In this section, students further explore "rate per 1" and solve various problems involving rates.

Students observe that using rates per 1 is a helpful way to make comparisons. They learn that a rate per 1 is a "unit rate," and that each ratio \(a:b\) has two associated unit rates: \(\frac ab\)and \(\frac ba\). If 8 pounds of apples cost 6 dollars, then 1 pound costs \(\frac 68\) dollar and 1 dollar buys \(\frac 86\)pounds. In interpreting unit rates in context, students see that one unit rate might be more helpful than the other, depending on the question.

Students generalize that when two ratios have the same unit rate, the ratios are equivalent. For instance, 3,000 meters in 20 minutes and 2,550 meters in 17 minutes are equivalent ratios since they both have a unit rate of 150 meters per minute.

Likewise, when ratios are equivalent, they have the same unit rates. For instance, \(10:4\), \(15:6\), and \(20:8\) are equivalent ratios, so they have the same unit rates, \(\frac 25\)and \(\frac 52\).

In a table of equivalent ratios, each unit rate is a factor that relates the values in the two columns.

As students progress through the section, they encounter problems with less scaffolding. In the last lesson, students reason about the movement of two objects relative to each other. This lesson is optional because it exceeds the expectations of the standards.

6.3 Section B: Rates