This is an account of (part of) the 7th lesson exploring different bases using Cuisenaire rods with a class of 8-11 year olds.

There were two aims of the lesson:

- To be able to explain how to add and subtract with different coloured rods.
- To create easier and harder examples.

I designed these prompts to stimulate children to create addition and subtraction examples in a base (rod) of their choice, for which they had to work out the solutions.

I then asked them to write their favourite examples on yellow (easy) and orange (hard) cards. I will laminate them and give them to the students to work on next lesson. Here are the 'easy' addition examples:

Here are the hard addition examples:

There are some lovely examples in here. It is interesting not note that although the majority of calculations are written in columns, nearly all of these children were performing the calculations with rods. All of these hard examples (except one) require the exchange of whites for a rod (a.k.a. 'carrying').

Here are the 'easy' subtraction examples (although some of them are not

*that*easy!):

Finally, here are the harder subtraction examples. I had a sense that the children generally understood the difference between easy and hard subtraction examples, harder ones involving the exchange of rods to 'free up' more whites (a.k.a. 'borrowing'):

I asked the children to choose an example they had created, and write an explanation of how to carry out the calculation so that someone else could understand it. Their explanations are shown below. I think it is worth spending some time reading them (click to navigate). Personally, I am staggered by their clarity and creativity.

Finally, here's an absolutely lovely one from a child that I had been worried about, as she had seemed not to be engaged / enjoying / getting much out of the lessons. Today, she created some great examples, showing a secure understanding of the mathematical ideas; I was so pleased to see this beautiful explanation: