Wednesday, 7 October 2009

What the... ?!?!?

Okay, so we all know (Derren Brown aside) that the odds of winning the lottery are roughly 1 in 14 million.

What the hell are the odds of this...

At the start of September, the exact same 6 balls were drawn out in 2 consecutuve draws in the Bulgarian lottery.

Sept 6th - 4, 15, 23, 24, 35 and 42

Sept 10th - 4, 15, 23, 24, 35 and 42

I say again... What the ?!?!?!

But how unlikely is this?

Quote from Reuters:
The chance of the same six numbers coming up twice in two consecutive rounds was one in more than 4 million but was not impossible, respected mathematician Michail Konstantinov has said.

Really? Less likely than winning the damn thing in the first place??

Kids immediately destroyed this quote - they know their gambling - and I'm planing on coming at this investigating conditional probability, tree diagrams, extending to see how likely this is if there were 3, 4, 5, 6 balls etc.


One of my students pointed out that the only reason it is surprising is that given that it came out one week, it has become a sequence we recognise, like 1, 2, 3, 4, 5, 6, but it obviously has the same chance of coming out as anything else.

{side discussion from K.- "why would you win less from betting 1, 2, 3, 4, 5, 6 on the lottery compared to pretty much any other set of numbers?"}

This brought to light a mass debate on the nature of randomness - I asked them to stand around the room randomly. Naturally, every kid tried to space themselves evenly from one another. I was non committal when kids asked if they had done it right.

Then we all sat back down, picked our MP3 players / mobiles out and hit random.

For those of us with mighty Sony Walkman, this randomises the order songs play in, but will play all songs through before starting again (admittedly in a different order).

Kids: "Not random"

Some mp3 players did genuinely randomise though (25 did, the rest did not)

Out of a class of 30 plus me (does it say a lot that between us we had 47 devices capable of shuffling music? there's an investigation there i think...)

All these devices on random/shuffle, 1 kid got the same song twice in a row.

We talked about why this could happen (and why we wouldn't want it to happen in an mp3 player) before getting to the idea of random meaning everything having an equal chance of happening - even if it has just happened.

Asked them before they left to stand randomly around the classroom.

Some still spaced themselves out, but some clumped together. Some didn't move at all.

Sincerely - isn't it awesome when a 14 year old can write a better lesson plan than you?

Saturday, 3 October 2009

Bidmas Shooter

Discovered a nice, easy to use game generator at via the last Let's Play math carnival - this is what i produced in 3 minutes. I quite like it!

Click here for full screen version

Wednesday, 30 September 2009

Negative times negative

Came across a few posts asking for a concrete explanation why negative x negative = positive.

Whenever I'm doing this with my kids i tend to show them videos.

This video, shows a man walking forwards (in a rather silly fashion...). When played forwards, which way does he go?

What would happen if it was played backwards?

This is a video of a (sadly now deceased) man walking backwards... If i play it forwards what way does he travel?

What would happen if i play the same video backwards? He moonwalks forwards!

So the first vid is walk forwards (+) * played forwards (+),

the second is walk fwd (+) * played backwards (-)

The third vid is walk backwards (-) * played forwards (+),

the last one is walk backwards (-) * played backwards (-)

This then leads to obvious questions like "right, MJ moonwalks 6 steps, how far and what way would he go if i play that vid backwards 5 times?" - then do it - play it back 5 times and count where the dude goes..

The nice thing about this is it allows me to cue massive moonwalk practise for my classes...

Tuesday, 18 August 2009

The quietest lesson

Late last year I was doing a bit of revision of basic averages with a (low-ish ability) class who kept getting confused between mean, median and mode.

The homework for the previous week had a question at the end inviting them to tell me their favourite terrible joke.

We then used these to look at averages in context - i gave them a list of rubbish jokes (obviously pretending i thought they were the funniest things ever...) and they found average number of words per sentence, letters per word etc. Very amusing and a decent reminder of why we divide by the total number of items - letters per word is different from letters per sentence.

We then moved this to look at Stylometry - i gave each group a different writing sample. Group A had an essay written by "Julia" and Group B had an essay written by Aaron. Group C had an essay but didn't know who wrote it...

Yeah, alright you can all see where this is going...

I told them that these two kids handed in the same essay. One of them has obviously copied the other persons work. How are we going to find out who is the cheater?

Suggestion 1 was handwriting- but this was shot down because things are all word processed now. One kid suggested we stick them suspects in an interview room and sweat it out of em a la Homciide:Life on the Street, but i gently weaned him off this idea.

Given what we had just done, lots of kids realised straight away that we could find the average number of words per sentence etc for each piece and use this to compare the "copied" work to other pieces. The person who copied the essay will be the person whose average writing style is nothing like the average writing style of the copied work.

My kids always get involved in things if there is some sort of crime or mystery involved. Basically absolute silence here whilst they collected data, to the point where i started going round and winding kids up cos i was bored. They are either gonna all grow up cops or they're gonna be the most elusive criminals around...

Thursday, 30 July 2009

Carnival Of Maths 55 (i think...)

Err, right. I'm popping my carnival cherry, had no write ins, so this is just a few stuff i've seen or liked. Some of this may seem really old or basic, but i'm not gonna apologise for that. I'm sorry, that's just the way i am (C) Homer J Simpson. Is it really arrogant to put something of mine in? And first? This guy must love himself!

