A Complete Model for Operations on Integers

Teaching student the four basic operations on the set of integers in a meaningful way is a difficult task. The task could be made easier, however, if there was a single physical model for the integers in which all four basic operations could be represented. The number-line model, though useful, has serious shortcomings and is incomplete. As an alternative, some author have suggested the “positive-negative charge” model (Frand and Granville 1978, Grady 1978), but they used this model only for representing addition and subtraction. In this article I will describe the “charge” model and demonstrate how it can be extended to all four operations on the set of integers.