Pizza Pi: Sizing Circles and Watering Lawns
Shared by A STEM Educator
Students will derive and apply the formulas C = πd and A = πr² to solve problems involving circular pizza sizes and sprinkler watering coverage, while distinguishing between circumference and area and correctly interpreting radius versus diameter.
Lesson Overview
Students explore circumference and area of circles through the real-world contexts of pizza sizing and sprinkler coverage, discovering π through hands-on measurement and building toward the area formula via a wedge-rearrangement activity.
Materials
- Circular bottle caps (3–5 per pair of students)
- String or yarn (cut into ~30 cm strips)
- Rulers
- Printed pizza size comparison handout
- Scissors
- Tape
- Markers
- Plain white paper (for wedge-cutting activity)
- Compasses or circular tracers (bowls, cups)
- Basic calculators
- Whiteboard and markers
Scaffolded Task Progression
Work with a partner. Wrap a piece of string around a circular bottle cap to measure its circumference. Then measure the diameter of the same cap with a ruler. Divide circumference ÷ diameter and record your result. Repeat for two more bottle caps of different sizes.
| Bottle Cap | Circumference (cm) | Diameter (cm) | C ÷ d |
|---|---|---|---|
| Small | |||
| Medium | |||
| Large |
What do you notice about the C ÷ d column?
Estimate the circumference of a 10-inch diameter circular plate using .
The plate has a diameter of 10 inches. Use the approximation to find a quick estimate.
[ Interactive graph / diagram, available in the full lesson ]
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