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A circle has radius 10 centimeters. Suppose an arc on the circle has length
The central angle of this shaded sector measures 45 degrees, and the sector’s area is
Kiran says, “We can find the area of the whole circle, the arc length of the sector, and the circumference of the circle with this information.”
Priya says, “But how? We don’t know the circle’s radius!”
Do you agree with either of them? Explain or show your reasoning. Calculate as many of the values Kiran mentioned as possible.
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
Ask your partner for the specific information that you need. “Can you tell me
Explain to your partner how you are using the information to solve the problem. “I need to know
Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know
Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.
We can work backward from information about a sector or arc to get information about the whole circle.
Suppose a circle has an arc with length
For more difficult problems, we can write equations. Suppose a circle has a sector with area
Solve this equation to find that the circle’s area is