Maths at SBHS

The Chopped Cubes

2011-11-14T20:28:00.001Z

We'd done a lesson or two on volume/surface area of a cube & cuboid.

We began Monday showing the kids this wicked GIF of a dude/dudette slicing a large cube:

We chatted about how to create it (some were familiar with online stop-motion software that i'd never heard of!) before one of them asked the question i'd missed:

"It doesn't work though, does it?"

I asked what he meant, and he just said simply that the guy/guyette ends up with 9 little cubes, but you couldn't stick them back into the original shape.

Why? (I said as i face-palmed, having intended to ask them a question about the surface area that would be near impossible for them to answer... *)

He said you could put them in a square, but not 3D unless they were all different sizes, but they seemed the same size.

A couple of the kids spotted that 9 isn't a cube number - we'd need to get rid of one little cube, or get another boatload from somewhere.

One suggested we could make a video that made mathematical sense, i thought this was a great idea and scrapped my lesson.

The kids split into teams and used card to draw nets and build themselves big and small cubes.
One team even went to the trouble of having stages of increasingly small shapes (eg actual size after 1 cut, them after 2 cuts etc) whereas most just went for 1 big cube, and 8 small ones.

We plan to upload and create our own GIFs tomorrow, will post the results when we get done.

Really excited me this one, cos it hits loads of maths, is pretty creative, and came entirely from the kids.

*I was going to ask how much larger the total surface area of all the small cubes was compared to the large cube - could they answer this or am i just being thick?!

Blood Spatter

2011-10-10T19:36:00.000+01:00

Spent some time this week after watching season 1 reruns of Dexter:

From October 10, 2011

Showed the kids this, asked what the hell they thought he was doing.

I'd also seen this infographic over summer:

And we chatted about why a 10 degree angle of impact would leave a different shape etc.

Kids correctly surmised that it was related to the height/width of the droplet, so i dropped the formula on them, and we did some investigatin'!

After drawing some random blood droplets and swapping with neighbors, we jumped in and messed around in Geogebra creating the activity below (with some help from me in terms of the input aspect):

BloodSpatter - GeoGebra Dynamic Worksheet

BloodSpatter

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
OG, Created with GeoGebra

Most entertaining if slightly bloodthirsty, led into using arcsin etc in trig very nicely.

We also created crime scenes that we could analyse, by drawing huge drops of blood on paper and tacking them to the walls, then going all Dexter with bits of string!

This basically works out the angle of elevation from the surface - not sure how we could find the "horizontal" angle to the surface though... Any thoughts?!

Online Dating # 2

2011-01-16T13:02:00.008Z

(Again, data shamelessly ripped from OK Trends.com)

Started with the Question:

Which of these options would you rather be true:

people either think you are beautiful or cute

people either think you are beautiful or ugly

people either think you are cute or unattractive

people either think you are beautiful or unattractive

We voted, with unsurprising results (R asking if he could choose "unattractive to everyone" as an option aside..)

Flashed over to some data from OK Trends:

Nice scatter, posed a couple of questions - and ended up identifying a couple of points with the same attractiveness but wildly different numbers of messages received.

Invented two sets of stats about these two women, and asked kids to give me some possible ratings they could have had to give them an average rating of "7" (for our purposes, the average was the mean):

Started talking about the differences between the two sets of ratings - pleasingly, words like "range" started coming up with only minor prompting.

They decided that by and large, the first girl had a larger range (the boys also decided by and large that they preferred the first girl!)

We then talked about what we could do to examine the "spread" of our data, and I gave them some data that we constructed histograms from (always surprised how difficult our little ones find histograms!)

One of the kids piped up that the first graph didn't make sense, that she should get more messages as basically no-one finds her unattractive.

We agreed, but then again, more people thought the second girl was super hot.

We compared a few other comparable women from the site:

and saw the pattern repeated.

We formed a hypothesis: you're more attractive if men argue about you.

again, from the data set given, the kids this time found the standard deviation of each woman of a similar level of attractiveness (i.e. all rated 7), and compared this to the number of messages received per week (the thick grey line is the average messages per week.

and came to the conclusion that if everyone thinks your hot, you get less messages, if there's disagreement, you get loads.

Hypothesis confirmed!

We didn't really get time to head on to the equation that OK Trends proposed, which explicitly shows that some types of ratings detract from your message possibility, which was a pity (as i say, histograms, damn!) but a good, eye opening lesson drawn (largely) from the real world that had kids arguing, which i generally take as a good sign!

The lesson PPT and Handout can be found at the links.

One Billion

2010-11-14T16:22:00.005Z

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.

The Lego House

2010-09-04T18:32:00.005+01:00

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___!

F Question #5: The Comic

2010-08-13T20:59:00.003+01:00

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.

F Question #4: Sulphur

2010-08-08T19:49:00.003+01:00

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"

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...

