Lesson 17

In previous lessons students have calculated and worked with rates per 1. The purpose of this lesson is to introduce the two unit rates, \(\frac{a}{b}\) and \(\frac{b}{a}\), associated with a ratio \(a:b\). Each unit rate tells us how many of one quantity in the ratio there is per unit of the other quantity. An important goal is to give students the opportunity to see that both unit rates describe the same situation, but that one or the other might be preferable for answering a given question about the situation. Another goal is for students to recognize that they can just divide one number in a ratio by another to find a unit rate, rather than using a table or another representation as an intermediate step. The development of such fluency begins in this section and continues over time. In the Cooking Oatmeal activity, students have explicit opportunities to justify their reasoning and critique the reasoning of others (MP3).