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Lesson 12: Putting It All Together
• Use geometric thinking to solve problems. Lesson Narrative
In this lesson, students apply their understanding of circles and trigonometry to solve problems in context. Students calculate viewing distances from atop tall objects on Earth under ideal conditions, and help to divide a slice of pizza fairly with the stipulation that one of the two people splitting the pizza slice does not want any crust.
Students reason abstractly and quantitatively when they decide how to apply circles and trigonometry in context and interpret their solutions (MP2).
Required Materials Geometry toolkits
Scienti c calculators
Student Learning Goals
• Let’s use geometry to solve problems. 12.1 A Fair Split
15 minutes
In this activity, students have the opportunity to use what they know about trigonometry and circles to decide how to divide a pizza slice between two people equally so that one of them doesn’t have to eat the crust.
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.
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Teacher Guide