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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. Give a few minutes of quiet work time before asking students to share their explanations with their partner. If there is disagreement, ask students to work to reach agreement.
Student Task Statement
The 3 angle bisectors of triangle meet at point . The segments , , and show the distances from to each side of the triangle.
1. Explain how you know the lengths , , and are all equal.
2. What other congruent gures can you nd within the triangle? Explain your reasoning.
Student Response
1. must be the same length as because lies on the angle bisector of . In the same manner and must have the same length because lies on the angle bisector of .
Unit 7 Lesson 9: Circle Inside a Triangle
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