I wrote about my plans for lesson 1.5 here. Honestly, this was kind of a frustrating lesson. I was worried about my ELL students understanding the chain letter context in the original, so I rewrote the problem to be contextualized in twitter. Some of my colleagues made a version grounded in instagram, which probably resonated with the students more, but my twitter version had the retweet symbol integrated into the text, which I thought would be helpful for my newcomers.
Literally every class struggled to understand that the context involved multiplying at each successive step. I hadn’t had a chance to make a tree diagram ahead of time, and I think that might have contributed to the confusion. I did get a few good student-generated ones in my last class of the day, so of course none of the other periods had the benefit of seeing them until day 2.
The kids weren’t that invested in the context, and confusion about the context seemed to be distracting from the core mathematics of geometric sequences, so I didn’t really push for a deep and thorough lesson discussion at the end. We’ll see plenty more exponential functions again.
One key take-away I did have, however, was that students tend to scale their graphs by evenly spacing the numbers in their table. This means they essentially create a log scale for the y-axis and make their exponential functions look linear. I’m undecided if I want to address this by letting the mistake occur and discussing as a class, or if I want to give explicit directions on scaling axes so that they’ll see the shape of exponential functions. I feel like the ideal is letting the mistake occur and discussing it, but sometimes there are so many things that need discussing that that may not be the best use of time. TBD….