Page 80 - IM_FL_Geometry_Print Sample

Lesson 1: What’s a Circle?
• Explore the relationship between angle, arc length, and sector area. • Know the precise de nition of a circle
Lesson Narrative
In this lesson, students re ne their de nition of circle and use various tools to examine sectors and arcs of circles. An arc is a part of the circumference between two radii, and a sector is a region inside a circle bounded by a central angle and its arc. When students use a sector of a circle to make statements about the whole circle, they are anticipating the work of upcoming lessons about radian measure, arc length, and sector area.
Students use tools strategically to investigate as much as they can about a sector of a circle and its relationship to the whole circle (MP5).
Required Materials Compasses
Geometry toolkits Protractors Rulers
String
Required Preparation
Cut one 2 in piece of string for each student to explore measurements.
Student Learning Goals
• Let’s describe a whole circle when given only a part.
1.1 Math Talk: Fractions of a Circumference
Warm Up: 5 minutes
The purpose of this Math Talk is to elicit strategies and understandings students have for reasoning about arc lengths of circles. These understandings help students develop uency and will be helpful later in this lesson when students will need to be able to nd an arc length of the circle that is equal to the radius.
Math Talks build uency by encouraging students to rely on what they know about properties of operations to mentally solve a problem. In this activity, students use repeated reasoning to understand that an arc length is a fraction of the circumference (MP8).
Unit 7 Lesson 1: What’s a Circle? 7