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• “What makes these problems the same? What makes them di erent?” (The di erent problems ask to solve for di erent measurements: area, radius, or central angle. They all use the same basic structure that the area of a sector is a fraction of the whole circle, and that fraction is given by the central angle measure out of radians.)
5.3 Practice with Circular Arc Lengths
Optional: 15 minutes
This activity is optional because it includes additional practice that all students may not need. Students use the relationships between radius, central angle, and arc length to solve various problems.
Look for students who use these strategies for nding arc length in question 2: • Multiply the fraction of the whole circle with the circumference.
• Multiply the radius by the radian measure. 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
Ask students to check their responses with their partner, and if there is disagreement, work to reach agreement. Encourage students to sketch pictures of the problems as they work.
Student Task Statement
Give answers in terms of along with decimal approximations rounded to 2 decimal places, if necessary.
1. A sector has radius 6 cm and a central angle of radians. What is the length of the arc enclosed by the angle?
Unit 7
Lesson 5: Angles, Sectors, and Arcs
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