Page 194 - IM_FL_Geometry_Print Sample

Launch
Ask students to check if their calculators are in radian mode. Arrange students in groups of 2. Give a few minutes of quiet work time before asking students to share their ideas with their partners.
Student Task Statement
Elena and Andre want to share a big slice of pizza so that each of them gets the same amount, but Andre doesn’t like the crust. How can Andre and Elena divide the slice of pizza into 2 equal pieces so that Andre doesn’t have to eat any crust? You can assume the pizza slice is a sector of a circle with a radius of 20 cm and a central angle that measures radians.
You can also assume that Andre and Elena will make a cut that is parallel to the segment that connects the corners of the pizza where the sides meet the arc.
Student Response
The distance between the center of the slice and their cut is approximately 13.47 cm. Possible strategy: the cut decomposes the slice into an isosceles triangle and the rest of the sector. Use trigonometry to solve for the base of the triangle in terms of the height. Set the area of the triangle equal to half the area of the sector and solve for the height of the triangle.
Activity Synthesis
Ask students to share their strategies for deciding where to divide the pizza slice. Ask students,
• “What would change if the radius and central angle were di erent? What would stay the same?” (The process would be the same, but when the angle increases past a certain point, the isosceles triangle whose congruent sides are radii starts to have a smaller area than the rest of the sector, making the problem impossible.)
12.2 As Far as the Eye Can See
15 minutes
In this activity, students use the Pythagorean Theorem, trigonometry, and circles to gure out the relationship between height and ideal viewing distance on a sphere.
Launch
Ask students to read the introductory paragraph of the task. Ask students how they might represent a tall object on a sphere with pencil and paper, and what the segment between the top of the tall object and the horizon would look like. Ask students to include measurements in their drawings. Here is an image to guide your planning:
Unit 7 Lesson 12: Putting It All Together 121