One is that I did the lesson. I managed to resist temptation, and allow the students to explore on their own without any eye-glazing attempt to explain a proof or whatever. The only major intervention was to say that the ill-starred attempt of some of the boys to find a mathematical pattern in Minecraft Creeper faces with Cuisenaire rods wasn't going to work.
The second development is that I've been thinking about Miles Berry's proof, and backsliding a little.
The problem that was nagging at me, was that his way of filling the hundred-square so that it can be (almost) filled with 4--rods with four different colours
There's going to be a kind of repeating latin square. For instance, taking this square:
I'm really not sure I've got to the bottom of this though, and would value someone else's thought.
The proof still stands for the position of the lone 1-rod in a hundred-square filled with 3-rods though:
And the last development is that Helen J Williams has had a go at the same activity with her maths club too, with good results:
@Simon_Gregg @CuisenaireCo "see this gap it's because 30x3=90 &3x3=9 so you'll still have 1 left over." pic.twitter.com/xU7hS0VXWbFantastic!
— Helen J Williams (@helenjwc) January 25, 2015