Monday, March 26, 2012

Three typical lessons

Systems of equations are something that I had trouble teaching last year, so when I rebuilt the unit I had some concerns. I think that most of my goals have been met. Also, things were moving pretty quickly, which is a major concern for me this time of year.

Day 1 was pretty much solving "catching up" problems and then giving those a name. Day 2 was solving systems graphically, and tying that into the "catch up" problems. Day 3 was convincing kids that there's a limitation on the graphical technique, and then providing them with a technique for "merging" equations by substitution.

I think that there are a couple of good things about these p-sets/worksheets. First, there are some good questions interspersed throughout. I also like the way that the abstractions are latched onto some concrete structures. These are examples (plumbers, walkers and music subscriptions) that students are familiar with from the linear equation unit earlier in the year. I also like the way, in Day 3, I had the students see the limitations of solving by graphing.

Here are my docs. Feedback, please? Help me make these better?

Here's what makes it fairly typical of my work right now:

  1. It's a problem set. Problem sets and problem solving are more or less at the center of my classroom, right now.
  2. It's made from scratch. My school doesn't have materials for me. I wasn't happy/didn't understand the stuff that Park Math, Exeter, Arlington Algebra or Sam's VFC had made available. I have no idea how I taught this last year, because I have nothing saved. My lesson plan was probably scribbled on the back of an envelope and I probably printed off a worksheet from the interwebs. Yeah, first year was awesome.
  3. I wrote it on the day of the lesson after reflecting in a lesson plan document where I thought about "hard parts" and some "good questions" to ask in class.*
  4. I had very, very little time to teach this. I know we all have coverage issues, but I REALLY have coverage issues. 
* It's like a diary. It'll be great fun to read next year when I'm planning.


  1. I really like page 2 of day 3. I like how it makes concrete *why* we set equations equal to one another.

    You said the earlier days are supposed to be about graphing, but there's no explicit direction on *how* to solve 8a-8i on day 2. I imagine this was covered in class? Otherwise, if I didn't know what I was doing, I would just guess and check.

  2. Good eye, on 8a - 8i. That was something that I did with the whole group. Because of their experiences in Day 1, about half the class seemed to be able to make the leap to solving the systems by graphing. I filled in the rest of them on the board with a big old Venn Diagram and a graph of the lines. There was a straggler or two on Day 3 that I needed to fill in. Part of that was that I wasn't sure how to put that on the problem set, part of that was that I didn't think that I needed to.

    Also, full disclosure: didn't finish Day 3 on the actual third day.