How this task is used is very important!
There is an assumption that pupils have worked on my multiplication of negative numbers task and other related tasks, before engaging with this task sequence. This task, like the multiplication task, takes advantage of variation theory to help pupils spot patterns in the cells in the table.
The idea of division as the multiplicative inverse is essential for pupils to fully grasp what is happening here.
The first and second sections of the task are rooted in the idea of partitive division. That is, for example, “share -6 into 2 equal groups”. This metaphor is less easy for pupils to grasp in the third section, so I argue that measurement/quotative division makes more sense here. That is, for example, “how many groups of -3 are in -6”?.