In this meeting, we explored the sums of consecutive numbers (inspired by a CAMI meeting led by Usha Kotelawala in June 2017). The meeting is also based on a two-day lesson I led with the support of other teachers during summer 2020 problem-solving meetings with CUNY adult education students.
Before the meeting, I shared this post on the CAMI email list:
There were a LOT of responses.
After a warm-up conversation on the topic of learning in groups, I started the meeting by modeling the introduction of the lesson we used with adult education students this summer. We talked through a few of the introductory slides of a distance learning lesson:
I then shared an activity originally suggested by Usha Kotelawala the CAMI meeting a few years ago (link above). One of the nice things about this activity is that all students can get started adding consecutive numbers together to fill in pieces of this chart. As a group, they can work together to fill in holes. They will also start to see patterns in the sums that can help them predict other solutions.
After we had a few solutions, we went into breakout groups to complete the table and brainstorm questions about the sums of consecutive numbers. Each group chose a few of their favorite questions, then we came back together to share them:
When I taught this lesson over the summer, I asked my students to give their age as the sum of consecutive numbers as well. Over WhatsApp, one of my students gave the following solution:
There are five different ways to write 45 as the sum of consecutive numbers! I was really impressed. And it made us all wonder which numbers are like 45? What is it about 45 that makes so many solutions possible?
We spent the rest of the meeting working in groups, then sharing our discoveries as a group.
Note: I set up a Jamboard (online whiteboard at http://jamboard.google.com) for use in this meeting and then had everyone made their own copy of the Jamboard for editing. It didn’t work very well since people couldn’t see each other’s edits. And I didn’t do a good job of collecting the group’s work at the end of the meeting, so I don’t have everyone’s notes. 🙁
I think it would have been better to have one Jamboard for the whole meeting which we all edit together. Each group could have made their own pages within the Jamboard, and then we would be able to see each other’s work easily and also save the work of the meeting in one place.
If you have notes from the meeting or ideas that you would like share about the question posed above, please post in the comments.
