Page 85 - IM_FL_Geometry_Print Sample

Launch
Tell students that it is their job to use all the tools available to nd out as much as they can about a whole circle when they are only given a piece of the circle.
Student Task Statement
Here is a region inside a circle bounded by a central angle and its arc, called a sector.
1. What can you nd out about the whole circle? Be prepared to share your reasoning.
2. If this sector were dilated, what would change? What would stay the same?
Student Response
1. Answers vary. Sample response: It takes just over 6 of these pieces of the circle to make the whole circle, so the arc will be a little bit less than the circumference and the area of the
piece will be the same fraction of the whole area. The radius and the arc are both 6 cm. The angle measures roughly 57 degrees. The circumference of the whole circle is centimeters and the area is square centimeters.
2. The lengths and areas would change, but the angle and the ratios of lengths and areas in comparison to the whole made would remain the same.
Activity Synthesis
Ask students to share their responses and show their reasoning. Some important features of the piece of the circle to highlight during discussion are:
• The arc is the same length as the radius.
• The circumference of the whole circle is centimeters and the area is square
centimeters.
• The arc is a little less than of the circumference. The area is this same fraction of the whole area.
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Teacher Guide