Wednesday afternoon: I chose to go to a session from conference veteran Bob Vertes, who introduced us to a series of fascinating games and puzzles. The first involved a circle of paper, on which we drew a sequence of three joined chords. We then drew three more which were parallel to one of the first three.

We were asked to think about why we ended up where we started (assuming our parallel lines were accurate, of course).

Whilst I was pondering this, Bob introduced a very intriguing ‘find the treasure’ game. The simple rules of this game bely the complex thinking required here; like any good maths activity, it allowed us to investigate deeper and consider similar triangles, patterns, midpoint theorems and extrapolation. I had a nagging feeling that this related to our first task but Bob was giving nothing away.

Next we were given an Islamic design and asked what the ratio of hexagons, triangles and squares was. Curiously I found this quite easy to think about, but the clever approach suggested was to find a tessellating shape, and counting the number of each shape. Ironically, this took me much longer, and made me realise how frustrating it must be for students to be forced to use a prescribed method for a problem that they know how to solve. (My 20-second solution was correct, but I totally failed to find a successful tessellation.  Food for thought.

Next Bob showed us some pop-up cardboard shapes – these are great fun – pull the string and create a cube, etc. We were given nets to help us think about whether there were other ways to make the same shape. It made me reflect back on the idea of the ‘single cut’ from Katie’s plenary (see previous blog post).

Our penultimate game was called ‘Cover 3’. This may have been my favourite as it was very simple to get started but involved some great reasoning.

Finally Bob introduced us to Hexiamonds; there are 12 possible ones. (Shapes drawn on isometric paper containing 6 triangles.)

After a quick tea break it was time for the final session of the afternoon. One of the best things about conferences is catching up with old friends. My great friend and long-time mentor Lynne McClure and I headed to a practical session led by yet more friends – Cath Moore and Nicole Cousins.

This was a good choice for the final session of a busy day, as it was hands-on and accessible. I liked what Nicole said at the end, which was (roughly) “The curriculum is full and it is hard to fit this stuff in but if we see it as actual mathematics rather than a nice ‘add-on’ we are helping to build a generation of mathematicians.”  Bang on.

Dinner was excellent, and I enjoyed the conversation, although a room full of mathematicians could not apparently solve the problem of how to halve their queueing time (Spoiler: plates are in the middle, then split left and right to identical serveries – you’re welcome!).

Time for a spot of maths-jamming, chatting, and bed. See you tomorrow.