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.

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## About Linda

I have been involved in secondary mathematics education in Victoria, Australia for over 25 years.

Hi,

Could you please share with me how you used grids and blocks to teach simultaneous equations?

Thanks!

Esther

Hi Esther – thanks for the query. In the previous post, I mentioned that I thought the Soft Drink Cans activity from the Maths 300 series of lessons was an ideal entry point to simultaneous equations as it used the strategy of dealing with one thing at a time to simplify the solution process. I said: “I did come away with a couple of lovely ideas I will put into practice this coming term. I hadn’t seen the Maths 300 Soft Drink Cans activity. It was recommended as a ’strategy lesson’ at the conference – to teach students about breaking a problem down into manageable chunks, considering one aspect at a time. For those who don’t know it, students are given a 6×4 rectangular grid and 18 cubes. The problem is to place the cubes onto the grid in such a way that every column and every row has an even number of cubes in it. This proves to be quite tricky and frustration tolerance is tested. After about 5 to 10 minutes, the class is stopped and the teacher brings everyone around one student’s table. He/she asks the student to arrange the blocks on the grid so that every row has an even number, forgetting about the columns for the time being. When this is done, the teacher says…”Now, slide cubes along the rows – but keeping the rows intact in total – to make the columns all even” The problem becomes incredibly easy with this simple instruction”

Hope this helps.