# Lesson 8

Ratios and Rates With Fractions

### Lesson Narrative

Before this unit, students worked with ratios of whole numbers and with whole number percentages. Now they start to work with ratios of fractions and fractional percentages. In this lesson they encounter situations where a ratio of fractions arises naturally. They compute scale factors and unit rates associated with ratios of fractions. They consider a situation involving a ratio where the second number is 100, in order to prepare for thinking about a percentage as a particular type of rate, and they compare rates associated with different ratios. The representations they use—tape diagrams and double number lines—are the same as they have used previously, but in the context of more complicated ratios.

The Mona Lisa task has more than one reasonable answer, and students must make sense of the situation in order to choose one (MP1).

Teacher Notes for IM 6–8 Accelerated
The original version of this lesson included an activity called Scaling the Mona Lisa, which applied ratios with fractions to a situation involving scale drawings. That activity is not included in this lesson, because students have not yet studied scale drawings. You can ignore the references to this activity in the lesson narrative and required preparation.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) different strategies for solving a problem involving equivalent ratios with fractional quantities.
• Explain (orally and in writing) how to find and use a unit rate to solve a problem involving fractional quantities.

### Student Facing

Let’s calculate some rates with fractions.

### Required Preparation

For the activity Scaling the Mona Lisa, consider showing a picture of the Mona Lisa painting.

### Student Facing

• I can solve problems about ratios of fractions and decimals.

Building On

Building Towards

### Glossary Entries

• 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 $$2 \div 12 = \frac16$$.