I put the children into groups of two or three. The problem was to divide a pizza up between two friends. We first discussed the terms divide and fairly. The children came up with the fact that it needed to be cut up so that they each got a piece and fairly meant that the two friends got the same amount of pizza or that it was equal. I gave each group a picture of a pizza asking them to show me how they would share it fairly between the two friends.
The children first just looked at the picture vaguely saying you need to cut it here with a wave of their hand. They kept discussing where to cut until one child went and got the scissors and actually cut out the pizza. He then cut it in half. This meant there was a scurry to cut the pizza as the others saw what he was doing.
We came together to discuss what he had done - yes he had divided it into two. Was it fair and how could he show us? Another child said we could measure it. Can you show me? He suggested his finger.
I then suggested there was another way they could show that the pieces were exactly the same. There was much discussion and putting the pieces side by side, together, end on and so on until one girl walked up to the boys and simply put one on top of the other saying - "They are exactly the same. See! Nothing is hanging over the edge."
This was a more engaged discussion. Perhaps the topic of sharing pizza or sharing food was something they had experienced. I was more conscious of trying not to lead the children's thinking and to let them show me their thinking. I was very surprised at the suggestion to use a ruler and also the child who came up with the idea to simply put one half on top of the other.
Of course there were still those who found group sharing difficult but they at least helped cut out the pizza and tried to join in the pairs discussion. The lack of mathematical notation in the exercise meant that all the children were able to participate in some way using their knowledge of shapes and dividing them up.
Where to from here? Some groups need refining. Discussion rules need to gone over particularly reminding them of giving thinking time for others. A smaller group size instead of whole class maybe easier to get around to hear where thinking is at (although there were only 14 children present). How do I introduce a problem with notation and still get a high level of engagement?