Page 90 - IM_FL_Geometry_Print Sample

Lesson 2: Measuring Angles
• Determine an angle in radians, given an arc length and a circle’s radius. • Know the de nition of radian measure.
Lesson Narrative
In this lesson, students de ne the radian measure of an angle. First, students look at constants of proportionality in circles. Then, students draw circular arcs on a given angle and examine the ratio of arc length to radius for that angle. Students determine that each angle has its own ratio that doesn’t depend on the size of the circle, and that this ratio increases as the angle takes up a larger portion of the circle. This connection between angles and circular arcs gives a new way to measure an angle: draw a circle of any size with center at the vertex of the angle and measure the ratio of arc length to radius. This ratio is the radian measure of the angle.
Students will deepen their understanding of radian measure in the next lesson, where they establish that angles can have measures between 0 and radians in the same sense that they can have measures between 0 and 360 degrees.
Required Materials Copies of blackline master
Geometry toolkits Rulers
String
Tracing paper
Required Preparation
Print and cut slips from the blackline master. Prepare 1 copy for every 2 students.
Have 2 in pieces of string available for students when investigating relational measurements. Students will add to their Unit 6 Reference Chart, so be sure those are available.
Student Learning Goals
• Let’s learn about radian angle measure. 2.1 All Circles are Similar
Warm Up: 5 minutes
The purpose of this activity is to review the fact that all circles are similar. Students describe a sequence of rigid transformations and dilations that takes one circle onto another. This is important
Unit 7 Lesson 2: Measuring Angles 17