Following previous lessons on the diagonals of quadrilaterals, we started today's upper primary lesson (ages 8-11) with this task, as a kind of summary of what we have done so far:

There were also a number of lovely unexpected solutions, such as a triangle in the top middle region (above, right).

I asked the children to give feedback on this work on diagonals. They generally thought it a bit hard, but enjoyable.

We started with a discussion about why there were 360 degrees in a circle; I suggested it was because 360 is divisible by lots of numbers, allowing the circle to be divided in various ways. I noted that a couple of the younger children didn't know that a circle is divided into 360 degrees; I hope this work will be useful for gaining familiarity with this.

I invited the children to find as many factors of 360 (which was a nice connection to previous discussions about factors) as they could:

I then demonstrated how to make a 9-pin board, marking off a point at every 40 degrees - a nice physical representation of factor pairs - and then invited the children to choose a pin-angle pair of their own and construct their own boards:

I gave the children the choice of pin-angle pair in the hope of giving greater 'ownership' of their board, as well as possibly exploiting the variation later on. This idea came from recollections of an ATM session on pedagogical variation run by Anne Watson and John Mason.

- Symmetry: Is it possible to create shapes with 1, 2, ... lines of symmetry?
- Regular polygons: which are possible on various geo-boards? Which are not?
- Quadrilaterals: which ones can be made on an n-pin geo-board? Which cannot? Does the number of pins matter?
- Angles in triangles, and then other polygons... Exploring the isosceles triangles formed using the centre-point of the circle.

More thoughts on this below.