Lesson 6

Interpreting Rates

Lesson Narrative

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).

Learning Goals

Teacher Facing

  • Calculate and interpret the two unit rates associated with a ratio, i.e., $\frac{a}{b}$ and $\frac{b}{a}$ for the ratio $a:b$.
  • Choose which unit rate to use to solve a given problem and explain the choice (orally and in writing).
  • Comprehend the term “unit rate” (in spoken and written language) refers to a rate per 1.

Student Facing

Let’s explore unit rates.

Learning Targets

Student Facing

  • I can choose which unit rate to use based on how I plan to solve the problem.
  • When I have a ratio, I can calculate its two unit rates and explain what each of them means in the situation.

CCSS Standards

Addressing

Building Towards

Glossary Entries

  • unit price

    The unit price is the cost for one item or for one unit of measure. For example, if 10 feet of chain link fencing cost \$150, then the unit price is \(150 \div 10\), or \$15 per foot.

  • unit rate

    A unit rate is a rate per 1.

    For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because \(12 \div 2 = 6\). The other unit rate is \(\frac16\) of a pie per person, because \(2 \div 12 = \frac16\).