## Saturday, 30 January 2016

### The L Shaped Room

So, Year 4 can multiply a teens number by a one-digit number, using Cuisenaire rods, and the grid (box) method. At least when we do that as a specific lesson.
Most of the students can multiply two small two-digit numbers this way:

And when we give a simple real-life situation, like we did in this 3-Act task last week, they could use it.

In the next few weeks we should abstract away from area questions and see whether they reach for and can use this tool for non-area situations. But J, my partner teacher in the other Year 4 class would like to do some more area situations, but more complicated. L-shapes, that kind of thing.

Well, Graham Fletcher has provided a nice one that we'll do on Tuesday, one of his great 3-Act tasks. It's Paper Cut. I'm really interested to see how students respond to this, without telling them too much.

So, for Wednesday... an L shape...

Our staff room is L shaped, so before I went home yesterday I had a look. I think it could work...
It's carpeted with our half-metre long squares. From the back of the fridge on the left across to the door on the right is the length of eight carpet squares.
Rounding a little, and adding a grid, I've got the dimensions, measured in carpet-tile lengths:
I think I'll suggest we start by giving them this shape, and asking what they notice and wonder. This has gone well before. And then, what?

Perhaps off individually to write in their journal what they noticed and what other people noticed?

Then, if it hasn't come up, introduce the idea of area, by showing the staff room picture and plan, with the question 'How many carpet tiles would you need for this room?'

How shall we go then? Perhaps individual reflection on how to do it first, then sharing in pairs, then having a go at it in pairs.

What would you do?
____________________

Notes in response to John's comment:

The 3rd act could perhaps be in image form:
or as a video?

 This room is a better start, if we round some of those dimensions
This would do for choosing an L shape:

Read how it went in the next post.

## Sunday, 24 January 2016

### How we wrote numbers

So, we've completed our couple of weeks around how we write numbers. How did it go?

There was lots of good stuff in there. I was particularly pleased that we got to look together at how important India and the Muslim world were in the story of our number system. In particular, at this time when Islam is being viewed so negatively in Western media, it's important to see how figures such as Al Khwarizmi (from whom, as a garbled version of his name, we get the word algorithm; and from whose book we get our word algebra) contributed to the 'rebirth' of Europe.

We had a brilliant response to the piece of homework (you can see these as some of the posts labeled 'Numbers') which asked the students to blog about numbers, in a different language or with different symbols or from a different time. It was a real celebration of different cultures, of similarities and differences.

Lots of students were grabbed by Roman numerals. E kept writing them out for me on a whiteboard
And I don't know when B and M practiced this to show me, but it seems to me that there's a lot of understanding in being able to count like this, even with a few slips.
The book, Blockhead! was ideal, and really had the students attention. I've also been reading occasional pages from Johhny Ball's colourfully illustrated book, Think of A Number:
As for working in bases, it went well. The students understood it with Cuisenaire rods
even though sometimes writing the numbers was a bit tricky!

One of the surprises was the discussion around this, slightly modified version of a Fibonacci question:
I'd shared it with the original idea of situating the new Hindu-Arabic numerals within the early-capitalism of thirteenth century Pisa, Our 'central idea' is that there are discoveries that change the world, and I wanted them to see the sorts of questions Fibonacci was interested in, maybe see that the new numbers would help with trade. But they could see this quickly. So, instead we discussed how to share the profit. I wish I'd written it all down, there were so many great arguments and ideas! T for instance thought that if they all had fair shares, next time there would be no reason to put more money in. R on the other hand thought they should all get fair shares because they all needed the same amount of money!

The pattern on dress of the "Mathematics Fairy" too generated some good thinking.
It really hit the spot for K, who made his own book about the pattern at home;

There was a late entry just as we were finishing. Someone tweeted about Which Script? This lesson was all about place value, and also about scripts, and generated so much reasoning and discussion!