Some thoughts from a lovely Mathematics classroom in the lovely North West of England
#MakeOverMonday - Sun Room Carpet, 28th June 2013
I've been following Dan Meyer's blog for a few weeks now and have decided that it's about time I joined the Maths Blogsphere and respond to his Monday Makeover Challenge. In order to do this, I've had to resurrect my previously barely alive website and also join Twitter for the first time. Perhaps I'll have a bit of time to add some actual 'design' to this site before too long!
Here's the problem. How do we improve this task.
My experience of this task is that pupils have no idea about the practical aspects of the task. They have never laid carpet. Neither have they employed someone else to lay carpet. So, my first thoughts on this task are to try to give them the experience of laying a carpet. This seems a really good way of introducing a practical bit to the lesson - strips of paper that are 12 feet wide (scaled obviously!) so that they can experiment with different ways of laying them on a scale drawing of the room.
Secondly, the problem talks about 'nap'. Again, this is adding a 'context' that is simply not experiencable (should be a word) for pupils in the context of this problem in a classroom. Why not say 'pattern'? Now we could print a pattern on our previously mentioned 12 foot wide (scaled) strips of paper. Pupils can easily conceptualise that the pattern needs to line up.
I am English. I am pretty comfortable using either metric or Imperial units. However, all our shops use metric units so I always make measurements in metric. I would love my pupils to leave school with some vague feeling that they are aware of the history of measurement and some sense of how Imperial units relate to their metric equivalents. Imperial units are so much 'nicer' than metric. I hate measuring in metres even though I know that it is so much more sensible from any sort of number theory point of view. And metric units are a waste of time when talking to your Granny! But honestly, if I'd measured the room in metres and then found that I needed Imperial (for some inexplicable reason), I'd just go and re-measure the room! This is a silly extra complexity to the question that only exists in Questionsetterland.
I wonder about simply setting the task as "How much would it cost to carpet this classroom?" The room would not be as complicated a shape but the task would require pupils to ask questions ranging from "how big is the room?" (issuing in questions of which units to use possibly) to "what does carpet actually look like before it is stuck to the floor?". We know that carpet is sold in 3 or 4 metre widths off a roll that is (for our purposes) as long as it needs to be but do our pupils know that? Perhaps a photo of rolls of carpet in a carpet shop would help. And then "how do you stick it to the floor?" and "what happens at the joins?" become questions that pupils may well raise as part of the problem. And why don't we project an actual website with real carpets and prices on? Homework - "How much would it cost to buy a new carpet for your bedroom?"
I know that I am posting these thoughts after Evan Weinberg has posted his thoughts. I really like your ideas and I know that there is a lot of overlap. However, I decided that I wanted to contribute a couple of days ago but it has taken me a couple of days to actually get the tech together to manage to do this. I could say 'I've missed the boat on this one' and wait for next week but if I'm actually going to get into this malarkey I feel I should go for it, check things like the website actually work and that if I tweet this back at you all, some people will actually see it. I hope as a fellow first timer you will agree with my reasoning!
I hope my next reply will be quicker!