Page 86 - IM_FL_Geometry_Print Sample

• The angle at the center is about 57 degrees.
• The entire circle measures just over 6 rad, even though students do not yet know what a rad
is.
Another important takeaway is that, while total areas and lengths would change upon dilation, the
piece of the circle will still be the same portion of the whole circle, which is slightly less than . The radius and arc length would still be the same, because each will have been dilated by the same
scale factor.
Lesson Synthesis
In this lesson, students have re ned their de nition of the word circle and explored relationships between a sector of a circle and the whole circle. Here are some questions for discussion:
• “What angle would each piece of a circle be if you wanted there to be exactly 10 pieces of the same size?” (36 degrees, because 360 degrees divided into 10 pieces gives 36 degrees per piece.)
• “How could you nd the arc length of a piece of a circle if there were exactly 10 pieces of the same size?” (Find the whole circumference and then divide it by 10.)
• “How could you nd the area of a piece of a circle if there were exactly 10 pieces of the same size?” (Find the area of the circle and divide it by 10.)
1.4 How Large a Slice?
Cool Down: 5 minutes
Student Task Statement
Priya tries experimenting with di erent angles for her pizza slices. For each angle, determine what fraction of the entire pizza each slice is. You can assume the pizza is a circle and the slices meet at the center.
1. 2. 3. 4.
Student Response
1. 2.
Unit 7 Lesson 1: What’s a Circle? 13