Unit 7, Lesson 11
A New Way to Measure Angles
Geometry
Preparation
Lesson Narrative
In this lesson, students work with a situation to develop a deeper understanding about the relationship between arc length and central angle. Then they learn that the ratio of arc length to radius is called the “radian measure of an angle.” Students use string to measure arc length in terms of a circle’s radius, and they connect the results to the definition of the radian measure of an angle.
Students have an opportunity to reason abstractly (MP2) as they consider the connection between radian measurements and arc lengths.
- Comprehend (in spoken and written language) that the radian measure of an angle whose vertex is the center of a circle is the ratio of the length of the arc defined by the angle to the circle’s radius.