Sunday, 14 November 2010

One Billion

Some things are made easier/better/more fun by contexts, games, activities.
Some are just inherently interesting.

Ask a group of kids how long it would take to count to a billion and they go crazy...

After discussing how big a billion actually was (for the record, it's enough to buy every single person in our town a brand new ford Fiesta, and if you stacked a billion BK whoppers on top of each other they'd go 10 times further than Venus) I challenged the class to find out how long it would take to count to a billion.
They were off!

Almost every group started by simply timing how long it would take them to count to 10, then multiplying by 100,000,000 (getting around 300 million seconds as an answer)

They were pleased until we looked at it more deeply.
I asked "What numbers take longest to say?"

seven, eleven, seventeen all came back at me.

One chimed in that 7 was the kicker - the only 2 syllable single digit number.

I asked which number between 1 and a billion would take longest to say - the groups decided on 777,777,777 as it contains a whopping 23 syllables (i had said it contained 18, and the kids to me to the cleaners saying i'd forgotten we'd need to say the words million and hundred!)

We timed a few kids saying this number on its own and they ranged between 3 and 7 seconds.

One pointed out that it had taken longer to say this single number than it had taken her to count 10 separate numbers.

So what's my point? I asked.

We aren't taking a fair sample are we sir? was the spectacularly on the ball response.

This said, i asked the groups to get back together and think of away they could take a fair sample and get a more accurate estimate for the time it would take.

A couple of groups shared a great plan to keep their original time for 1-10 (3 seconds)
but also take another 2 samples - they timed
777,777,767 to 777,777,777 (which took a full minute)
and also took a sample between
222,222,222 to 222,222,231 (which took 40 seconds)

They took an average of their 3 times (short, medium, long) and decided the average block of 10 number would take about 34 seconds, estimating 3,400,000,000 seconds (or 66,666,666 minutes) to count to a billion.

Their comment was this was fairer as most bunches of number from 1 to 1 bn would have 9 digits, so to just take the first 10 and last 10 would skew their data. Delicious logic.

After taking a few different solutions from the class (our average guess was 3 bn seconds) we then though about whether this was possible or not.
That take years some kids said. I agreed!

In changing this value to years, we estimated that it would take 95 years to count from 1 to a billion.

Pointless, contextually irrelevant, but a fab investigation.

This was then followed with a discussion of freaks - namely freaks who can talk at ludicrous speeds.
As far as I'm aware, Fran Capo is GWR holder for words / minute (667) and we amused ourselves watching this clip (from about 1:40):


and deciding how many years she would take to get to a billion.
(we googled that the average person speaks at 120 wpm, so we think she'd only take 17 years!)

This intrigued us, so we watched a couple more vids that we found at this link and tried to see how fast these guys could get to a billion.

Nice, easy, accessible and fun lesson with aboslutely no motivation aside from playing with numbers.







Saturday, 4 September 2010

The Lego House

After watching this video of the weird and wonderful James May's LEGO project:


We thought we'd investigate.
The first time i'd done this, I asked "how many bricks will it take?"
The second time I asked "How much would it cost?"
This time the problem was "Pretend I've got 300 grand. Can I afford to do it?"

This last question was infinitely more engaging than the first two. No real difference to the second one mathematically, but way superior in getting the guys hooked.

We decided we'd just build the "shell" of a house - i.e. four wall and a roof.

The kids asked all the right questions:
how much is LEGO?
how big is the house?
how big is a lego brick?

We travelled to the LEGO site and saw a box of 221 bricks for £10.
I happen to have some lego in the classroom anyway, so some kids measured the different bricks and decided the average measurements were 5cmx3cmx2cm.

The rest of the kids measured the room (7mx7mx3m) and decided the house would have 4 rooms down, 4 rooms up, so said each panel would need to be at least 14m x 6m with a 14mx14m roof.

There was some discussion about how thick the walls would need to be (would it just be one row of bricks, or several? should they be hollow or solid?) and we settled on solid walls, 40cm thick.

