Sunday, 28 June 2009

Circumcentre and Orthocentre

Imagine we recieve data from 3 mobile phone masts telling us our suspect is 5 miles from tower A, 4 miles from tower B, 3 miles from Tower C.

We can find the suspect by triangulating his signal. He will be in the circumcentre of the triangle the phone towers make, and the orthocenter of the triangle between the phone towers (This might be useful, as if we only had information from 2 phone towers, we could station someone where they meet as a starting point).

Thursday, 25 June 2009

What can you do with this?


Being a fan of Dan's media rich blog, we spent some time with class this week reacting to this video of Dougal being, well, Dougal...

This led to a lot of conversation

(a) about how stupid he is

(one pupils asked if I ever felt like I was Ted and they were Dougal)

(b) how perspective can trick us.

We decided to make a couple of basic shapes and try to photograph them as if they were the same size.

Then we got some simple pictures of animals and enlarged them. Some groups made them twice as big, others enlarged them with a scale factor of 3 and we measured how much further away the enlarged shape had to be to look the same size.

A few kids were clever enough to start guessing that if it was 3 times as big, it would need to be 3 times further away, and then tested this theory (of course, this led to the discovery of the concept of centre of enlargement which was, if i'm honest, a totally unexpected bonus).

A couple of kids asked if they could make them half as big and see what happened, to which i responded with an unusualy gangsta "hell yizzle". (Note to self: less snoop dogg on the way to work)

Thoroughly enjoyed, the genius of Bluetooth meant they could all hand in their work by sending their pictures to my phone (in the first photo, the blue pig is twice as big as the other one, in the second photo the blue kangaroo is three times as big as the other one)

Worryingly, one of the pupils has the bluetooth name "Gerry Mangoes" but i've chosen not to worry about that..

Next up, we're gonna stretch a kid. Maybe.

Wednesday, 24 June 2009

Is this wasting time?

Today we spent some time watching the awesome Rushmore-esque video for The Decemberists track "16 Military Wives", then analysing the opening verse.

Sixteen military wives

Thirty-two softly focused brightly colored eyes

Staring at the natural tan

of thirty-two gently clenching wrinkled little hands

Seventeen company men

Out of which only twelve will make it back again

Sergeant sends a letter to five

Military wives, whose tears drip down through ten little eyes

we try to Venn diagram the relationships, but struggle and go to a 2-way table. We ask logical questions about it - we manage to pretty much destroy logic - for example, when i point out that 16 wives and 32 eyes meant that they all had two eyes each, D. refutes this asking the unexpected but valid question - "are we assuming that all these women have two eyes each, or could there be a freaky one with 3 eyes?" "well, " says J. "that means there'd have to be a woman with one eye as well..."

This opens up a world of discussion - if there was a woman with 3 eyes, how does this affect her chances of finding her fictional hubby has died? K. thinks it made her safe, as if she was crying, there would be 11 little eyes crying, but H. counters that if the oned eyed woman was crying as well that would make it ok. We decide that, assuming ther was only one woman who had one eye, and one woman with three, their respective happiness depended entirely on each other - if one's husband died, then other must have too.

From there to conditional probability, tree diagrams and beyond, a totally worthwhile waste of time.

Hot Sweaty Guesswork

On this unreasonably warm week, my year 8s are taking tests.
They've done pretty well, not staggered me, but pretty good skills.
On the way out of the non-calculator test, i had this exchange with one pupil:

Me: Well, what did you think?
P: It was pretty hard, i hate it when it's all multiple choice.

These are the government issue Year 8 Optional Tests (our mighty leaders appear to issue the exact same ones every year, but I digress). Upon taking the time to go through the paper, out of 60 marks 23 were of a multiple guess style (either ringing the correct answer, or drawing lines to the right answer)

Personally, I dislike these type of questions, I'd have none of them - every time I see one I picture some faceless examiner Tarranting the kid "is that your final answer?" accompanied by ridiculous over dramatic background muzak.

But I was amazed that over one third of this paper (to put it in context, pure guesswork could get a pupil a grade D equivalent) was open to wild guesswork.

However, far be it from me to question the examining powrs of the mighty higher ups, so i felt it befit a level of analysis. I asked some random pupils in my form to completely guess every multiple choice answer (P1 guessed the first option for each one which i enjoyed very much as an experimental method - his logic was that he figured people would never expect the right answer to be written so close to the question, so the examiners would view it as 'guess proof' - more fool them, we've seen through your little ruse!)

Anyway, total guessing led to the first kid getting 9/23 (actually, pretty impressive since he guessed all "a"s - a lesson learned - guess a for good grades!), p2 got 8 and p3 got 11.

Anyone else concerned that a kid actively instructed to not read the question or think about it at all can gain around 10 marks out of 60 of this exam?

Saturday, 20 June 2009

Fave lesson this term was dead simple, with a year 7 class who were struggling to get their heads around transformations - particularly translations.

We as a class are naturally giddy about the new transformers movie (yeah, yeah, i don't care - it's robots fighting and blowing things up - game on) so we combined the two and did some translations taht made a Transformer.

For some reason, having had a total nightmare with this the lesson before, they were awesome at it. That said, some chose to decorate their finished work pink and green, which nearly led to me giving them a detention for insulting the good name of Optimus Prime.


Well, as i've been prety much absent this year at this blog address, i thought i'd try to get back on the horse.

Was reading some article about how "the young people nowadays" ((C) My Dad) live in an Echo Chamber type world where ideas are more or less instantly fed back on, which reminded me of a story in the NY Times last year about how top class football (they said soccer ... Bah!) players succeed because of not just practise, but deliberate practise. The difference being that they recieve immediate feedback on specific tasks, and wondered how i was addressing these two linked ideas at the moment.

So i've been on a quest to hit this immediate feedback at often as possible. Somtimes this is just flat giving them the answers to start with (so they can concentrate on method rather than outcome) but i've found the most useful way is using my old friend MS Excel and it's sweet conditional formatting so that when a kid answers a question, they immediately know if it is correct or not.

Result? Well i experimented like this for 2 parallel classes i teach.

I gave both the same material, one as a standard pen and paper exercise, the other on latpops with immediate feedback.

Class Pen & Paper did ok, and completed their work in the lesson.

Class Laptop did the same.

In the test the week after, class laptop scored a full level higher than class pen and paper.

(P&P average National Curriculum level 4.2, Laptop NC 5.4*)

* it should be said that some of this group said they'd saved a copy of the spreadsheet and used it to practise at home - this may have had an influence

Anyway, this is usually the time of year i like to experiment (more free time as year 11 and 13 have finished their exams and left) so going to keep on with this and see how it affects other classes.