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IM 7.3.10 Lesson: Distinguishing Circumference and Area

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

About how many cheese puffs can fit on the plate in a single layer? Explain your reasoning.

Sort the cards into two groups based on whether you would use the circumference or the area of the circle to answer the question. Pause here so your teacher can review your work.

Your teacher will give you cards with questions about circles.

Your teacher will assign you a card to examine more closely. First, write which card you have. Then, explain what additional information you would need in order to answer the question on your card?

Estimate measurements for the circle on your card.

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

Use this applet to create a display.

How many feet are traveled by a person riding once around the merry-go-round? Here are two students’ answers. Do you agree with either of them? Explain your reasoning.

  • 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.”

How much room is there to spread frosting on the cookie? Here are two students’ answers. Do you agree with either of them? Explain your reasoning.

  • Clare says “The radius of the cookie is about 3 centimeters, so the space for frosting is about  .”
  • Andre says “The diameter of the cookie is about 3 inches, so the space for frosting is about ”

How far does the unicycle move when the wheel makes 5 full rotations? Here are two students’ answers. Do you agree with either of them? Explain your reasoning.

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

A goat (point G) is tied with a 6-foot rope to the corner of a shed.

The floor of the shed is a square whose sides are each 3 feet long. The shed is closed and the goat can't go inside. The space all around the shed is flat, grassy, and the goat can't reach any other structures or objects. What is the area over which the goat can roam? 

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