This is a description of my third maths lesson with 'upper primary' children (ages 8-11) at my local school in Westray. It lasted just over an hour.

I started by reminding the children what we did last week by showing them this, and praised the quality of their descriptions. Then we started work on this task, designed to help the children gain familiarity in converting between base four - part of our ongoing exploration of different mathematical tasks in different bases - and base ten.

Here are some responses to the (reasonably straight-forward) questions on the first page. Notice the different representations/language used:

Here are some responses to the questions at the top of page 2:

*ultimate rubix cube*", and "

*4 squares*". The response "1 0 0 0" shown above came after a lovely moment: the children in question noticed that 63 whites was "3 3 3", but were not sure how to express 64 whites, suddenly realising that an extra column was required.

We had a class discussion about the 'objects' represented by this extra column:

I felt that these questions were helping students gain a real familiarity with working in base 4. However, this lesson really 'caught fire' when students started creating their own questions:

This is what they wrote:

There is a lovely range of questions, and points for debate, including:

- The use of the term "mega cube" in the middle one.
- The top middle question has changed the order in which the objects are presented.
- The bottom middle question asks to convert to "pink sticks", not whites.
- The bottom right question has a lovely 'minimal' design.
- Middle right is beautifully ambiguous, and created a lot of discussion.
- Initially, the bottom left one had the question and the answer, which was later rubbed out!

The children then spent the last 20 minutes of the lesson having a go at each other's questions; there was a great deal of energy, excitement, and mathematical thinking :

There is so much here that we can discuss next week, before doing this. I think the way the children respond to the 'patterns' part of this task will be really interesting.