I really dislike it when I forget to write a post because the events of the current day and previous day bleed together and I have a difficult time separating my thoughts and reflections. Ah well.
Monday was the first day back from Spring Break. I took Patrick Honner’s advice from a few weeks ago when I was feeling discouraged and had several days of lessons prepared already. I was able to come in Monday morning, set up the bellringer, write the agenda and objectives on the board, and get to work.
The next unit in the planning guide is on exponential functions. I didn’t want to come back from a week-long break and hit my students with notes followed by drill-and-kill. Heavily inspired by this video but wanting the students to work for the answers given away in it, I created the following lesson.
It needs tweaking but I was happy with it as a first draft and besides, I was so ready for that spring break that I wasn’t overly concerned with getting it exactly perfect. Just good.
I started the lesson by giving everyone in the class a blank piece of 8.5×11. I told them that the record for folding the paper in half repeatedly was 7 times and if they could beat it I would give them candy. (I explicitly told them what I meant by “in half”.)
I got some really good engagement from all of my classes and quite a few laughs because students would call me over and then slowly unfold while I counted, only to find out they had 6 folds. This happened repeatedly. It went well. In my last class I was really proud of some students who managed 8. I don’t know if they looked up the general technique needed to get more than that dreaded 7 limit, but it seemed like genuine discovery (and I wasn’t too picky about how flat that final 8th fold was).
We then transitioned to the questions on the sheet and I had them help me build the first part of the table together before releasing them to work on the rest. I told them that the lab was due by the end of the block.
I realized quickly in my first block that I made my classic mistake (I’m so sorry, EdRealist) of expecting too much at once. Since the lab was printed front-and-back with 4 pages on two total sheets, I had them separate the pages, submit the first on in class, and work on the second sheet for homework due Friday. This turned worked much better for pacing and I had the rest of the blocks do that from the beginning like I had always intended it to be that way. (Except some of my students wondered about the staples. “Mr. Belcher you are wasting staples, why didn’t you just give it to us as two separate pages.?” Shhh, my children, shhh.)
After they finished the first half I had them do the Desmos Polygraph for exponential functions. My Exit Ticket didn’t quite work the way I wanted since I changed my plan on the fly, but it wasn’t a huge deal.
I really want to revisit the first part of this lesson for when I teach it again in the future. My students struggled to connect the folding of the paper to the doubling of thickness and also to finding an expression for the thickness after n folds. I want to develop that line of questioning and introductory tasks to scaffold the transition better. (Yay education buzzwords. But they communicate what I mean decently well. At least to other ed folks anyway. Sorry, other readers.)
My only major disappointment was that I didn’t get to see what I considered the “pay-off” of the lesson: how many folds it takes to get to the moon. When I rework this lesson I may try to move that into the first half and leave the other questions as extensions.
I think this is the third time I have taught some form of this lesson. but in the previous two times I showed the video that I linked earlier and then had students do paper folding. I did it without the video entirely yesterday, but I think this lesson would also work well, or even better, if you show the video at the end after the students have already done the work. That way answers aren’t given away and they are better primed to follow what the video says. (Although I guess you could make the argument that doing the work spoils the video. I don’t know. I enjoy it every time I re-watch it.)
Thanks for reading.