# Lesson 12

### Lesson Narrative

In this lesson, students strengthen their understanding of the relationship between radian and degree measures. They use double number lines and proportional reasoning to make connections between degrees and radians, then develop their intuitive sense of radian measures by shading sectors of circles with given radian measures.

Students have an opportunity to attend to precision (MP6) as they choose portions of a circle to shade in the Pie Coloring Contest activity.

It’s more important that students build their intuition around radian measurements than it is to develop a formal algorithm to convert between radians and degrees.

### Learning Goals

Teacher Facing

• Coordinate (orally and in writing) between representations of angles measured in degrees and in radians.

### Student Facing

• Let’s get a sense for the sizes of angles measured in radians.

### Student Facing

• I understand the relative sizes of angles measured in radians.

### Glossary Entries

The radian measure of an angle whose vertex is at the center of a circle is the ratio between the length of the arc defined by the angle and the radius of the circle.

• sector

The region inside a circle lying between two radii of the circle.