And we were off.

A few interesting different approaches - I'd worked out how many bricks were needed by fitting them along the measurements (so think for 14m along, would need 280 bricks etc), which is the route many groups took. A couple spotted a shortcut (that i have to admit i hadn't even considered - well played guys) and simply found the total volume of the walls and roof, and divided this by the volume of one brick. Love it when they get one over on me!

The kids were delighted to find that i'd be about £20,000 over budget, mocked me (although some very kindly offered to let me have their old lego) before one astute young lady pointed out that i'd probably want windows in the place, so if you subtract the legos for the windows, i'd come in just under budget - cheers L___!

Friday, 13 August 2010

F Question #5: The Comic

What is the most expensive comic ever?
Most went for a batman comic (this was recently after most of them had seen The Dark Knight...) and were surprised to hear it was Action Comics.

Guesses as to why?
"first one in colour?"
"first one with a lesbian kiss?" (I just love this kid.)
"last one hand-drawn?"
"Did it have a wombat in it with rainbow coloured poo?" (Err... No. Therapy required?)

Most kids hit on the idea that it was the first of something - M___ finally settled on first Superman comic.
How much?
We used a form on Google Docs for this one, and got kids to input a lowest bet and highest bet in a form.
No-one was anywhere near the $1,000,000 it went for. Seriously, not even close, and till i showed them the story a lot were unconvinced.

"How much did it cost when it came out?" ($0.10)
"When did it come out"? (Wikipedia tells us 1938)
"Yeah, but how much would that be now?" (Great question, we took a few guesses - all were too high, mine included. Went on DollarTimes which told us it'd be about $1.50)

So if i'd bought it in like 1938 ... "
(This devolved into a spirited debate about the possibilities of this: "you weren't born then..." "you'd need to have a time machine" "if he had a time machine he could just go get it now.." "my time machine broke down next week" - this made me chuckle for a while. I have stolen this gag, and passed it off as my own since!)
"Yeah, but what if i'd bought it now...How much money would i have made?" (We worked out he'd get 666,666 x his investment. We had a bit of a conversation trying to work out how much first gen IPods etc would be worth given the same inflation.)

Three days later i had kids in my room at lunch time looking for comics just about to start a run so they could buy first editions and make a billion pounds.


Sunday, 8 August 2010

F Question #4: Sulphur

What happens when you inhale Sulphur Hexafluoride?

Guesses:
"you die?"
"it gives you rainbow coloured poo"
"does it make you high?"
"it makes you all squeaky"

A:

What did the class do with this?
"Show it again! Show it again!" (We did. We laughed again. We did impressions. Our throats hurt.)
"Is that what they use to disguise people's voices on Crimewatch?"! (I think this was genuine...)
"So what would a balloon filled with that do?" (Class response was split here: some said it would just sit on the ground, a couple said that it wouldn't even inflate. I assume the first group were right, but not sure - any ideas?)
"Would anything denser than air do that? Like, if it was ten times denser would your voice be really deep?" (I do not know. We thought it might be dangerous though...)
"What does dense mean?" followed by "how dense is air?" (Speaking to our science faculty, about 20 kids hassled them over the next 2 days asking if they had anything denser than air that they could inhale as an experiment...)
After explaining that density more or less mean how tightly packed things are, mass per volume etc, one kid dropped the hammer with
"so, is hot air less dense than cold air?"
followed by another kid "yeah, that's why hot air balloons fly!"
Is it weird that i had never actually considered that hot air is less dense than cold air? Everyday is a learning day and all that...

Saturday, 7 August 2010

Longest Shot

The plan:
show this spectacular Basketball shot:

Then show this one.


Argue, take bets about which one is longest.

Drop some data on when requested (hopefully people will instantly say that the 2nd one is farthest as it has a longer horizontal distance).



I'm planning here to do a couple of scale drawings so we can measure to see which one is the longest before dropping the pythagoras hammer.

