The purpose of this lesson is to introduce the concept of a proportional relationship by looking at tables of equivalent ratios. Students learn that all entries in one column of the table can be obtained by multiplying entries in the other column by the same number. This number is called the constant of proportionality. The activities use contexts that make using the constant of proportionality the more convenient approach, rather than reasoning about equivalent ratios.

The activities encourage students to look for and make use of structure in a proportional relationship (MP7). The last activity is optional because it provides an opportunity for additional practice with a new context.

In these materials, when we say “ is proportional to ” we usually put in the left hand column and in the right hand column, so that multiplication by the constant of proportionality always goes from left to right. This is not a hard and fast rule, but it prepares students for later work on functions, where they will think of as the independent variable and as the dependent variable.