Page 123 - IM_FL_Geometry_Print Sample

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, 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 a radius of 4 units and a central angle of radians. What is the area of the sector?
2. A sector has a radius of 20 units and a central angle of 1.3 radians. What is the area of the sector?
3. One sector has a central angle of 0.9 radians and a radius of 2 units. A sector of a di erent circle has a central angle of 2.5 radians. What does the radius of the other sector need to be in order for the two sectors to have the same area?
4. One circle has a radius of 5 units and another circle has a radius of 8 units. What angle does a sector on the larger circle need so that the area of the sector is the same as the area of the small circle?
Student Response
1. square units, or approximately 5.24 square units. 2. 260 square units.
3. units or equivalent.
4. radians, or approximately 2.45 radians.
Activity Synthesis
Ask students to explain their reasoning for question 3. If time allows, ask for responses to other questions. Consider asking:
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Teacher Guide