I tried a new method for getting kids to rearrange equations this week. Astonishingly, given the amount of stuff out there, I haven't been able to find it anywhere on the web, but I'm sure I can't be the first to think of it.
It was stunningly easy. The majority of the class could already do basic rearranging, such as 3a + 4 = 2a + 6 . I gave them that question then, after they demonstrated the method and answer, asked them to divide themselves into 2 roughly equal groups, based on confidence. Now, I hear what everyone seems to be saying about grouping by ability, but I had a real reason for this. Also, it was the kids' own choice which group they went in. Some of them surprised me. Most got it right. The ones that didn't quickly realised and moved.
Each group then got given a bunch of equations on slips of paper, and each student taped one to the top of their whiteboards (held portrait). The more confident group got fiendish, nasty, horrible equations. The others got ones of the sort above. They sat in a circle. Each student had to write the first step of rearranging the equation under the taped paper, then pass the whiteboard to their left. They would get handed a whiteboard from their other side, read what was on it and write the next step for that equation.
It was fantastic. The amount of brilliant maths talk, productive arguing and explaining was huge. Students were teaching each other and figuring out what worked and what didn't. A sample exchange:
Kid 1 'This step isn't right' *passes board back*
Kid 2 'Yes it is, see, I multiplied by 3p'
Kid 1 'Huh, yeah, I guess you did'
pause
Kid 1 'But I can't see what to do next, after that step. I don't think we can solve it starting like that. Can you do a different step?'
Kid 2 'Oh, I guess not, ok, sure'*
I sat with the less confident group to start with, and when they'd got on the the second set of equations I moved over. The others were really struggling, but making lots of progress. At the end, I did the litmus test.
'So, who learned something today?'
'Who was challenged today'
A resounding success. So much so, that next lesson I got them to split into 4 smaller circles, and we did some more.
*For interest, this equation had a quadratic on the top of a fraction, which they needed to cancel - if they didn't, they ended up needing to factorise a quadratic with a non-1 value of x squared.
It was stunningly easy. The majority of the class could already do basic rearranging, such as 3a + 4 = 2a + 6 . I gave them that question then, after they demonstrated the method and answer, asked them to divide themselves into 2 roughly equal groups, based on confidence. Now, I hear what everyone seems to be saying about grouping by ability, but I had a real reason for this. Also, it was the kids' own choice which group they went in. Some of them surprised me. Most got it right. The ones that didn't quickly realised and moved.
Each group then got given a bunch of equations on slips of paper, and each student taped one to the top of their whiteboards (held portrait). The more confident group got fiendish, nasty, horrible equations. The others got ones of the sort above. They sat in a circle. Each student had to write the first step of rearranging the equation under the taped paper, then pass the whiteboard to their left. They would get handed a whiteboard from their other side, read what was on it and write the next step for that equation.
It was fantastic. The amount of brilliant maths talk, productive arguing and explaining was huge. Students were teaching each other and figuring out what worked and what didn't. A sample exchange:
Kid 1 'This step isn't right' *passes board back*
Kid 2 'Yes it is, see, I multiplied by 3p'
Kid 1 'Huh, yeah, I guess you did'
pause
Kid 1 'But I can't see what to do next, after that step. I don't think we can solve it starting like that. Can you do a different step?'
Kid 2 'Oh, I guess not, ok, sure'*
I sat with the less confident group to start with, and when they'd got on the the second set of equations I moved over. The others were really struggling, but making lots of progress. At the end, I did the litmus test.
'So, who learned something today?'
'Who was challenged today'
A resounding success. So much so, that next lesson I got them to split into 4 smaller circles, and we did some more.
*For interest, this equation had a quadratic on the top of a fraction, which they needed to cancel - if they didn't, they ended up needing to factorise a quadratic with a non-1 value of x squared.
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