Mathematical Art

So what do you do when you arrive in your classroom 15 minutes before the start of afternoon school, after being out all morning , to discover that your PE lesson has been cancelled, it’s raining so you can’t go outside and you have absolutely nothing planned?

Panic obviously! Not helped by the fact that it was indoor play and the children kept wanting to come and talk to me and show me pictures of their new guinea pigs etc. And I hadn’t had any lunch!

Escher tesselations obviously. No preparation necessary apart from a supply of paper and some card. This was partly an activity that I have done several times before but modified/improved after our last session at NTU.

I by putting on this youtube video
http://www.youtube.com/watch?v=njp6yexWbfw and just let them watch it while I cut card into small rectangle pieces. Then we watched it again together because I love the soundtrack.  This time they looked more closely at how the tesselations were created and tried to see if they could spot the base shape. They had done some tesselations previously of complex shapes such as Christmas trees etc last term so the idea wasn’t new to them.

The lesson was interrupted by the head teacher who wanted to dicuss Bittersweet Symphony as it is one of his all time favourite tracks so we watched all again. They loved looking at all the different images and kept finding new things to talk about.

Then I displayed the lesson notes from Primary Resources
http://www.primaryresources.co.uk/art/docs/Making_Escher_Patterns.doc

This gives the children a very basic idea of how to create an interesting tesselation from a basic rectangle. I demonstrated one to show them how easy it could be and then let them get on with it.

35 year 5 children who varied from being statemented to very able, all dived in and worked without any fuss. The biggest problem in the whole session was only having one roll of sellotape between everybody.

Their tesselations were varied, some were very complex and created really interesting patterns. Others were very simple but just looked really effective. Everychild completed a tesselation pattern of their own shape. Then they had the fun of turning them into fish, monsters or whatever. None of the patterns is finished but we will display them on the class blog when they are done. Their first question was “Can we put them on the blog”.  They love the fact that their work has a wider audience now.

I will pursue this by looking at how shapes tesselate in more detail and link with work on angles. I also want to see what other shapes they could use to create other patterns. Lots of investigative work to come.

I have lots to reflect about MaST at the moment and also things that I have read recently. I will catch up on posting when life gets a little less hectic and I’m not doing the Lambeth Walk everynight.

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Making maths more interesting

I feel that I need to liven up some of my maths lessons. I have a very boy heavy group and some of them find it hard to maintain concentration. The murder mystery was great with all of them totally involved and on task for the whole lesson so it might be worth while looking at other video clips that could be used to stimulate maths lesssons. I know that there are starters on Teachers TV but I wonder what else would work? Any suggestions gratefully received.

One of my aims for this year is to get everybody making more use of our fantastic school grounds for maths. I’ve already done some measuring and will do some work on area and perimeter next term. I want to use the parachute as well to do some number bonds work. Physically moving should hopefully really get them thinking about the properties of numbers.

We’re doing ratio later on this week so I have been a bought a pack of mini smarties as an incentive. Last year this lesson worked really well (it’s based on a resource from primary resources) but of course there is no guarantee that it will work as well this time.

I have another HEI session tonight at NTU so it’s going to be a long day 😦

Lacking time or motivation?

This week has gone by in a flash. It doesn’t seem 5 minutes since I got home from the residential last week and it’s already Sunday afternoon. I realised with a bit of shock that I still haven’t really done any work for this year’s module of MaST. I’ve attended a network meeting and been to the residential but I haven’t actually done any work of my own. It’s very easy to say that I’ve just been too busy but being totallyhonest, I’m not sure that would be entirely true.

Yes, I have been busy as ever during term time. Also, I’ve been pleased by the interest shown by the children in their class blog and I have been keeping the momentum going by posting their work. Their enthusiasm and delight when their work gets posted is brilliant but it does all take time. All the time spent loading stuff up is time that I could spend on MaST. But I doubt whether I would.

Last year it was all new and we were all inspired and fired up. This year the novelty has worn off to a certain extent and we are all well aware how difficult it is going to be. I still haven’t cracked the issue of reflecting on my observations and until I get that sorted, I’m not really going to be able to go much further. At least I’m not in the position of having to resubmit or redo last year’s assignment and I really feel for those people in that horrible situation. It’s in situations like that when the distance learning thing seems to break down slightly.

I have a network meeting on Tues and maybe that will cast some light on things. Failing that, I think that I will put the whole thing on hold until the Easter holidays when I can really spend some time reading and thinking about what I am going to do and how to get things moving in school.

MaST Residential or Jellybeans galore!

Having to get up at 6.40 on a Saturday was difficult to say the least. Not a good way to start what was bound to be a very intensive weekend. It was surprising how empty the roads were at that time in the morning (or maybe it wasn’t, every one else had more sense).

However we were greeted by coffee, biscuits, fruit and sweets so life started to improve.

The main focus of this residential was to look in more detail at algebra and geometry and how these fit into the primary curriculum. There was a lot of emphasis on how important reasoning skills are and how algebra supports the development of children’s ability to reason.

We looked at how algebra can be introduced at an early stage by looking at the structure of operations and calculations, particularly those involving unknown numbers. There was a clear understanding that we were looking at how we could introduce the early stages of algebra, not simply introducing algebra early.

I did find some of the tasks we were given quite daunting which is a good reminder for me of how my pupils probably feel. I remember finding algebra quite puzzling but being pleased on certain occasions when I thought I had found the key to it. Looking back, they were probably the few times when I managed to understand the underlying structure of the operation.  It seems to me that I need to give children the opportunity to achieve that same sense of satisfaction.

At school we have been looking at how we can develop children’s reasoning skills and so it should be possible to incorporate ideas from this weekend.

The weekend was memorable for the amount of food provided. This included apparently endless supplies of jellybeans which were magically renewed before every session.

Subtraction

Subtraction has been a nightmare for my class this year.

We have used number lines in every possible way and concrete apparatus but nothing has really worked. Whenever I give them a problem or a calculation to solve involving subtraction,  most of them cannot arrive at the correct answer. If I go over a particular method before giving them the problems then it’s not too bad but it doesn’t stick. The errors aren’t uniform either. There doesn’t seem to be any pattern to the mistakes they make or reasons as to why they make them. The majority of the class just seem to be confused.

So in desperation I decided to show them how to do subtraction using decomposition. I did a couple of examples on the whiteboard and then got them to work some out in pairs using their mini boards. They were all interested and immediately got the connection with column addition which they are not bad at. There was a real feeling of excitement as they found they were arriving at the correct answers quickly.

I had one or two who still weren’t sure so the next day I did some more teaching, This time I used the idea of money and changing a 10p piece for 10 1p pieces and the actual amount of money staying the same. This visual image seemed to help them and they seemed much more confident. The rest of the class were all looking at subtraction problems and using the method confidently.

Today we did some further problems and every child got the correct answers!

I know that it is still fresh in their minds and that next week they may well forget and make the usual mistakes but I don’t care. They feel that they have cracked subtraction. They love using the new method and their confidence has soared.

Next week we will look at examples of when it is not a good method to use so they don’t get too carried away.

This is a real example of how useful an algorithm is if the children are ready for it. They really do seem to understand the process behind what they are doing and not making any of the typical mistakes that happen when children don’t truly understand. I almost wish that I had taught it earlier in the year but then the understanding may not have been there.

It was a lovely lesson to end the week on. I’m now ready for my weekend of maths on my MaST residential. The only real problem is having to get up at 6.45 on a Saturday morning!