What is delicious here is that in the youtube description for the first video, they have actually done the pythagorean calculation - so i can show that as confirmation.


The great thing about the description here is that it takes into account the inaccurate nature of their measurements leads naturally into some work on estimates and boundaries - i've chosen 160 feet as the horizontal distance for the first shot - if i'd chosen 150 feet (the lower bound) would it still be farther?

Got kids to send me their favourite goals from Pro Evolution Soccer 2009, took screen grabs of these, turned em into a worksheet, asked the simple question - whose was the best shot?


Friday, 6 August 2010

Outlying Abed

I'm in love with "Community". Few shows have made me laugh as loud as this all year - if you could drop Ron Swanson & Tom Haverford into it, it might be the perfect comedy.

Watching the 4th episode, then, thrilled me as it gave me an excuse to roll this baby out in class - We we're looking at data handling, so were all over averages and charts.

We watched this, and asked the kids for some interpretation.

I paused this at the point where Troy slides out (heartbroken that there is no butt stuff...) and asked the kids if they agreed with the professor's statement "the longer they take, the harder they break" - most disagreed and said Chang's initial flip out was way more than some of the others.

I'd made up some data from the study about when they break (Name,Minutes to Flip, Force Of Flip - ranging from Snr Chang to Troy), so I then asked the class to analyse it. Some drew nice bar charts, some found what the range of times was, some found the mean/median time. (This in itself was interesting for me to see what kind of analysis they performed.

Then we hit play and saw Abed ruin the study. I asked them now to add him into their analysis. The guys with the bar charts went nuts, cos he flew way off the top of their scale. The guys who'd found a mean naturally ended up with a way higher value. The guys with the median basically didn't notice much change.

We drew conclusions (My favourite being "don't find the mean if you've got weirdos")

The line at the end ("He's ruined my study...") brought the most interesting discussion.
This time last year, we had an almighty bust up when discussing correlations when G___ suggested that taller people weighed more. Of course, one of our guys said "no i know a really big guy who's well skinny.." "I know a dead short fat dude..." and they suggested that this proved G___ wrong.
So one of the guys involved in that immediately piped up with "That last dude is an outlier!" (I wish i'd had the next 10 seconds of footage, where the professor starts screaming "you've ruined it you stupid outlying piece of data.." to give him validation from Hollywood rather than just from little old me...).

This was good, but didn't kill like i'd wanted it to. Any thoughts on fixing this?

Thursday, 5 August 2010

F Question #3: Election Draw

How was an election settled when the votes were tied last year in Arizona?



What did the class do with this?
Before the answer:
"A wrestle"
"Yeah, both the [candidates] got a spear and a leotard..."
"Did Simon Cowell decide?"
"did they ask the guys who didn't vote for either to pick their favourite?"

Post Answer:
"Who shuffled? Cos you can rig a deck..." (interesting point about fairness. I told them that a judge shuffled!)
"What cards did they get?" (I had no idea. We ran a simulation with G__ getting 3H and demanding a do-over cos he was sure he'd lose. He did.)
"Was the Ace high or low?" (Again, i'd no idea, but the class were adamant that it should be low.)
"I was playing a game and cut cards once and got the rules of bridge..." (not sure what to do with this, but it made me smile)
"Surely they did best out of 5 or something. You can't leave an election to chance" (Irony dripping off D___'s every syllable here. Immense. I did steal this and ask what the odds of winning were if you lost the first 2 draws. Answers ranged from 0 to 50-50)


Wednesday, 4 August 2010

F Question #2: Millionaire

What month are most Millionaire's born in?

September.

