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.
- Determine what information is needed to calculate areas and circumferences of circles and ask (orally) questions to elicit that information.
- Let’s see what we can figure out about a circle if we’re given information about a sector of the circle.
- I can gather information about a sector to draw conclusions about the entire circle.
The region inside a circle lying between two radii of the circle.