Today we finished out first unit for A Level. I feel I should have distributed more hi5s to the kids for this.
For those who don’t know the A level course in the UK, the first unit is called (imaginatively) Core 1 and covers algebraic manipulation, quadratics, surds, circles, differentiation and integration and maxima and minima problems.
95% of what they do is context free, just algebra on a page.
The other 5% is applications of differentiation and maxima and minima to something that vaguely resembles what examiners believe real life to be:
Having spent 6 weeks doing very little in context (My bad, new teacher at the school not rocking the boat syndrome, will do better for core 2; there’s trig and radians and logs and everything) The first group that did this from my super dry and uninspiring examples:
and found it incredibly difficult to visualise any of the problems,
So the second group got this:
With a bit of scaffolding as to what I meant:
And a pile of paper, scissors and glue.
We spent a bit of time doing this and making trays (no pics of that I’m afraid, I totally need to start bringing in a camera/check what the college rules are on photos of students working/their work) and then gathered up some results:
Before doing the algebra on the side to find out exactly how close we got:
And then chucked our function for volume into Wolfram Alpha to find the local maxima:
I then set them off on some examples to do, and they found it much easier to visualise beyond the abstraction they were already given. (Or is this below on the ladder of abstraction? I think it may be)
I felt better about that lesson. Still not awe inspiring teaching, but we’re getting there – I think that the value of actually telling me how to do the abstraction was huge. Hopefully I can do something cool to introduce networks to my Use of Mathematics class later in the week (Google maps and motorways here I come).
Next year we’re having pictures of pig farms, and real questions.
And I’ll remember to give them this extension:
Edit: Found this
Also, someone else did it here, long before me.