[Before reading this post, it would be useful to first read the process I followed when planning this lesson.]

The plan, in essence, was to explain what the lesson was about (the children creating their own mathematical questions), to allow some time for play / formation of questions (during which time I would talk to each child about their question), and then allow the children a choice of which question they would work on (their own, or someone else's), during which time I would also get round each child and talk to them about what they were doing. In addition to the plan, I allowed ten minutes at the end for a brief record of what they had done, so that we can continue working on it next week.

The lesson went almost exactly to plan. Each practical decision had been thought through in advance. One thing I noticed was that I repeat myself more than I planned to, perhaps because I felt the children were not always attending. But saying this, I still felt I was being more concise than usual.

As I talked to each child during the period of play / question formation, a number of them said they found it difficult to come up with a question. I then asked: What have you been doing that you have found interesting? This was enough for them to show me a something they were playing with, from which I could offer suggestions (but resisting the urge to be too directing, which would have defeated the object of the lesson). They formed some great questions:

I added a word here and there before reading them out, and then I laid them all on the table, before inviting the children to either work on their own one, or someone else's that they found more interesting.

Quite a few children chose the question 'How many triangles...'. In their reflection at the end of the lesson, I asked them why they chose the question they did. Many of the children who chose this question did so because it seemed easy, but then found there was a large number of triangles.

There were very few instances of children approaching this question systematically, apart from one child who described moving one vertex a pin at a time to create new triangles. We will talk about this. Also interesting about this question is that it would be easier if constrained, perhaps to: 'How many triangles can you make with one vertex at the centre', or '... with all vertices on the circumference'. This presents an opportunity to talk about freedom and constraint.

It seemed to me as though those children who chose to work on their own question (around half) seemed to get more out of it. Here is some of their work, along with their reflections [click to view each gallery].

*Jack, upon discovering that he couldn't make a regular pentagon on his 12-pin geo-board.*

*Sarah, considering the differences between n-pin geo-boards, and exploring the meaning of 'regular'.*

*Violet, starting to think about finding the triangles systematically.*

*Milos, exploring symmetry because he likes it. I asked him if he could create a shape with 3, 4, ... lines of symmetry..*

*A-, exploring irregular octagons on an 18-pin board... highly original, and challenging!*

*Caleb, working on his 6-pin geo-board. Are there only*

__three__different triangles!?*Stewart, exploring beautiful overlapping patterns. He made a number of these by shifting the distance between points by one each time*.

*Megan, exploring her question about 'recognisable' shapes. Notice the tentative (faint) 'parallelogram?', middle-right.*

*Connor, exploring angles in triangles/polygons. I asked him if he could calculate the other angles in these triangles next week.*

There is so much to work on here in the coming weeks. Where to start?