The purpose of this lesson is to make it explicit to students that equivalent ratios have the same unit rates. To arrive at this insight, students reason about equivalent ratios and unit rates in a direction opposite of that in prior work.

Previously, students calculated unit rates from given ratios and then identified the ratios with matching unit rates as equivalent. For instance, they saw that 4,200 meters in 30 minutes and 6.5 kilometers in 45 minutes both have 140 meters per minute as a unit rate. This means both distance-to-time ratios are equivalent: they describe two things happening at the same rate (traveling at the same speed). Here, students reason the other way. They see that if two or more ratios are equivalent, then they have the same unit rates. For instance, , , and , which are equivalent, all have and as their unit rates.

This understanding offers a new insight for reasoning with tables of equivalent ratios. In addition to reasoning across rows (understanding that a factor relates the values in any two rows), we can also reason across columns (understanding that another factor—a unit rate—relates the values in one column to the values in the other column.)

Students use these insights to find unknown quantities and to compare rates. Later in the lesson, students work to generalize their observations: All ratios that are equivalent to have and as their unit rates.