Exploring the Area of a Circle

5 min

Narrative

This warm-up prompts students to compare four figures on a grid. In making comparisons, students have a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the figures for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three figures that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

<p>Four figures labeled A--D on a grid.</p>

Sample Response

Sample responses:

A, B, and C go together because:

  • They do not have a hole in the middle.

A, B, and D go together because: 

  • They have straight sides.
  • We can figure out their areas.
  • They have an area of 24 square units.

A, C, and D go together because: 

  • They are 5 units wide.
  • They don’t have any acute angles or obtuse angles.

B, C, and D go together because: 

  • They have line symmetry.

Synthesis

The goal of this discussion is to get students wondering about the area of Figure C.

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Because there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology that they use, such as “length,” “width,” “height,” “area,” “straight line,” “angle,” etc. and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?”

If determining the area of each figure does not come up during the conversation, ask students to discuss this idea. The key takeaway is that students have enough information to determine the area of Figures A, B, and D. They all have an area of 24 square units. The goal is to leave students wondering how they could approximate or determine the area of Figure C.

Standards
Addressing
  • 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
  • 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

20 min

20 min