What did the class do with this?
"Oh my god I'm gonna be a millionaire!" (J__, realising he was born in September)
"Why?" (opened to the class. they reckoned it was cos you'd be the oldest in your year at school, so you'd be bigger and more confident. Liked this very much.)
Following on the previous: "So are there like none born in July then?" (sadly i did not have this data, but a great follow up question.)
"What will I spend my first million on?" (J__ again)
"Yeah, but how many is most? Cos if there's like 10 a month, and September has 11, that doesn't really mean anything does it?" (Magnificent question. Wish I'd thought of it. A quick bit of research tells us that Forbes reckons 42/380 millionaire are born in Sept. A few wanted this turned into a percentage - 11%, a couple found that there were only 30 per month for the remaining 11. Nice.)
"Is a millionaire the same everywhere? Cos I read that in Zimbabwe you're a millionaire if you have 20p" (I called this rubbish, but with the hyperinflation over there 20p was worth more than a million Zimbabwean dollars)
"Awesome I'm going to Zimbabwe with a fiver I'll come back and be rich!" (oh if only life were this simple...)
"I might buy you a new car sir, cos yours is rubbish" (The benevolent J_ again)

Project...

One aspect of my teaching that I have embraced to the point of psychosis this last couple of years is finding ways to bring bizarre, weird, interesting and unusual things from our world into my classroom. I recently read a quote via the soft skills conference about creating a positive classroom atmosphere that said "The biggest thing is that I find ways to give kids space to be weird".

Couldn't agree more. What started as a random idea or two occasionally dropped into lessons has become an insane, unquenchable thirst for ridiculous amounts of trivia. Basically, every lesson question f on the starter tends to be something not at all tied to maths. The kids are encouraged to bring a mathematical understanding to it, but they are not required to. This is aimed at a 5 minute class discussion that can go basically where the students want it to.
(It has in no way affected our ability to cover the scheme of work...)

So I'm going to spend some time this month sharing a couple of "f questions" that my kids have used this year.

F Question#1: The McFarthest Spot
f) What, in the USA, is the McFarthest Spot?

South Dakota.
(the place furthest from a McDonalds)
If you live in America's lower 48 states, you are never more than 145 miles from a McDs by car.

(There is a great counter to this in a map showing the distribution of McDs in Australia)

So. What did the class do with this?
"what's it like in England sir?" (I did not know. This is good, they seem to believe i know everything... I remind them several times that i am not smarter than them, just more experienced. They guesed somewhere in Devon from looking at a map would be the farthest)
"Mr G___ said that the cost of a big mac tells you how poor a country is..." (apparently this is true, and the big mac index was something i learned about that day)
"Once i went to McDonalds and ordered a chicken tikka masala just to mess with them" (this kid rocks. When asked what he did when they told him that they didn't serve CTM, he said he looked, debated for about 2 minutes, then asked for a Chicken Bhuna. Legend.)
"so how far is it then?" (this confused me, and i was about to do that teacher thing where you can't think of anything to do but repeat what you had previously said but slightly slower and louder... Until another kid pointed out that he meant in terms of time.)
"Is that further than from here to london?" (Google maps tells us that it is not, but it is not much less. This brought genuine 'oohs' from the class, who can't imagine being a capital city apart from the golden arches)

Something maths brought in (but only when the kids asked for it - i guess in some ways this would be WCYDWT-lite) but a positive start to the lesson which made me laugh at least twice.

Tuesday, 20 April 2010

Wheel Spin

One of my classes have just sat a pretty hard exam and are a bit disappointed with their results.

One question they all did poorly on asked:
A wheel with a diameter of 20cm rolls for 30m. How many times did it spin?

Frankly, they didn't know what the hell they were expected to here, and several just did 30 / 20 = 1.5

So we decided to revisit this but let them control it.

Firstup: show this video.
Ask class: How fast is the car going?
Take bets Vegas stylee.
The clip lasts about 5 seconds. Several kids asked how far the car went.
It told them i wasn't going to tell them, but that i would tell them that i have 18 inch wheels on my car.
I put the clip on loop.

Because they were now looking at the wheels, one of them noticed that there a "white thingy" as he so eloquently put it on my wheel. This was true, i'd stuck a piece of tin foil on the front driver tyre.

One said we could count how many times the wheel actually spun, but we tried this and it was too difficult to see.

"Sir, can you slow the video down?"

Hell yes I can, god bless the VLC gods, this was nothing more than a click away.

