Applying Circumference
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students examine pictures of circular objects that have one measurement given. They identify which measurement is shown and then use the given measurement to reason about the other measurements of the circle. Students can find the diameter given the radius, or vice versa. However, they do not need to do any calculations that involve pi at this time. They will continue working with these situations in a later activity.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by 2 minutes of partner discussion.
Advances: Conversing, Reading
Student Task
For each picture, which measurement is shown? Be prepared to explain your reasoning.
-
Wagon wheel: 3 feet
A picture of a wagon wheel with a measuring tool starting from one point on the wheel, goes through the wheel center to a point on the other side of the wheel. -
Plane propeller: 24 inches
A picture of a plane propeller with three identical propeller blades. A measuring tool starts from the center of the propeller and goes to the end of the blade. -
Sliced orange: 20 centimeters
A picture of a sliced orange. A measuring tool goes around the entire circular region of the orange.
Sample Response
- For the wagon wheel, the measurement of the diameter is shown. The measuring tape goes all the way across the wheel.
- For the plane propeller, the measurement of the radius is shown. The measuring tape goes from the center to the edge of the propeller.
- For the sliced orange, the circumference is shown. The measuring tape goes around the outside of the orange.
Activity Synthesis (Teacher Notes)
Display this table for all to see, without any measurements filled in.
| object | radius | diameter | circumference |
|---|---|---|---|
| wagon wheel | |||
| airplane propeller | |||
| sliced orange |
For each picture, ask students to share which measurement is shown in the picture. Record the given measurement in the corresponding cell of the table. Then, ask students what else we know about the measurements of this circle.
- For the wagon wheel, we know the radius is 1.5 feet, because 3÷2=1.5.
- For the airplane propeller, we know the diameter is 48 inches, because 24⋅2=48.
- We also know that we could find the other measurements by multiplying or dividing by pi. However, it is not necessary to do any calculations involving pi at this time.
Continue recording measurements in the table as students share their reasoning and come to an agreement. By the end of the discussion, the table should have these five measurements in place.
| object | radius | diameter | circumference |
|---|---|---|---|
| wagon wheel | 1.5 ft | 3 ft | |
| airplane propeller | 24 in | 48 in | |
| sliced orange | 20 cm |
Standards
- 7.G.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.
- 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.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Applying Circumference
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students examine pictures of circular objects that have one measurement given. They identify which measurement is shown and then use the given measurement to reason about the other measurements of the circle. Students can find the diameter given the radius, or vice versa. However, they do not need to do any calculations that involve pi at this time. They will continue working with these situations in a later activity.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by 2 minutes of partner discussion.
Advances: Conversing, Reading
Student Task
For each picture, which measurement is shown? Be prepared to explain your reasoning.
-
Wagon wheel: 3 feet
A picture of a wagon wheel with a measuring tool starting from one point on the wheel, goes through the wheel center to a point on the other side of the wheel. -
Plane propeller: 24 inches
A picture of a plane propeller with three identical propeller blades. A measuring tool starts from the center of the propeller and goes to the end of the blade. -
Sliced orange: 20 centimeters
A picture of a sliced orange. A measuring tool goes around the entire circular region of the orange.
Sample Response
- For the wagon wheel, the measurement of the diameter is shown. The measuring tape goes all the way across the wheel.
- For the plane propeller, the measurement of the radius is shown. The measuring tape goes from the center to the edge of the propeller.
- For the sliced orange, the circumference is shown. The measuring tape goes around the outside of the orange.
Activity Synthesis (Teacher Notes)
Display this table for all to see, without any measurements filled in.
| object | radius | diameter | circumference |
|---|---|---|---|
| wagon wheel | |||
| airplane propeller | |||
| sliced orange |
For each picture, ask students to share which measurement is shown in the picture. Record the given measurement in the corresponding cell of the table. Then, ask students what else we know about the measurements of this circle.
- For the wagon wheel, we know the radius is 1.5 feet, because 3÷2=1.5.
- For the airplane propeller, we know the diameter is 48 inches, because 24⋅2=48.
- We also know that we could find the other measurements by multiplying or dividing by pi. However, it is not necessary to do any calculations involving pi at this time.
Continue recording measurements in the table as students share their reasoning and come to an agreement. By the end of the discussion, the table should have these five measurements in place.
| object | radius | diameter | circumference |
|---|---|---|---|
| wagon wheel | 1.5 ft | 3 ft | |
| airplane propeller | 24 in | 48 in | |
| sliced orange | 20 cm |
Standards
- 7.G.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.
- 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.