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).
- 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.
Let’s calculate some rates with fractions.
For the activity Scaling the Mona Lisa, consider showing a picture of the Mona Lisa painting.
- I can solve problems about ratios of fractions and decimals.
A percentage is a rate per 100.
For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.
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 \(2 \div 12 = \frac16\).