Video solutions to help Grade 7 students learn how to give an informal derivation of the relationship between the circumference and area of a circle.

Related Topics:

Lesson Plans and Worksheets for Grade 7

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Common Core For Grade 7

• students learn how to
examine the meaning of quarter circle and semicircle.

• Students solve area and perimeter problems for regions made out of rectangles, quarter circles, semicircles,
and circles, including solving for unknown lengths when the area or perimeter is given.

• The area of a quarter of a circular region is 1/4 of the area of a circle with the same radius.

• If a problem asks you to use 22/7 for π, look for ways to use fraction arithmetic to simplify your computations in the problem.

• Problems that involve the composition of several shapes may be decomposed in more than one way.

Lesson 18 Opening Exercise

Draw a circle of diameter 12 cm and a square of side length 12 cm on grid paper. Determine the area of the square and the circle.

Brainstorm some methods for finding half the area of the square and half the area of the circle.

Find the area of half of the square and half of the circle, and explain to a partner how you arrived at the area.

What is the ratio of the new area to the original area for the square and for the circle?

Find the area of one-fourth of the square and the circle, first by folding and then by another method. What is the ratio of the new area to the original area for the square and for the circle?

Write an algebraic expression that will express the area of a semicircle and the area of a quarter circle.

What is the area of the quarter circle?

Find the area of the entire placemat. Explain your thinking regarding the solution to this problem.

If Marjorie wants to make six placemats, how many square inches of fabric will she need?

Marjorie decides that she wants to sew on a contrasting band of material around the edge of the placemats. How much binding material will Marjorie need?

Draw a diagram to assist you in solving the problem.

What information is needed to solve the problem? Next, find the area.

2. The circumference of a circle is 9π cm.

a. What is the diameter?

b. What is the radius?

c. What is the area?

3. If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.

4. Find the area in the rectangle between the two quarter circles if AB = 7 ft., FB = 9 ft., and HD = 7 ft. Use π = 22/7.

2. In the figure below, Ken’s company has placed sprinkler heads at the center of the two small semicircles. The radius of the sprinklers is 5ft. If the area in the larger semicircular area is the shape of the entire lawn, how much of the lawn will not be watered? Give your answer in terms of π and to the nearest tenth. Explain your thinking.