Today was the first day of school, but our high schoolers (it’s a K-12 school) don’t have regular classes for the first two days, so it was a little odd. They have Orientation, which is basically a series of seminars. I did lead two math seminars today, one for the juniors & seniors and one for the freshmen & sophomores.

I had a little more than an hour and a half with each group, which was way too long; I’m going to request that the times be reduced for next year. I split the session into two parts.

The first thing we did was based on George Woodbury’s post on doing a study skills inventory. I did a lot of asking, “How do you do that?” For example, a few kids listed “organization” as something that’s characteristic of a successful math student. We talked about what it means to be organized as a math student, and how one can make that happen. It was a pretty good discussion, but I think a lot of the kids were zoning out. That may have been related to their schedule for the day (lots of seminars, as I said), but I think even so I should work on making sure ALL students take part if I do this again in the future.

For the second part of the seminar, I took an idea from @Mythagon and decided to have them investigate spirolaterals. I chose this because it’s accessible to all of them, regardless of math course level, and because it was something I could do to get them thinking mathematically, looking for patterns and using mathematical terms to describe what they saw. Here is the worksheet I developed. (Buddy the Bunny is one of the stuffed animals who lives in my classroom, just as an fyi.) The kids really got into doing the spirolaterals, and they were engaged and working hard to find the patterns.

With the younger group, I didn’t get into questions 4 and 5, except to point them to this website where you can make those changes and generate more spirolaterals. But the students in that group were asking fabulous questions as they tried to articulate the rules they were developing about the kinds of patterns they were seeing – a lot of “what ifs” came from them. It was really awesome to have them so into what we were looking at, and it was great to say, “That’s a great question. Here’s another sheet of graph paper – why don’t you try to figure it out?” We didn’t have time during class to explore whether palindromes in spirolaterals make any particularly cool patterns, but I think it will be something to investigate!

Tomorrow I don’t have any classes, and then Wednesday will begin the real deal. I’m excited. :)