From the text: {\it D. Küchemann} [“Positive and negative numbers", in: K. Hart (ed.), Children’s understanding of mathematics: 11‒16. London: John Murray. 82‒87 (1981)] has written about the difficulties of creating models for integers that are consistent across the four arithmetic operations. He advocates adopting a model“in which the integers are regarded as discrete entities or objects, constructed in a way that the positive integers cancel out the negative integers." My aim in this paper has been to put forward such a model. In doing so, I have adopted a shorthand notation, replacing $^+1$ by “$+$’ and $^-1$ by ‘$-$’. Of course, in doing so, I can be accused of abusing standard notation. I acknowledge this. However, I would point out that almost all textbooks do something similar; instead, of writing $^-3$, they write $-3$ and so on. In other words, they leave out the signs whereas I leave out the numbers!