Describe how you could represent the fraction 4/10 using a model or number line.

As a model for representing fractions, the number line differs from other models (e.g., sets, regions) in several important ways. First, a length represents the unit, and the number line model suggests not only iteration of the unit but also simultaneous subdivisions of all iterated units. That is, the number line can be treated as a ruler. Second, on a number line there is no visual separation between consecutive units. That is, the model is totally continuous. Both sets and regions as models possess visual discreteness. When regions are used, for example, space is typically left between copies of the unit.

Third, the number line requires the use of symbols to convey part of the intended meaning. For example, Point A in a of Figure 1, when a is taken as a number line, has no numerical meaning until at least two reference points are labeled. Two possible number line meanings are given in b and c of Figure 1. Parts d and e, however, do convey meaning without any accompanying symbols, though their interpretation requires some standard conventions about the nature of a unit. The significant issue is that the number line requires an integration of two forms of information, visual and symbolic; this integration does not seem essential with other models.