Seventh Grade · Math · week 28

Circles: discovering pi by measuring

Discover that the ratio of circumference to diameter is the same constant, pi, for every circle, by measuring real circular objects.

Every circle, no matter its size, shares one hidden number: divide its circumference (the distance around) by its diameter (the distance straight across through the center), and you always get the same result, about 3.14. That constant is called pi.

This is really just proportionality from earlier in the year -- circumference is proportional to diameter, and pi is the constant of proportionality. Measuring real circles is the best way to discover this for yourself instead of just being told.

📋 For the teacher
Teach it (10–15 min):
  • Actually measure a few real circular objects together -- a plate, a lid, a can -- with a string or tape measure for the circumference and a ruler for the diameter.
  • Divide each pair of measurements and notice the ratio lands close to 3.14 every single time.
  • Introduce radius as half of the diameter, and practice converting between them before circumference comes up again next week.
  • Explain that pi is a never-ending decimal (3.14159...), and 3.14 is just a useful, accurate-enough estimate.
Talk about it:
  • What is pi, in your own words, after measuring it yourself?
  • How is the radius related to the diameter?
  • Why is 3.14 called an ESTIMATE of pi rather than its exact value?

Mastery looks like: They explain pi as the constant ratio of circumference to diameter, and confirm it by measuring or computing real circles.

Common stumbles: Confusing radius and diameter (using radius where diameter is needed, or the reverse); treating 3.14 as the exact value of pi rather than an estimate.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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