Page 113 - IM_FL_Geometry_Print Sample

Activity Synthesis
Ask for 1 or 2 brief responses from students before moving on to the next activity. The important point is that for the same price, the large slice gives more pizza, making it a better deal.
4.2 The Big Slice Special
10 minutes
The purpose of this activity is to build on students’ work from the warm-up to analyze the cost e ciency of a slice of pizza that isn’t cut into a de nite number of slices. The use of radians is appropriate because it may be practically easier to estimate the arc length to radius ratio of a large slice of pizza than it would be to estimate the number of degrees. This activity provides a sca old for analyzing a slice of pizza that students can use to organize their work in the next activity where they compare many di erent slices of pizza.
Instructional Routines
• Think pair share
What: Students have quiet time to think about a problem and work on it individually, and then time to share their response or their progress with a partner. Once these partner conversations have taken place, some students are selected to share their thoughts with the class.
Why: This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and con dent, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that she can purposefully select students to share with the class.
Launch
Arrange students in groups of 2. Ask students to check their responses with their partner, and if there is disagreement, to work to reach agreement.
Student Task Statement
Elena was researching di erent deals in the brochure for the upcoming Pizza Palooza festival. One deal caught her attention—the Big Slice Special. From the picture, she was able to estimate that the arc length was roughly twice the radius. In other words, the central angle of the slice was about 2 radians. The brochure listed the radius as 20 cm and the cost as $5. Give your answers exactly in terms of and rounded to the nearest tenth.
1. What would be the area of the whole pizza?
2. What fraction of the whole pizza is the 2 radian slice? 3. What is the area of the slice?
40
Teacher Guide