Well…I’ve done the lesson on simultaneous equations as I outlined in the previous post and it all went very well.
We started with two simple equations as part of their daily quiz – to solve for a and b in a + b = 3 and b = a + 1 (ie something they could do relatively easily by trial and error). I then challenged them with 2a – 3b = -1 and a = b + 1. We briefly talked about needing a strategy for more complicated ones.
I then handed out the grids and blocks. The little activity itself generated interest, engagement and a challenge. In a class of 22, I had three students who found one solution in 10 minutes and I asked them to try and find another whilst walking around the room and checking on what the rest of the class was doing. I probably wouldn’t keep it going for any longer than 10 minutes. We then all went to the desk of a student who hadn’t found a solution as yet and I asked her to fill in the rows with an even number of blocks and not worry about the columns as yet. She was a trifle daunted by the prospect of doing this in front of everyone but, although I don’t think she enjoyed the ‘exposure’, I think it pushed her thinking and learning behaviours in positive ways. She needed some assistance to then finish the problem but the majority of students ‘got it’ and they went back to their own problems to get at least one solution happening.
I then asked about a possible connection between the activity they just did and the two equations. Quite a few of the students realised the connection and got excited. We talked about how we could obtain the value of one variable then find the other. I showed them the substitution method. I kept repeating the main idea – that to solve two equations with two unknowns by hand, we had to keep using the strategy of finding one variable first then thinking about calculating the value of the other.
In subsequent lessons, we talked about pairs of equations that didn’t have a ‘letter on its own’ and what we could do but I made sure to always come back to the strategy – how can we solve for one pronumeral first? I was very pleased with the way the activity added to their understanding that the two algebraic methods of solution were just different forms of the same strategy and the way in which it engaged and made all feel as if they were in control of what they were learning – not just copying down a procedure that someone else had thought about.