I wanted to see how well my students could cope with the idea of being given a simple problem, and being ‘let loose’ to investigate it. No spoon-feeding from the teacher, no coursework style suggestions that in order to get full marks, they would have to use algebra (hint hint…). Just ‘go for it’.
I was pleasantly surprised!
The problem was: What rectangles can you find that have the same area and perimeter? (from the newest version of ‘rich tasks – soon to be uploaded!)
Some predictably just spent the lesson trying out different numbers, and got no further. Some went off on fantastic tangents about triangles, or putting together 4×4 squares to make a rectangle.
At the start of the second lesson, I asked them what they wanted to share. No-one shared actual measurements of rectangles that work. They shared things like:
- you can’t have a side that’s 1.
- you can’t have a side that’s 2.
- I think they have to be even numbers.
- I think they have to be at least one even number.
We were able to try to figure out why the side of 2 didn’t work – there is a pattern – and then I showed them on the board with a rectangle, a 2 and an x, why the area would always be 2x and the perimeter 2x + 4.
This sparked quite a bit of algebra in the room (okay, maybe that counted as a hint…).
The TA’s had been furiously scribbling together, and had proudly come up with some algebra to show what relationship between the numbers was needed, and that meant they were able to go and support some students with their algebra. I deliberately stayed out of it, as I wanted them to have that sense of independence. Having to ask a TA to check over your algebra is not the same as needing the teacher to show you how. It meant they retained control of their work.
I’d told them they needed some form of write-up to show me afterwards.
They were rightly proud of what they’d achieved by the end of the two lessons, and the write-ups look very impressive – some really good, systematic approaches, and good recording techniques too.
The most important factor for me though was that they’d done it all on their own. Maths in the big wide world after school is about seeing a problem and figuring out what to do to solve it. No-one will spoon feed them the methods then. More independent challenges to follow methinks!