Lesson 2

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).

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.

Learning Targets

Student Facing

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

CCSS Standards

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 \(2 \div 12 = \frac16\).

Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In