All 3 entries tagged Trigonometry
October 21, 2010
September 30, 2010
Today was a really fun day!
This morning we had Robert Ward-Penny (who is now officially off my Christmas card list after refusing to autograph his article in my ATM magazine) for some subject knowledge enrichment. We started off with a game where we were in three teams and one from each team had to use play-doh to represent a word that Robert gave them. Pictoral things like pie chart were easy, more conceptual things like algebra were more difficult. I think Charlie did a great job of modelling the play-doh for our team (I have to be extra nice about Charlie now after dissing him in an earlier post, which he read today).
Oh that reminds me, I was in the toilets today (don’t worry, it’s not one of those stories) and as I was washing my hands I heard some girls talking about my blog! I feel a little bit famous! Now I just need to attract some advertisers… Did I mention I absolutely love Casio calculators, for me they are far and away the best calculators you can buy, and very reasonably priced too (hint hint).
Anyway, the next thing we did was the best activity ever and the best laugh I’ve had all year. We were doing about the properties of quadrilaterals. We had to, in our usual groups, pretend we were on QVC (the home shopping channel, for those lucky enough to have never heard of it) and were selling the quadrilateral of our choice. Alternatively, you could pretend you were on Crimewatch, and there’s a criminal quadrilateral on the loose. Our team decided to stick with QVC and chose to sell the humble square. I am going to attempt to type up an approximate script of our little skit because it was absolutely hilarious. So stay tuned for that very exciting blog post. I had absolutely no idea until today that Paul was such a comic genius! Poor Giulian couldn’t actually speak when it was his turn to talk, he was literally crying with laughter!
Apart from being such a laugh, there are other great things about this activity. It engages some of the pupils who are not normally engaged by maths lessons. The creative pupils who are good at English and drama but not maths would love this activity. Another good thing about it is it makes something quite dull very memorable. I personally feel I will remember our QVC presentation for a long time, and that includes all the facts about symmetry and angles.
Next we moved onto something called curves of pursuit. This is like when a dog is chasing after a car and it runs towards where the car was, rather than working out where the car will be and meeting it there. You can plot this path that the dog takes and some interesting patterns can appear. Similarly, if you have three missile launchers in a triangle and A aims at B and B aims at C etc you also get a cool pattern. What’s weird though is that even if the triangle is isosceles or scalene, the missiles will all collide at the same time at the same point.
Then we moved on to talking about parabolas. Why are they so important? Why are they the first curve we really learn about? Here are all the everyday uses I can remember: car headlights, satellites, telescopes (?), suspension bridges, projectiles… Then R W-P showed us some holiday photos of parabolas: some fountains in Italy and the Golden Gate Bridge. We were given the task of finding the equation of the Golden Gate Bridge using the measurements we were given. Then we were told to find out whether the McDonald's arches are parabolas. It turns out they’re not. There are a few ways to show this. You can work out an equation for it based on it being a parabola, so you get something like y=ax^2 and then you can put other values into the equation to test whether it works. Or, you can paste an image of the arches into Autograph and try and fit a graph on top of it. Victor had a cool method, he put two together with the stationary points facing outwards and showed that they made an ellipse (wait, or was it that it didn’t make an ellipse… my geometry is quite poor).
We then moved on to Mechanics, my least favourite part of maths. Annoyingly, there are quite a few physicists around who love mechanics and find it really easy. We had to draw distance time graphs for some marble runs which I found really hard to do. I just didn’t really get it. I would have to actually make a table of values and sketch it based on that.
Then we had to do this work sheet designed to point out misconceptions about forces. Luckily, because I have so few conceptions of mechanics, I didn’t really have any misconceptions. So yay for that!
Then we explored the fact that when you rest a ruler on your two index fingers, if you try to slide your fingers together only one will move at a time. This is because of friction or moments or something. I still don't really get it.
We finished the morning off with a game of Marco Polar. Someone (Tim in this case) stands in the middle blindfolded and shouts out “Marco!” then someone else in the room shouts out “Polar!” and then the blindfolded person has to describe the position of the shouter using polar coordinates. EXCEPT when we did it today the angles were taken clockwise which is NOT how you do the argument in polar coordinates (I only remembered this when I got home). So really it was about bearings, but I’m sure R W-P just couldn’t resist a good pun. Then Tim was given some bean bags and told a bearing and a distance, and he had to throw the bean bag in that direction. He failed narrowly the first three times, but then Victor managed to catch the one aimed at him. Luckily no coffee was knocked over onto laptops, but there were a few close calls.
In the afternoon we had Jenni who was teaching us about questioning. We saw a variety of different questions and discussed where they fit on Bloom’s taxonomy (or taxidermy to Charlie) and what sort of mathematical thinking they encouraged. We then had to come up with our own questions which tested whether pupils understood the trig identities. Lydia was typing that up so if she puts it on her blog I’ll link to it later.
Wow what a long day it’s been! And now I’ve got to do a little bit of reading for tomorrow and do some paperwork. I’m excited about tomorrow because a) it’s Friday and b) some of us are going to the pub afterwards for some friendly banter and food out of dog bowls. (Good grief, I wrote bowels first by accident! Eating out of dog bowels would be too disgusting even for Varsity, I think!)
Emma x x x
September 29, 2010
I made a little cheat sheet for trig identities and I thought I'd share it with you:
At the bottom there is a really cool method for remembering/working out the values of sin, cos and tan for the most important angles. I call this the Curly-Stan mathod because the guy who showed it to me was from an Eastern European country that sounded a bit like Curly-Stan but I thought he was saying... Curly-Stan. My Geography is not good.
Emma x x x