Longest Shot

2010-08-07T15:28:00.009+01:00

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?

Outlying Abed

2010-08-06T16:03:00.003+01:00

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?

F Question #3: Election Draw

2010-08-05T17:58:00.005+01:00

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

By cutting cards.

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)

F Question #2: Millionaire

2010-08-04T16:06:00.004+01:00

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...

2010-08-04T15:28:00.003+01:00

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.

Wheel Spin

2010-04-20T16:57:00.004+01:00

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.

How many balloons?

2010-03-14T20:00:00.005Z

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...)

Dodgeball

2010-03-02T16:39:00.004Z

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.

Online Dating

2010-02-15T18:18:00.004Z

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

2010-02-15T17:57:00.005Z

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....

2010-02-15T17:52:00.003Z

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.

What the... ?!?!?

2009-10-07T18:07:00.003+01:00

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.

But.

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?

Bidmas Shooter

2009-10-03T17:01:00.001+01:00

Discovered a nice, easy to use game generator at ClassTools.net 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

Negative times negative

2009-09-30T22:10:00.004+01:00

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...

The quietest lesson

2009-08-18T15:12:00.000+01:00

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...

Carnival Of Maths 55 (i think...)

2009-07-30T14:25:00.004+01:00

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 swoopo.com- 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.

Bras Glorious Bras

2009-07-08T17:01:00.009+01:00

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!

Project: DragonFly

2009-07-04T10:34:00.005+01:00

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.

Circumcentre and Orthocentre

2009-06-28T19:39:00.007+01:00

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).

What can you do with this?

2009-06-25T23:49:00.008+01:00

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.

Is this wasting time?

2009-06-24T17:43:00.006+01:00

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

2009-06-24T17:21:00.003+01:00

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?

2009-06-20T15:09:00.005+01:00

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.

Yo

2009-06-20T13:50:00.006+01:00

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.

As Promised...

2008-07-01T21:30:00.003+01:00

Look at me. Actually following through on something I said I'd do! It's as if I'm organised.
Here the video requested. I'll leave it up for a couple of weeks before i take it down.
Enjoy.
And I must say, the last minute is awesome. Particularly James smashing Hardy on the head.

Hola. Last chance for revision

2008-05-23T11:13:00.001+01:00

Hi team. If anyone has any panic attacks about anything, leave me a note in the comments and i'll try to help asap. Obviously, jess, this only applies to panic about maths related things, not your usual all-round stress.

OG.

Make your own maths comic strip

2008-03-26T14:27:00.003Z

Found this tool online at bitstrips.com to make your own comic strips - have a go!

Easter

2008-03-13T21:47:00.003Z

Howdy Pilgrims.

If you've come this way looking for Easter revision, you have come the right way.

Well, sort of. You need to follow this link

http://www.geocities.com/piebucket/mathnasium.htm

Easter revision is the first file. When you click on it, it'll ask if you want to Open or Save it.

Mr OG's top tip of the day is to save it!

Oh, and a lolly for the first commenter who can tell me what the sum on that dude's hands equals.

Tenuous Mathematical Link Of The Day

2008-03-13T21:45:00.002Z

If, like me, you find it unbelievably irritating to watch US TV shows where spoilt rich kids tell each other to "Do the math" when any sane person could tell that they should be saying "Do the maths", you'll be delighted by Los Campesinos new single, Don't Tell Me To Do The Math.

If you are not like me, and do not find this unbelievably irritating, what the devil is wrong with you? Song's good though...

Algebra Week ( or two..)

2008-02-05T21:17:00.000Z

Okay - I'm planing on putting some short revision videos up here covering the basics - starting with algebra.

In theory this is algebra week, but as I'm shockingly organised, it may well turn into algebra month by the time I get finished.

Keep checking, if there's any topic you want to see, leave it in the comments.

OG.

Algebra1 - simplification

Change Of Password

2008-01-20T13:02:00.001Z

A reminder to you all that if you want to use MyMaths from February 1st the password changes!

From Feb 1st:

Username: sowerby

Password: seven

Cheers.

Straight Line Graphs

2008-01-17T16:10:00.000Z

Hola.

Here as promised is a bit of help on finding the equation of a line if any one is struggling.

Leave me something in the comments if you have anything to say - did it help, was it useless, whatever.

OG.

2008-01-16T18:04:00.000Z

Hey up. For any of our year 11s thinking of A-Level and wanting to practice any of the additional maths stuff we've been looking at, heres a short video showing you how to find some online resources that are ace! It's fairly quiet, but if you listen carefully it's narrated by some sort of genius maths teacher with silky pipes.

Tougher Than Mr T

2008-01-03T12:07:00.000Z

Not sure this is appropriate, and i'm equally unsure whether i should be appalled or amused by this, but apparently, I could take 21 five year olds in a fight with no worries whatsoever.

Oh yeah. I'm hard.

