Grade 7 › G7U07 Circles & Area

Grade 7 › G7U07 Circles & Area › L2
GRADE 7 · ALBERTAOUTCOME AB-G7-SS1

L2 · Pi and the circumference formula

Learning goal

“I can explain that π (pi) is the exact 'a little more than 3' that links circumference and diameter, and I can compute a circumference with C = πd or C = 2πr, using π ≈ 3.14 - and work backwards from a circumference to a diameter.”

Pi (π) — the number of diameters that fit around a circle: C / d. It is the same for every circle, about 3.14 (3.14159... - the decimal never ends or repeats).
Formula — a rule written with letters that works for every case, like C = πd.
Approximate (≈) — close to the true value but not exact. Because π never ends, every circumference we compute with 3.14 is approximate.
Worked example

A circle has diameter 10 cm. Find its circumference. Step 1: L1 said C is "a little more than 3 diameters." That "little more" is exact and has a name: C / d = π ≈ 3.14, for EVERY circle, big or small. Step 2: Rearranged, the formula is C = π x d. Use π ≈ 3.14 for hand work. Step 3: C = 3.14 x 10 = 31.4 cm. Compare with the L1 estimate: a little more than 30 - it fits.

Check yourself — explain it

Why is 31.4 cm an approximate answer, not an exact one?

Paired problem — example still visible

Diameter 4 cm -> C = 3.14 x 4 = 12.56 cm

Faded completion — last step is yours

"Diameter 8 cm: C = 3.14 x 8 = ___ cm" -> 25.12 cm

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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