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6-8 Grade 7 Unit 3 Lesson 7

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

Grade 6 •Grade 7 Grade 8

Unit

Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11

K-5
6-8
9-12

Grade 6
Grade 7
Grade 8

Accelerated 6
Accelerated 7

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11

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Unit 3, Lesson 7

Exploring the Area of a Circle

Grade 7

Practice

Problem 1
Student Task Statement
The -axis of each graph has the diameter of a circle in meters. Label the -axis on each graph with the appropriate measurement of a circle:
radius (m), circumference (m), or area (m²).

A
First of three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's. First graph is curved upward from left to right, begins at the origin, passes through 2 comma 3, 3 comma 7, 4 comma 12, 5 comma 19.

B
Second of three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's. Second graph is a upward line from left to right, begins at the origin, passes through 2 comma 1, 4 comma 2, 6 comma 3, 8 comma 4.

C
Third of three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's. Third graph is a upward line from left to right, begins at the origin, passes through 2 comma approximately 6 and 28 hundredths, 4 comma approximately 12 and 56 hundredths, 6 comma 18 and 84 hundredths.

Lesson 7 Resources

Student Materials

to access Practice Problem Solutions.

Problem 2

Student Task Statement

Priya drew a circle with a circumference of 25 cm. Clare drew a circle with a diameter that is 3 times the diameter of Priya’s circle.

What is the circumference of Clare’s circle?
Noah drew a circle with an area of 500 in². Han drew a circle with a diameter that is 3 times the diameter of Noah’s circle.

Estimate the area of Han’s circle. Explain your reasoning.

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Problem 3

Student Task Statement

Each picture shows two squares and a circle.

Explain why the area of this circle is more than 2 square units but less than 4 square units.

Two squares and circle on a grid of 4 units by 4 units. In the center of the grid is a square that measures two units high by two units wide. Within the square is a circle, with a diameter of 2 units. Within the circle is another square, rotated so that the each of the four vertices of the square meet with a point of the circle and the midpoint of the larger square.
Explain why the area of this circle is more than 18 square units and less than 36 square units.

A square with a circle inside of it and a square inside of the circle. The shapes are drawn on a grid. The outer square has side lengths = 6 units. The Circle has diameter = 6 units. The inner square is turned such that its four corners correspond with the midpoints of each side of the outer square.

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Problem 4

ForLesson 3: Exploring Circumference

Student Task Statement

Point is the center of the circle, and the length of is 13 centimeters.

What is the radius of this circle?
What is the circumference of this circle?

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Problem 5

ForLesson 4: Applying Circumference

Student Task Statement

The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.

In one rotation of the carousel, how much farther does Mai travel than Kiran?
One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?

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Problem 6

ForLesson 5: Circumference and Wheels

Student Task Statement

Lin’s bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels?

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Problem 7

from an earlier course

Student Task Statement

Each student has a goal to read for 40 minutes. How many minutes has each student read so far?

Elena has read for 25% of the goal.
Tyler has read for 75% of the goal.
Jada has read for 150% of the goal.

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