Lesson 3

In grade 6 students solved ratio problems by reasoning about scale factors or unit rates. In grade 7 they see the two quantities in a set of equivalent ratios as being in a proportional relationship and move towards using the constant of proportionality to find missing numbers. This is useful in the sorts of tasks they are studying in this unit because the tasks involve repeatedly applying the same number (for example, a unit price) to different amounts. The unit price is a constant of proportionality between the amount purchased and the amount paid. When students describe the proportional relationship behind the repeated operation of finding the amount paid, they are engaging in MP8.

In this lesson students move toward solving problems involving proportional relationships by more efficient methods, especially by setting up and reasoning about a two-row table of equivalent ratios. This method encourages them to use the constant of proportionality rather than equivalent ratios.