Well to be fair this isn't mine, my old economics teacher showed it to me, but i've never seen an activity that works for pretty much every kid (and i teach abilities ranging from 16 year olds who can't tell the time to 11year olds who are happy solving quadratics) it's called Lobsters. Basically, split your class into teams tell them they run a lobster fishing business for the day. Options are simple-they start with 6 lobster pots, which they can choose to put in the shallow area or the deep area (or split between eg 5 shallow, 1deep). Simples, eh? If it's good weather, anything in shallow gets u £2, anything in deep gets u £5. No brainer, right, bung em all in deep! But if it's bad weather, anything in deep gets destroyed so they get no money for it (plus they lose that pot). Demand and supply dictates that anything in shallow now will be worth more-£6. Weather forecast says a 1/3 chance of bad weather, we decide this by rolling a die after the teams have placed their pots for the day. At any time during the game teams can buy more pots at £3 each. That's the game, kids r responsible for keeping their own accounts and r fined if they make banking errors, winners are the ones who make most profit. Some teams play it safe, some teams blow their budget buying loads of pots some go for a high risk strategy (with brighter kids i tend to offer a loan at a Rate of 10%per day). Try it, it is superb. Cheers mr Jervis!

Right, that was like the bag of Doritos u sneak while waiting for the taxi, onto to main course!

Over at futility closet a blinding old puzzle called petals around the rose-i love this because for some reason my weaker students tend to crack it before the more able ones.

Dan kicks summer school off with a great idea for getting kids to understand why we name lines and points the way we do-i've already nicked this and used it when teaching loci!

Not a maths site by any means, but there's an idea waiting for a lesson at begs ideas of break even points, and is an abject lesson for any poker player about not getting pot committed.

I don't know if this is cheating as the number warrior submitted this idea about applying probability to the math teachers at play carnival, but i loved it so it's going in here.

Slightly off topic, but from an education point of view this article in the ny times about soccer players struck home with me, deliberate practise indeed.

A fab article from freakonomics showing a relationship that initially seems counter intuitive.

This compass activity constructing Kenny from South Park is something kids in my school love doin (link now active!)

Project dragonfly is a great tool for making plan views and 3D visualisations of a home, but the presence of measurements makes it a great tool for working with area and perimeter.

The math hombre collects a few very good links to different kinds of math related media

This youtube vid begs all kinds of questions about rates of change as we see the world's fastest, well, everything!

SquareCircleZ has a good collection of math software but i've not explored it all yet.

And finally, this has very little basis in curriculum, but my kids dug the fact that a wombat has geometric doody.

Right, thanks for reading, hope I've not screwed it up too badly.

Wednesday, 8 July 2009

Bras Glorious Bras

Read a brilliant story the other day about the apparently famous Bra fence in Cardrona, NZ.

Apparently, people just keep leaving bras on it. weirdos.

After a little discussion related to how many we think there are (answer: 1,500 ish) we moved on to look at how this had happened. People started leaving them in December 1999 and they were taken down by the police (Boo!) in late 2006.

A basic discussion about rates followed (how many per year, month, week etc) and we figured that a rate of roughly 4 bras per week seemed sensible.

We then did a bit of sampling. In the pictures we estimated how long each section of fence was (they reckoned about the length of a radiator, so we measured this and it was about 2 metres).

So we figured that if we could count how many bras were in one section, we could use that to predict how long the fence was altogether.

After cracking this and making a couple of small scale models of the fence using sheets of A5 paper to represent a fence section (decorated with bras lovingly drawn by the kids) we looked at graphing it. I had started with the assumption that we'd make some data up and draw something like the graph on the left below, using the rate we'd calculated earlier. But many kids suggested it should look more like a curve, because as it has gotten more famous more people would leave bras (G.- "man if i was there i buy a bra just so i could leave it!") altought this was countered by S. who suggested that if she was short of bras, she could just pop over to Wanaka to help herself to some free undies. The burgeoning kleptomania of S. not withstanding, we figured G. was right and the rate would increase as more people heard about it (a little checking proved him correct - good man, this kid knows his celebrity)

So we got em to draw both and estimate how many bras there should be at a few points depending on the shape of the graph (each graph went up to 1500, and along from 1999 to 2006).

All in all a pretty varied lesson thanks to our very pecuilar friends in the Southern Hemisphere feeling the need to undress near a field.

God bless you New Zealand!

Saturday, 4 July 2009

Project: DragonFly

This website, which lets people design their own rooms is frickin awesome.

Once you get to grips with the intuitive control system (and your ancient laptop stops crashing), you can have a cracking looking room created in ten minutes, with the option for different views. The really nice thing is that the 3D view looks best, but the plan view allows you to get the measurements added on as well - in the words of Stinson, Legen-wait for it.......dary.

Having made our rooms, i was then able to provide people with a couple of shopping websites, asking them to buy the carpet, enough paint to cover the walls, and skirting boards long enough to go around the room. They were then allowed to spend whatever money they had left on furnishings (note to self: all kids want to buy a 8 bajillion pound flat screen TV if given the chance, even if it means living in a cold baren room). Kids who had struggled with ideas of area and perimeter suddenly thought it was the most obvious thing in the world, although some of them struggled to price things up (one group said they needed to spend £4000 on paint...)
As a functional exercise in why they might actually need to understand area and perimeter & why they might need to understand simple ratios (eg 1 tin covers 4 square metres, my room is 20 square metres...) it was hugely entertaining diversion from what it generally a very dry topic area.
Next up, Project: Plastic surgery, where we investigate how to make ourselves look like Brad Pitt on a budget of £24.35.

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.