Thursday 27th September During the last half hour of today's time with my S4 class, I delivered an introduction to simultaneous equations. Given time constraints at the moment, I know I'm not going to teach simultaneous equations as in depth as I would love to so I will only be focussing on solving by elimination over the next few lessons. I told the class we were doing a new topic to do with equations. They have previously studied equations in great depth so I displayed the first task on the board and gave them the instruction to organise the equations into groups. A few pupils asked what kind of groups I wanted and I told them I was interested in what they noticed about the equations and they had to decide on their own groups. The discussion around the room was fascinating. One pupil kept trying to convince her partner that since a few of the equations equated to 10 that these had to be in a group of their own. Others were arguing that the equations with fractional variables had to be in a group by themselves. I found myself really intrigued by what was going on, especially from pupils who sometimes aren't the most motivated about Maths. I found myself not even wanting to go and speak to the pupils about the task. I just wanted to listen and to let them be in the moment without me interrupting. A pupil asked again at this stage if I was looking for a specific answer. I found myself telling her there was no right or wrong answer and that I was just interested in what they noticed. This is strange as I'd set the task hoping that they'd see some of the equations had one variable and some had two variables but in the moment I decided it didn't matter if they saw what I wanted them to see as the dialogue around the room was so interesting. I eventually wandered around the room and asked a few questions of certain pupils. This whiteboard was interesting as the pair have some equations in two of their groups. They were still in the middle of a heated discussion about where certain equations should be so I left to it so I could see more of what was going on around the room. This pupil told me that he'd noticed he could rearrange some of the equations to make other on board. He was trying to group them to see which ones were the same as each other when rearranged. Another pupil at one stage told me that if you rearranged then some of the equations would look like y = mx + c. I'll be honest, this was something I hadn't even thought of and certainly didn't expect them to notice. As I continued wandering around the room I noticed this whiteboard i.e. the answer I'd wanted originally when I set the task. The pupils in this pair told me well they've all got x, they've all got y and they've all got x and y. They had hit the nail on the head but I was still more intrigued by some of the other groups' chat.
We then had a discussion about already knowing how to solve equations with one variable and could we solve one equation with two variables. I then told them that we would find out how to do this soon but we needed to be able to do a few other things first. They completed a substitution task where I gave them values of two variables and asked them to ensure these values satisfied two equations involving these variables. If you've not already read Kris Boulton's (@Kris_Boulton) Simultaneous Equations blog post then I recommend you do so. https://tothereal.wordpress.com/2017/08/26/my-best-planning-part-3/ I used his task and the class were adding equations in no time. The minimally different questions confused them at first as they thought the first two questions were the same at first glance but then they noticed what was changing each time. Some pupils decided not to rub out their answers but just change the part which required amendment. After adding several equations, I displayed 10x + 5y = 12 and 2y + 3x = 8 on the board. This was met with some ohs, oohs and ahs...something which has never happened in this class before. Every one of them got it correct and someone even noticed it had been the same as the very first question. Then the bell rang. I'll continue tomorrow with this task which moves onto subtracting equations. I loved this half hour of my lesson as the reasoning the pupils were giving in the first task was great. Some might not have noticed straight away what I wanted them to originally but in a way this made it an even better lesson.
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March 2021
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