standard_description: Explain and use the relationship between the sine and cosine of complementary angles.
problem_activity: Warm-up
The purpose of this Math Talk is to elicit strategies and understandings students have for using tools to compare angles. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to compare or accurately reproduce angles to draw rotated figures.
Launch
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion. It is okay if you don’t get through all 4 problems.
Student Facing
For each figure, which pair of angles appears congruent? How could you check?
Figure 1
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Figure 2
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Figure 3
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Figure 4
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Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate
\(\underline{\hspace{.5in}}\)
’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”
Note that measuring angles is not the same as proving they are congruent, due to the limitation of measuring tools. Make sure all students are comfortable using a protractor to measure angles.
If not mentioned by students, there is no need to bring up arcs, chords, or congruent triangles. If students measure chords or arc lengths to compare angles, emphasize that the circles used to define the arcs or chords must be the same size.
Speaking: MLR8 Discussion Supports.
Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because . . ." or "I noticed _____ so I . . ."  Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no