-act tasks so beautiful…low-entry high-scalability.
— Graham Fletcher (@gfletchy) March 10, 2015
I want to thank Graham for conceptualizing this task and making it freely available to any teachers who want to use it!