We counted that the wheel spun about 20 times in the clip.
(one pair of pupils just counted one seconds worth, which i thought was clever as the first and last second of the clip are pretty hard to count.)

There was some dispute about this, so half the kids worked this as 3 spins per second, half worked as 4 spins per second.

Which brings us back to the exam question, as the kids are now asking how far do we go every spin? Several notice that this would be the circumference of the wheel, and we run on.

This all led us nicely into miles per hour (although we had to google how many inches there were in a mile)

The kids managed to calculate the exact speed of the car (i had a video of my tom tom showing current speed to prove it!) and i think now feel confident that they can deal with "rolling" questions.

Interestingly, kids at 3 spins per second came out about 10 mph, kids at 4 spins came out at around 13 mph which led us to a nice little debate about errors in measurement.

At this point, students felt happy that if the car had rolled for 30 feet, they could find out how many times the wheel spins.

Then we trotted out to the car park, measured some wheels and worked how how much faster Mr C's car would be going than mine if his wheels also span at 3 spins per second.

Sunday, 14 March 2010

How many balloons?

Watched "Up" the other night.
First of all, if you haven't seen it, i'd recommend you stop reading this, go out and watch it. Stunning.

Got me thinking about the physics involved, so my opener for year ten this week was "How many balloons do you think it would take to lift you?"

Got the kids to make a few guesses (it was my birthday last week, so we actually had a helium balloon in the classroom - let the kids do a few experiments to test - that balloon could support a pencil and an eraser!)

Then got a few kids starting to ask the important questions:
how much helium can it hold?
how much could it lift?

we took it as a sphere, and found the volume of an average balloon (15cm diameter), converted this cubic cm to litres, before we hit "HowStuffWorks" and found out that helium has a lifting power of 1g / litre.

Now we're cooking!

changed our weights into g (we reckon about 50,000g average per kid?) and worked out how many balloons it would take.

Fun lesson.

Then one kid dropped the question that'd been bugging me.

How many balloons for the house in UP?

Google tells us that the average UK house weighs around 450t, and we work out that it'd take about 30 million balloons to lift one.

Pete Docter (Pixar): " we calculated it would take between 20 and 30 million balloons in real life, we used about 20,000 in the film"

How much do i love pixar that they would take that into consideration?!?!

We then went backwards and worked out how big the balloons would need to be to lift a house if 20,000 of them could lift a house (we think about 3.5m diameter). One of the kids tells me you can actually buy them this size from Army surplus stores in England.

Interesting! The problem i now have is that my kids are determined to buy a load of balloons and orbit the school (we have not considered the cost of helium to be fair...)






Tuesday, 2 March 2010

Dodgeball

Asked the kids today what the biggest ever game of dodgeball was.

Took some bets.

Answer? 1200 people, this year in Canada.
Showed them this video:

Talked about assumptions (600 per side?) and then showed them a photo of our gym.
Could we do it in there?

W. asks: is our gym the same size?
Someone tells him not to be stupid, theirs has 2 indoor courts, ours only has 1.

One asks if for the sizes.
Showed them the measurements of the butterdome vs our gym (it should be said that i pretty much made these up based on the measurements of two 5-a-side football pitches).

Kids noticed that the area of our gym is roughly 20 x smaller, so assumed we'd be able to 1200/20 = 60 people in.

C.: But sir, we have like, 80 people in there sometimes for PE.

At this point, i think i'm done, let them run with it.

Some worked out that the record breaking attempt allows for about 8sq metres per player.
Some worked out that there'd be less than 1 player per sq metre.

Question: if we wanted to fit 1200 people in our gym, how many would we need to get in every square metre?

2.5 people per sq metre seems do able - we mark out a square on the floor and try it.

Kids reckon we can fit more in, so we spend a minute seeing how many we can fit in without falling over.

A few point out that we could do this, but it'd be ridiculous - no one wants to be that squashed.

So in pairs we mark out our comfort zones on the floor, and work out the area we'd be happy with.

