Circumference and Pi — Measuring the Circle

π is one of mathematics' great surprises: every circle, everywhere, has this same ratio. The child measures five circles, computes C/d for each, and finds the same number. The persistence of π is the control.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Geometry
• Level: Ages 9-10

Objectives

• Measure circumference and diameter of multiple circles
• Discover that C/d is constant across all circles ≈ 3.14159…
• Introduce π as the ratio
• Apply C = πd and C = 2πr

Materials

• Circular objects of varied sizes (jar lid, plate, coin, wheel)
• String and ruler
• Calculator
• Recording table

Instructions

1. Select a circular object. 2. Wrap string around the circumference, mark, measure. 3. Measure the diameter with a ruler. 4. Compute C/d on the calculator. 5. Record. 6. Repeat with four more circles of different sizes. 7. Note all ratios are close to 3.14159… 8. Introduce π as this ratio. 9. Derive C = πd, and C = 2πr (since d = 2r).

Educator tip

The moment of discovering π feels like a secret key. Let children be surprised — don't announce the answer.

Assessment

Note measurement accuracy, recognition of constant ratio, and formula application.

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