Today was sports day, and it was great. While there are a lot of activities, since there are so many children, the vast majority spend the vast majority of time waiting in the stands. Sure, there was some sport going on somewhere, and the occasional heated race ran us by, calling for our attention and support, but other times there were significant lulls. For me then, the most fun was had in teaching a dozen or so Year 8s yet more maths, poetry, economics and breakdance.
Sports are actually packed full of mathematics. It kicks off the with the discus, where I noted that the athlete first traces a circle as they turn, and then the disc can be modelled as a tangent from the point of release. This had the dual benefit of offering another opportunity to talk about the idea of ‘geometric modelling.’
A reasonable approximation to the mathematics of discus throwing
From there, what angle to the horizontal should something be thrown to reach maximum distance, whether discus, javelin or shot put? 45 degrees was quickly offered up as an options – turns out one kid had picked that up from video games.
I summed the discussions up into a life lesson about how subjects can overlap and relate in ways we don’t see straight away – the better an athlete understands the mathematics and science of their sport, the better they can perform, knowing precisely how to adjust the positions and movements of their body to achieve maximum results: brain and brawn working together, much as the Plato and Pythagoras would have had it (opportunity to throw in another history/philosophy lesson there).
The mathematics of projectile motion – also known as ‘throwing stuff’
Some kids started speculating whether there was an optimal angle for locking ones arms while running – 90 degrees they suggested. Seems to make sense to me, though I’m not a sports scientist, could be wrong! Moving on now to discuss the imagery of Shelley’s Ozymandias, one pupil asked if the ‘shattered visage’ described in the poem would be 1/4 the size of the ‘trunkless legs’. When asking what he meant, he informed me that in primary school they’d been taught that the face is 1/8 the length of the body. Assuming the legs are 1/2, he’s right, that would make the the face 1/4 of the legs – a bit of fraction division on the fly helping pupils to visualise the work of a great poet.
Would the ‘shattered visage’ be 1/4 the length of the ‘trunkless legs’?
Amidst all this, there was one outcome in particular for which I felt it worth interrupting the current series on ‘memorising poems,’ since it generated some further insight for me. A couple of weeks back I wrote this post, which included a simplified method of teaching area. I had never used this method with my 8.1 class; they’d only ever seen the more complex, technically exact explanations, combined with lots of practice and problem solving. So, I showed some of them the first set of diagrams and pointed out that area was always length times height.
‘Always? But what about… like when it gets complicated?’
‘Okay, so you mean like these shapes here, the triangle and trapezium? Well look it’s still length times height, but then you have to divide by two, since triangle starts with a T.’
‘Because it starts with a T?!’
‘Well no not really, that’s just a way of remembering it.’
‘What about the trapezium, that one was all complicated…’
‘Well look at the diagram again. It’s still the same thing as before, it’s just the length’s a bit weird, you have to add up both the top and bottom to get the real length.’
At this point I showed them the circle diagram.
‘Even with a circle, it’s still length times height.’
‘But circle is radius squared?’
‘Correct, but look again at the diagram… still length times height, but both the length and the height are…’
‘Yup, and then you times by Pi, because circles look like Pies.’
‘Really! Is that the reason!?’
‘No… but again it’s an easy way to remember it!’
A few things struck me throughout all this. One was how readily kids in non-uniform outside on a gloriously sunny sports day were happy to sit and listen to yet more chat about area, as if it’ll never end! Another was how almost relieved a few faces looked when I told them this way of thinking about area, as though something that had been difficult had suddenly become easy, or made sense in some new way – wish I had more time with them to see if that bears out. I also tried @dazmck’s idea of asking them how they thought they’d find the area of a stretched circle, an ellipse. They felt they could comfortably answer that question, which isn’t bad for an idle conversation in the sun between teacher and pupils who still often resist lines of mathematical questioning.
The day was a strange and complex mash of ad hoc lessons, most of which were freely and sometimes even eagerly entered into by the pupils themselves.
Conclusion: There is lots to be learnt on Sports Day, especially maths.