I pair up with J. and we reckon we'd be ok with about 0.4 sq metres.

We then average this out (it comes to about 0.3 sq metres, apparently i have a bigger social bubble than the kids!) and say, right, if we give everyone this,
how many can we fit in the gym?

Still about 1600 - we could hammer this record, which i sent the guys off to their next lesson (PE) to discuss.

Monday, 15 February 2010

Online Dating

Spent some time obsessing over the OK Trends website (seriously, how awesome is this thing?) and had a good laugh with my kids going over the findings.

Started with a minute or two getting kids to describe their profile photos to the class (this ended up with two kids totally unable to describe their photos, so recreating them for us - nice.)

Then asked them to put the photo types in order of success with women:
with pets, travel, with friends, doing something interesting, drinking, showing off muscles, outdoors

Most kids went with the photos with pets as least likely to be successful ("it's a bit gay isn't it sir?" was a common response to this - gay in the now OED acceptable "bad" rather than "sexuality" meaning) and were stunned when i told them that this was the the most successful.

They disputed it.

Naturally.

So i gave them some data about average responses by photo type, and gave them 5-10 minutes in pairs trying to prove me wrong.
Most went straight for the mean, that didn't work, so they hammered the median and mode, some tried range but realised that this wasn't any good, till we had to accept that pets were the way forward.

One of them (god bless kids natural instinct to try to prove me wrong) point out that yeah, even if a photo of a person with a pet gets an average of 9 responses, that only means it's the best out of these types of photos, what if just a bog standard photo gets 15 responses?

Glorious (and correct suggestion), i was almost apologetic to blow this out of the water and show him that the average for all photo type was only 5.8, so pets were waaaaaaaaaaaaaaaaaay above average.

They were most surprised to learn that showing off muscles was #2 with a bullet. ("but don't you look like a total poser sir?) so we checked this out too, trying to figure out at what age shirt off becomes a terrible idea ("you wouldn't have one with your shirt off though would you sir"? they were incredibly relieved when i told them i would not).

Running through this (graphing, finding a rule - don't take your shirt off if you're >35) led one of the boys to complain that the girls were getting off rather lightly here.

We finished with a look at the differences between male and female photos (taking the form of a stacked percentage bar chart) and almost every kid left trying to (a) understand what flirty-face was and (b) trying to do one on the way out.
Loads of stuff packed in there, really functional rich activity.

I'v attached the powerpoint of the lesson in case anyone fancies using it.

How to make a Histogram on Excel

Had been struggling to create a histogram in Excel, and desperately wanted to be able to do one for some self assessing materials for my year 11s.

Finally cracked it, was fairly easy so i thought i'd share it here.

The example above shows a simple one.
The coordinates in red are the key ones.
simply put they show the start and end point of each bar (your x coordinate) and the frequency density (your y coordinate)
Key here is the extra coordinate in between bars - eg 3rd one down (10, 0) - this makes the bar return to the baseline like the kids would draw it (otherwise you just get a "skyline" type chart, which is pretty sweet in its own right...)

You then select these 2 columns of data and plot a scatter graph.
Select an individual point of data, right click on it.
Click on "Format data series", and in the patterns tab, turn on the LINE and turn off the MARKER.

Voila, histogram.

When I selected my histogram, i set the red coordinates to reference the values in the table, that way it makes it very easy to create in future.

Also, it allows the kids to really easily see how a histogram is built up, and self assess themselves at the same time (as well as being amazed at how the graph is drawn...)


Returns....

It has been a staggering amount of time since i've written anything.
What can I say, mock exams, new job stuff and basic S.A.D. have all been barriers.

Here where i'm at.

1. oozing confidence about the chances my year 11 have of hammering exams
2. increasingly obsessed with peer-assessment/peer teaching
3. intrigued by the idea of non-exam board sponsored 'rich tasks'

1 & 2 going hand in hand at the moment.

will post more in the future.

Knackered like and glad of a week off.