In this lesson, students work to find missing information about a circle given a variety of inputs. They start by looking for a central angle given an area and radius, then move toward, for example, calculating arc lengths given a sector area and a central angle. The strengthened intuition that students build in this lesson about the relationships between angle, radius, and arc length will be an important foundation for the introduction of radians in an upcoming lesson.
Students have an opportunity to make sense of a problem and persevere to solve it (MP1) as they ask questions to extract the information needed to calculate the length of a circle’s radius.
Lesson overview
 9.1 Warmup: What’s Your Angle? (5 minutes)

9.2 Activity: Enough Information? (10 minutes)
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: Info Gap: From Sector to Circle (20 minutes)
 Lesson Synthesis
 9.4 Cooldown: Find the Radius (5 minutes)
Learning goals:
 Determine what information is needed to calculate areas and circumferences of circles and ask (orally) questions to elicit that information.
Learning goals (student facing):
 Let’s see what we can figure out about a circle if we’re given information about a sector of the circle.
Learning targets (student facing):
 I can gather information about a sector to draw conclusions about the entire circle.
Required materials:
 Preprinted slips, cut from copies of the blackline master
Standards:
 This lesson builds towards the standard:CCSS.HSGC.B.5MS.GC.5MO.G.C.B.4MO.G.C.B.5
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