Wednesday 20 July 2011

Lobster Fishing

It's almost the end of term for most of us, and pupils start to expect "fun lessons" instead of lessons involving actually learning anything. Of course, showing a DVD is unacceptable, unless it's related to your subject. When I was at school not so long ago, we always watched films on the last day of every term, except for in maths, which would generally be a normal lesson. We were always outraged!

What you need on the last day of term is something that is undeniably "mathsy", but still seems like a treat. For me, that absolutely has to be Lobster Fishing. I can't remember where I got hold of the PowerPoint and worksheet that I use for this activity, but google it and you'll find loads of different versions, so you can pick and choose.

It goes like this: pupils, working individually or in pairs, are given six lobster pots at the start, and £50. They have to decide where to place their pots: in shore or off shore. Depending on the weather (decided by rolling a die) the two locations give different amounts.

If you think I haven't explained it very well, that's because there are loads of different rules you could add in and loads of different ways of doing it. You can adjust how complicated it is to suit the class.

I used this activity with year 8 set 1, and they absolutely loved it. It very nicely fills a whole hour without anyone getting bored. You can spend some time at the end reflecting on the best strategies to use. You can get them to work out the EMV for each strategy if you feel like going into game theory (somehow I always feel like going into game theory, because I love it. My pupils love it too now!)

So if you're stuck for ideas for the last day of term, give lobster fishing a go. Then let me know how it went :)

Emma x x x

Sunday 10 July 2011

Fractal Cuts

This week's resource of the week comes from Kangaroo Maths. It's a lovely practical activity which gives the pupils something to take home and show their parents, which I think is important.

It's Fractal Cuts! The very easy way of making a 3 dimensional "fractal" out of a sheet of A4 card (or paper). Google "fractal cuts" and you'll find it.

I used this activity with a class who are working at level 7, but I think it works for a huge range of abilities. I started off the lesson by showing them loads of pictures of fractals, and told them what they are in very simple terms: pictures where if you zoom in again and again, it still looks the same. Then I got them to draw a fractal (the Koch fractal, but of course I didn't call it that to them, that would be asking for trouble!) I used questioning to get the pupils to think about what is happening to the area and perimeter of the Koch as they draw more and more iterations. I think this touches on a very interesting concept: the area gets bigger and bigger each time, but doesn't go to infinity. I demonstrated this by drawing a circle around the shape, and the pupils recognised that the area will never be greater than the area of the circle.

Then it was the fun bit: making 3D fractals! I'd made one in advance, Blue Peter stylee, and the pupils were like: woah! I gave them all a piece of A4 card and a pair of scissors and took them through the process step by step. We managed to do more iterations than the document above suggests. We ended up with squares that were about 0.8cm^2. They looked so cool.

My plenary was getting the pupils to answer the following questions in their books: What is a fractal? What's special about a fractal's area and perimeter? Finish this sentence: I think fractals are cool because...

Why I love this activity:
-It's engaging and goes a long way towards ensuring all pupils are on task
-The pupils can take their fractals home and show their parents: good because it means parents then ask what it is and the pupil then talks about what they've learnt, which makes it more memorable.
-It introduces concepts of convergence and infinity in a very tangible way.
-It would make an impressive wall display (sadly I'm not allowed to stick anything up at all in my room because it might ruin the decor. I don't even have a noticeboard).

With the end of term approaching, why not try this activity as a fun lesson? It's better than showing a DVD :)

If you do use it, let me know how it goes!

Emma x x x

Thursday 7 July 2011

Day of the Week Trick

Today I learnt something really cool: how to work out what day of the week any given date is. It's really easy actually.

 First, work out the year code as follows (here, [ ] means integer part, ie round down to a whole number)

Year code (2000 + x) = [x/4] + x (mod 7)
Year code (1900 + x) = [x/4] + x + 1 (mod 7)

Mod 7 means find the remainder once divided by 7. 

Example: 1989: [89/4] = 22
22+89 = 111
111 + 1 = 112
112 = 0 mod 7 (because it's divisible by 7).

FYI, 2011's year code is 6, and 2012's is 1.

You also need to know the month code. You have to just memorise these. 

6 (5)
2 (1)

 January and February are different if the year is a leap year.
 I memorised these pretty quickly by making up mnemonics. e.g. for May being 0 I remember mayo (which I hate by the way). For August being 1 I remember that A is the 1st letter in the alphabet.

 Once you've done that, add together the day, the month code, and the year code, and then reduce it modulo 7 (i.e. find the remainder once divided by 7).

 Then that tells you the day: Monday = 1, Tuesday = 2 etc.

Example: 4th March 2012
4 + 2 + 1 = 7 = 0 mod 7 so it’s a Sunday.

Example: 22nd February 1989
22 + 2 + 112 = 136 = 3 mod 7 so it was a Wednesday.

I can do it almost instantly for dates in 2011 and 2012. Other dates are harder because I have to work out the year code. But people are more likely to ask what day of the week an upcoming event is, so knowing these two years is very useful for impressing people.

By the way, I've edited my settings so that you don't have to sign up to anything if you want to leave a comment (well hopefully that's what I've done) so that commenting is now easier and faster. So please drop me a comment if you have a minute, I'd really appreciate it :)

Emma x x x