## Sunday, 29 November 2015

### Division without calculation

Rosy tells me that Year 5 (Gr 4) are about to do some work on division.

I've been thinking about some work that could be done with Cuisenaire rods on division, a lesson that would not necessarily help with learning a division algorithm but would develop number sense and reasoning. I looked through the division chapter in Madeleine Goutard's Experiences With Numbers in Colour and this caught my eye.

## How many brown rods are in six black rods?

 Black rods are 7 cm long; brown rods are 8 cm long.
Here's Goutard's diagram:

If I had the rods with me now, I'd make a little video (in the style of Peter James Jackson's great videos). But just to show the six blacks and ask the question would be enough. And then what? To show them the movement straight away? I think so, because the point of this is that calculation isn't necessary. It's about manipulation, transformation.

I think what I'd ask for next is for children to make another example of the same kind of thing with different rods. "See what you can do."

I'd go round as they were trying it, and maybe select some to show with the document viewer to the whole class. Then, when everyone had got the idea more clearly, we'd work on it a bit more. Would any children make an example where more than one rod has to be moved to the end? That would be great.

Then I'd ask them to draw and write about what they've done on squared paper. I wouldn't be looking for a general description. It would be enough that the children are exploring a number pattern and thinking about a way that numbers can be manipulated. But if there were some observations about what was going on, or questions, so much the better!

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Professor Smudge had a tweet with a question on this: