As the end of the year approached, I was invited to bring some open-ended problem solving activities to a few classrooms. A colleague that I met in a Math book study earlier this year had introduced me to 3 Act Math tasks and I thought it would be a perfect opportunity to try some.
I visited two Grade 4/5 classes and used Graham Fletcher’s Array-bow of Colours task. One of my favourite things about my job as a math coach is that I frequently get the chance to teach the same lesson twice in a short time span – such a great opportunity for reflecting and thinking about my practice.
I began in both classes by asking students to Notice and Wonder about the Act 1 video. Here were some thoughts from the first class I was in:
We focussed on the “how many skittles” question for this activity, but I love the variety of questions they came up with and I love how many of them were actually measureable questions. I was pleased that someone came up with the question: “What if not every small pack has the same number of skittles?” I actually brought packages of skittles for the kids to work with (everything is more fun with candy) and I had debated how to handle this question, so I was happy that one of the students thought of it before we got started. I was also so happy that it was a student who is typically not very engaged, and who doesn’t consider herself to be “good” at math. It was a nice opportunity to really value her thinking!
We did some estimating and, as usual, had a HUGE variety of thoughts here. You can see the range of the estimates in the first picture above – the lowest estimate in the class was 50 and the highest was 1050.
When we got to Act 2, the students knew they wanted to know the number of packages and number of skittles/package. This class (and school) has a focus on multiplication as their essential skill for this year, so pretty much every group (partners) knew that they were going to multiply and no one had a hard time getting started. Most groups quickly found the answer to 58 x 14 was 812. The interesting challenge for this class was how they were going to address the variation in the packages. As soon as students started opening their skittles, it became apparent that not every package was the same… 14 was the low end of the scale. The highest number of skittles per package was 19 and most kids had something in between. To account for this, some students added a constant at the end to account for there being “some” more skittles (ie. 812 + 50). Some students changed their multiplication question – 58 x 16 (because 16 is between 14 and 19). Some did two calculations – 58 x 14 and 58 x 19 and then picked a number in between. This gave us opportunities for some rich discussions in Act 3.
I did the same activity with another 4/5 class the following day and noticed some interesting differences. The second class was in an inner city school and they have not had the focus on multiplication as an essential skill. They generally struggled a lot more with this activity, but still had some good observations and ideas. Their estimates were wildly off – the range for the class was between 100 and 400. Overall, they knew they were going to multiply, but didn’t have the skills to do the 2×2 digit multiplication. They were much more confused about the variation in number of skittles/package. In hindsight, knowing that they were less comfortable with multiplication, I might have waited to hand out the skittles packages until the end and then we could have had a whole-class discussion about what to do with the variation in package size. I think this would have filtered out some of their confusion during act 3 – some students were really quite paralyzed by the variation in packages. I still think this activity was valuable for them.
One of the things I like about this particular task is the photo provided for Act 3. This gave us a neat little opportunity to talk about efficient ways of counting/grouping – it made for a good visual number talk at the end of the task.
I also recently visited a Grade 6/7 class and I used Dan Meyer’s “Super-Bear” task. The kids were really engaged (which is quite impressive for this particular class) and all groups ended up with a workable strategy. If I were going to do this again, I would encourage the use of calculators – most lots of groups just got bogged down in a problem that required long division with decimals (this is understandable… I’m pretty sure I would get bogged down tackling a long division with decimals problem too). I think the value in this activity is in the problem-solving nature and not in the calculation piece.
- I am eager to try out some more 3 Act Math.
- I love that they are such an engaging way to have kids problem solve.
- I enjoy giving the responsibility for all the thinking to the students… these tasks really make me feel like I am a facilitator rather than a teacher.
- I am really going to encourage teachers and schools next year to pick a topic or idea to really focus on in their Math instruction. I have been so impressed by the school that I have been working in that has really narrowed down their approach and really worked collaboratively to ensure that students progress.
- There are so many of these tasks available online and for such a wide range of grades and topics -I am so grateful to all the teachers who have spent time developing these and sharing so generously online!
If you are new to 3 Act Math tasks, I would highly recommend this video by Dan Meyer in which he demonstrates the implementation.
Happy summer to any other teachers out there who had their last day today!!