News

2007-12-13T19:25:00.001Z

Solutions Q1 - 10 are now up and running.

The Moby Equation

2007-12-13T19:23:00.001Z

This amused me.

Check to see if your favourite band is a sellout

The Moby Equation

Obviously, 'Towers Of London' fans need not even bother checking this.

Q10 - Pythagoras & Perimeter

2007-12-11T18:09:00.000Z

10 One of my Weasels is called Pythagoras (Yes that is another hint). I make him a racetrack that looks like this:

(imagine a 30cm x 15cm rectangle with a diagonal line across, then imagine I know how to put that image into this blog)

How long is the racetrack altogether (including the diagonal)? Answer to nearest centimetre.

(4 marks)

Perimeter of rectangle = 90cm.

Diagonal = 33.54.. Length = 124cm (nearest cm)

Q9 - compound Percentage change

2007-12-11T18:07:00.002Z

9 One of my weasels (Eric) got fleas. He had 300 fleas, and they spread at a rate of 4.5% per day. How many fleas did Eric the weasel have after 9 days? (3 marks)

ANS = 300 x (1.045 to the power 9) = 445.82... :- 445 fleas.

Forming and solving equations

2007-12-11T18:07:00.001Z

8 My friend John has w weasels, I have twice as many as him (2w), and my brother has 2 less than him (w 2),

a) Write an expression for the total number of weasels we have.

b) If we have 98 weasels altogether, how many weasels does John have?

(4 marks)

a) Total = 4w - 2

b) 25 weasels.

Q7 - Circles & circumferences

2007-12-11T18:06:00.000Z

a) 'Pi' the weasel (Yes that is a hint) likes to play in a wheel with a diameter of 15cm. What is the circumference of the wheel? (Give your answer to 2 significant figures)

b) Another wheel they like has a circumference of 40cm. If the wheel rolled for 30 metres, how many times would it have turned?

(4 marks)

a) Circumf = 15 x 3.14 = 47.1.. = 47 cm (2sf)

b) 3000 / 40 = 75 times

Q6 - substitution & changing subject

2007-12-11T18:05:00.000Z

6 Here is an expression: t = 4w 3c

a) Find the value of t if w = 5 and c = -7

b) Make w the subject of the expression. (it should look like w = )

(4 marks)

ANS

a) 41

b) w = (t - 3c) divided by 4

Q5 - Solving Equations

2007-12-11T18:04:00.001Z

5 This has nothing to do with weasels, but I've used the letter w anyway. Solve:

a) 5w + 10 = w + 2

b) 12 5w = 8w + 20 (4 marks)

a) -2

b) -8/13

Q4 - Pie Charts

2007-12-11T18:03:00.004Z

4 I decide to draw a pie chart to show the kind of food my weasels enjoy.

a) 30% of my weasels love Cheese (as do I). What angle would I draw to show the Cheese loving weasels on a pie chart? (Remember a pie chart has 360° altogether)

b) The pie chart has a slice with an angle of 24° showing the weasels that enjoy eating batteries. If I have 90 weasels, how many enjoy tasty, tasty batteries? (Hint: think what fraction of the circle 24° is!) (5 marks)

a) 108 degrees

b) 6 weasels

Q3 - Probability

2007-12-11T18:03:00.003Z

3 My weasels are likely to bit me, scratch me or ignore me. The probabilities are shown below:

Bite Me 0.23

Scratch Me _____

Ignore Me: 0.09

a) What is the probability one scratches me?

b) What is the probability a weasel either bites me or scratches me?

(4 marks)

a) 0.68

b) 0.91

Q2 - Splitting into a ratio

2007-12-11T18:03:00.001Z

2 I have 32 weasels. If I decide to give them to my mom and dad in the ratio 3:5, how many weasels would my mom get?

(2 marks)

ANS =Ma gets 12 the lucky lass.

Q1 - Ratio & Percentage

2007-12-11T18:02:00.000Z

1 The ratio of cats to weasels in a vets surgery is 4 : 1. What percentage of these animals are weasels? (2 marks)

ANS = 20%

New Start

2007-12-11T18:00:00.001Z

Ok guys, previous comments and posts have been removed for now, as this becomes revision central!

I'm gonna put the questions for HW here, answers/questions in the comments if you want.

I'll put the full solutions up here later this week.

OG.

This is a test!

2007-12-02T10:14:00.001Z

just testing to see if i can e-mail in posts. If you can read this, i can...

Howdo.

2007-12-01T15:51:00.000Z

Hello all. Mr O'G here saying welcome I guess...

thought i'd start by linking you to the Sowerby VLE, just in case you can't remember how to get there!

Use the blog to post comments on what you've done, found easy, hard, or just anything that interests you. Obviously, keep stuff appropriate please guys!

Oh yeah, apologies for the colour scheme. Any suggestions for an alternative will be greeted with the usual combination of gratitude, sarcasm and fury.

Good luck!