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
The purpose of this activity is to analyze a clock showing a time when it can be difficult to tell the difference between the hour and the minute hand. This activity allows students to discuss how they know where the hands are placed when the time is to the hour.
Launch
Groups of 2
Display the clock in the first problem.
“Diego and Priya read the clock and got two different times.”
“Who is correct? How do you know?”
Activity
2 minutes: partner discussion
5 minutes: independent work time
Monitor for a student who says the hour hand is pointing to 6 and one who says that for 12:30 the hour hand should be between 12 and 1.
Student Facing
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Diego says this clock shows 6:00.
Priya says the clock shows 12:30.
Who do you agree with? Why?
Synthesis:
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Student Response
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Activity Synthesis
Invite previously identified students to share.
“Why do you think Priya got mixed up? What could you say to help her revise her thinking?” (Priya mixed up the minute and hour hands. I could remind her that the short hand is the hour and the long hand is the minute. I could remind her that if it was 12:30 the hour hand would have to be between two numbers.)
“On the blank clock, draw hands to show 12:30.”


aligns: no