Your teacher will give you a set of cards with questions about circles.

1. Take turns with your partner to sort the cards into two groups based on whether you would use the circumference or the area of the circle to answer the question
   1. For each card that your partner sorts, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
   2. For each card that you sort, explain to your partner how you know which group it goes in.
2. Your teacher will assign you one card to examine more closely. What additional information would you need in order to answer the question on your card?
3. Estimate measurements for the circle that is described on your card.
4. Use your estimates to calculate the answer to the question.

In the previous activity you estimated the answer to a question about circles.

Create a visual display that includes:

• The question you were answering.
• A diagram of a circle labeled with your estimated measurements.
• Your thinking, organized so that others can follow it.
• Your answer, expressed in terms of and also expressed as a decimal approximation.

Here are two students’ answers for each question. Do you agree with either of them? Explain or show your reasoning.

1. How many feet are traveled by a person riding once around the merry-go-round?

   

   • Clare says, “The radius of the merry-go-round is about 4 feet, so the distance around the edge is about feet.”
   • Andre says, “The diameter of the merry-go-round is about 4 feet, so the distance around the edge is about feet.”

2. How much room is there to put glue on the back of a paper circle?

   

   • Clare says “The radius of the circle is about 3 centimeters, so the space for glue is about  cm².”
   • Andre says “The diameter of the circle is about 3 inches, so the space for glue is about  in².”

3. How far does the unicycle move when the wheel makes 5 full rotations?

   

   • Clare says, “The diameter of the unicycle wheel is about 0.5 meters. In 5 complete rotations it will go about  m².”
   • Andre says, “I agree with Clare's estimate of the diameter, but that means the unicycle will go about  m.”

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.