ABSTRACT

This chapter looks at some of the issues and nuances that require discussion in the classroom. Ratios in contexts present a challenge in the classroom because of the many nuances that occur in their everyday usage. A ratio is a comparison of any two quantities. A ratio may be used to convey an idea that cannot be expressed as a single number. A ratio is sometimes written in a fraction form, but not always; part–whole comparisons, operators, measures, and quotients are usually written in the fraction form ab. When a ratio compares measures of different types and is conceived of as describing a quality that is common to many situations, it becomes a rate. One of the most common rate situations is the distance–time–speed relationship. Like other rates, speed has a domain. That is, it applies to some explicit portion of a trip, which may or may not be the entire trip under discussion.