Sometimes tasks arise spontaneously. I was thinking about an activity to tie up some recent work on negatives, which would involve more demand than the traditional “check up” exercise.

I started the lesson with question one. (This was all handwritten on the board, I’ve typed it up for the site). I then invited pupils to share their solutions. This was to set the scene – there are multiple correct answers here. I, as the teacher, don’t know them all. My message to the kids was loud and clear “We can all learn from each other!” It was nice to listen to and value the contributions of a couple of pupils who have been struggling in maths this year. They were visibly chuffed to be able to contribute some mathematical insight that had arisen from their own creativity.

I then set part 2. Some fast finishers were challenged using the classic from Watson and Mason “come up with another way, and another, and another…”.

Finally we moved onto part 3. As I putting this up on the board I kept thinking about two Tom’s: Francome and Carson. TF has lots of lovely tasks like this in his book “Practicing Mathematics”, written with Dave Hewitt. It also echoed his idea of subordinating the main mathematical goal to some other form of activity. In this case, pupils were focused on finding out how many possibilities existed, while actually working on negative addition and subtraction. TC has spoken to me many times about teachers having available actions and identifying opportunities to act (or not) in lessons. I quote him on spontaneous task design in my book. I don’t know if TC would describe it as such, but I was reminded of him here as parts 2 and 3 were never part of my “plan”. This might sound dis-organised although I prefer to think of it as being responsive! I had a few options of where to go with the lesson, based upon how task 1 had gone. When it went well, I followed the route of generation that you see in task 2. If task 1 hadn’t gone well I might have come up with something to do with relating the calculations back to algebra tiles.

Credit: @chrismcgrane84 with some influence by the guys mentioned above!