Period 2 (sheltered ELD):
Some good tables and graphs. A couple of groups said the equation is 2n. One group said 2n+1, but their reasoning for the +1 was that it’s because it’s day 1. One group seemed to have a solid understanding of the equation, although I didn’t get to talk to them so I’m not sure if it’s the whole group or one kid in the group.
This was a day where I could really tell these lessons were designed for block periods, rather than the 59 min I have. Around the point that most groups started to lose focus or feel like they had done everything they could, we had about 7 minutes left in class. If it were a longer period, it would have been a perfect time to transition to a whole-class discussion.
I’m still trying to figure out how to break these lessons across a couple of days without having kids lose interest or momentum.
I ended up giving each group an 11″x17″ mini-poster and telling them to write down everything they had done on their #VNPS. This will hopefully help us launch our discussion tomorrow, and it gave me a less chaotic way to review each group’s work rather than worrying about figuring out what they did and also whether everyone was on task and helping each other.
It did, however, make the end of class a bit frantic, as kids really didn’t have a lot of time to transfer their work onto their mini-posters.
Periods 3 and 6:
Both of my gen-ed classes had about 10-15 minutes for discussion at the end. I asked them at the outset to focus on where we see that +2 in all of the various representations. They were super clear on it in the table, and after looking back over their notes, identified this as an arithmetic sequence.
They were super NOT clear on where this common difference appears on the graph. I think the concept of slope is fairly new and unfamiliar for most of them, so I’m not going to focus on it here since I know it will come up in much more depth later.
They were all pretty solid on the recursive equation, which they phrased as “Next=Current+2, Initial=3”.
In period 3, no one really attempted the explicit function, however two groups did work for #1 (how many push-ups on day 10) that could lead to an explicit equation. One group said 10*2+1=21. Another said 2*10=20+3=23. They also labeled the 2 as “growth” and the 3 as “initial”.
At the end of class, I pointed out that the group that got 23 has reasoning that seems to match the recursive equation, but that that somehow led them to the wrong answer (since we know 21 is right from the table). Hmm…. I’m hoping that comparing these will lead to a discussion on an explicit equation.
In period 6, I noted that one group said 2n+1 and another said 2n+3. We were pretty much out of time at that point, so I left that as something to be resolved tomorrow.
For both period 3 and period 6, I’m planning to start tomorrow by discussing these unresolved issues. After that, I would like to introduce formal function notation, starting with the explicit function, and then doing the recursive function. However, if they seem too squirmy to sit for notes after opening with a class discussion, I’ll have them make posters showing this pattern in multiple representations and we’ll save function notation for Wednesday.
Period 5 (sheltered ELD):
This class is super challenging. It’s huge (35 students!), it has some personalities that require constant supervision, and it’s all newcomers. On top of that, there is a HUGE discrepancy in background knowledge – more so than in any other class. There are some kids who literally wrote the explicit equation perfectly the moment they saw the bar graph, and others who struggle with the table.
I’m trying to instill a culture of collaboration, and I’m trying to combat the many status issues that this set-up engenders, but it’s been a challenge.
Like period 2, this class didn’t have time for any discussion, and they also had a bit less time (and were a bit more chaotic) than I felt would be reasonable for mini-posters, so I had them summarize their group’s work on the back of their notice wonder sheets at the end of class. I’m going to give them 10 minutes to make posters (maybe mini-posters?) tomorrow, and then do the discussion.