Eight Circles

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Objective

SWBAT find the area of a composition of circles

Big Idea

There is more than one circle. Now what?

Launch

5 minutes
  • POD

As students enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD allows students to use MP 3 continually based on the discussions we have about the problem each day.

  • Learning Target

The target for the day is also on the SMARTboard each day when students enter the room.  The target for today’s lesson is for students to calculate the area and circumference of a circle.

To start the class we need to discuss specifically how to find the area of a circle. I want to work through a problem to ensure they are comfortable with finding the area of one circle before they expand to find the area of a figure comprised of several circles. The question will require students to use their knowledge of not only the formula but of the relationship between radius and diameter. It will help me determine what kind of questions I should ask while students are working with their partners. It will also help me determine where I should direct my attention as I walk around to support students. Who needs scaffolding? Who might need some intervention? Are their partners I need to sit with to help?

Find the area of a circle whose diameter is 12 m.

Explore

30 minutes

Eight Circles is a task on the Illustrative Mathematics web site. The exploration today will ask students to find the area of a composite of circles. Students will work with a partner to find the area of the small circles in a figure. They will also find the area of the larger composite figure. They will really rely on MP 1 to get through this task. There are no written, step-by-step directions so they will have to rely on their own understanding and their perseverance to find a solution. I will walk around and talk to the different partners to support them as they work but it is important for them to grapple with the concept and make meaning of it. I want them to recognize the diameter of the larger circle and use that information to help find the solution. Are they able to find the area of the smaller circles? Do they see any relationship between the larger circle and the smaller circles? I am interested to see what they think is the important information and how do they apply that information. The discussion between the partners will be valuable as well. I will get to hear their discussion and rationale for the decisions they make.

Landing

5 minutes

To close the class I want students to continue thinking about their work during class. It is possible that students are not finished with finding the area of the figures so I want to ask a question to help promote thinking. They can write a response to help me determine what questions I can ask during the next class session.

How much area does the shaded part of the figure represent? Did you account for that space in your calculations?