In this lesson, students define rate. After coming up with a preliminary definition on their own, students identify situations that describe rates and situations that do not.
Students determine what is common among rate situations and then revise their definitions of rate based on these observations. Students present and discuss their work and together create a class definition. They compare the class definition of rate with the Glossary definition and revise the class definition as needed.
A good definition of rate has to be precise, yet general enough to be useful in a variety of situations. For example, the statement “a rate compares two quantities” is true, but it is so general that it is not helpful. The statement “speed is a rate” is true, but it is not useful in determining whether unit price or population density are rates.
A good definition of rate needs to state that a rate is a single quantity, expressed with a unit of the form A per B, and derived from a comparison by division of two measures of a single situation.
Goals and Learning Objectives
- Gain a deeper understanding of rate by developing, refining, testing, and then refining again a definition of rate.
- Use a definition of rate to determine the kinds of situations that are rate situations and to recognize rates in new and different situations.
- Understand the importance of precision in communicating mathematical concepts.