Geometry

Lesson 8

Math

Unit 6

7th Grade

Lesson 8 of 21

Objective


Determine the relationship between the area and radius of a circle and use it to solve problems.

Common Core Standards


Core Standards

  • 7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Criteria for Success


  1. Approximate the area of a circle using a grid.
  2. Informally derive the formula for the area of a circle using wedges of a circle.
  3. Know the formula that relates the area and circumference of a circle: $${{A=\pi r^2}}$$.
  4. Use the formula $${{A=\pi r^2}}$$ to solve problems.

Tips for Teachers


  • Lessons 8 and 9 focus on the relationship between a circle’s area and its radius. In Lesson 8, students determine this relationship and the formula that represents it. In Lesson 9, students will solve real-world and mathematical problems involving area.
  • Anchor Problem 2 uses a computer applet to investigate the area of a circle using decomposition and rearrangement of the pieces. For students to use this applet on their own or in pairs, they will need access to computers. Alternatively, teachers can use their computer and project to the class. 
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Anchor Problems

25-30 minutes


Problem 1

Use the centimeter grid to find an approximate area of the circle. Explain why your approximation is reasonable.

Guiding Questions

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Student Response

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Problem 2

Use this applet from Academo, Area of a circle (Rearrangement Method) to informally derive the relationship between the area of a circle and its circumference.

Start with a small number of sectors or wedges of the circle and then slowly increase the number. Click “rearrange” after each number.

Then answer the questions:

a.   How are the circle wedges being rearranged?

b.   What shape are the rearranged pieces taking?

c.   What are the dimensions of the rearranged shape?

d.   How can you determine the area of a circle?

Guiding Questions

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Student Response

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References

Academo Area of a Circle (Rearrangement Method)

Area of a Circle (Rearrangement Method) is made available by Academo. © Academo.org 2016. Accessed March 10, 2018, 11:26 a.m..

Problem 3

Use the relationship between area and radius to solve the two problems below.

a.   The radius of a circular patch of grass is 3 yards. What is the area of the patch of grass?

b.   The area of a circular plate is approximately $${50.24 \space\mathrm{in^2}}$$. What is the radius of the plate?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Problem 1

A circle is divided into 16 equal wedges, as shown below. Explain or show how you can rearrange the pieces to determine the area of the circle. 

Student Response

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Problem 2

Find the area of a circle that has a radius of 5 inches.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include spiraled review from the unit, including procedural problems solving equations if additional practice is needed.

Next

Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.

Lesson 9
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Angle Relationships

Topic B: Circles

Topic C: Building Polygons and Triangles

Topic D: Solid Figures

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