Lesson 8

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).

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.

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