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WHTW – Number puzzles, Pythagoras, Constructions and nice students!

January 21, 2018
Lots of ‘just getting on with things this week but, some interesting points came up.

Number puzzles

I spent lesson time allowing students (year 10 and year 9) to get stuck with this nrich maths puzzle. It was fascinating watching students really want to seek help from their friends despite me telling them that this was their opportunity to battle through something and demonstrate perseverance. What’s nice about the puzzle is that is completely understandable – a couple of clarifications means that everyone knows what they have to do, but it’s the how that’s the challenge. This is a classic example of maths where it isn’t the answer that’s interesting, it’s the puzzle of trying to find out how to get to it that’s the reward. I enjoyed having that conversation with students as it really doesn’t come up as much as it should.

Tilted squares

In the tilted squares investigation, I’ve got to the point where one of my classes has realised that it was actually pythagoras all along! It was great to see it dawn on them and alongside the “Couldn’t you just have told us that from the start” comments, there was also a sense of “Oh, so now we can get much further with this more quickly.”
I need to think of a more satisfactory way of working through the investigation backwards: If we are trying to find a square with an area of 21, how could we use pythagoras to do that, or, to show it’s not possible?


I’m not a fan of teaching constructions as it seems to take forever and there’s a lot of different techniques to remember. Having said that, this year, my year 11 students seem to be really good at using pairs of compasses. That’s practically unheard of but it did mean that the lesson went really well. I’ve had some of the best ‘centre of a circle’ constructions I’ve ever seen from this class and I might be coming round to liking constructions a bit more!

Odds and Ends

We had maths teacher interviews this week and have selected a great PGCE student from a strong field. One of the comments made was that it was obvious that the teachers in the department really loved maths. I already knew that was true and you might assume that all maths teachers love maths but I can assure you that it isn’t the case. I was pleased that this fact about our department comes through even to relatively brief visitors.

I marked the mechanics questions of my year 12 mocks this week. I’ve decided that I’m slightly warming to mechanics. If you know me and/or listen to the Wrong, but Useful podcast, you’ll know that’s quite a breakthrough.

It’s quite common at my school for students to say “Thank you” at the end of a lesson as they’re leaving. I was particularly struck by one student who, last lesson on Friday, left the room, realised they hadn’t said “Thank you” so made a point of coming back to say it. If you haven’t picked up on it yet, I’m in a rather nice school!

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