standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Narrative
This warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use geometric language and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as square, cube, triangle, circle, flat, and solid.
Launch
Groups of 2
Display the image.
“Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
Student Facing
Which one doesn’t belong?
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
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Activity Synthesis
“Let’s find at least one reason why each one doesn’t belong.”
“What are the names of the shapes?”
“I heard someone say _____. What does that mean?”


aligns: no