Cogito
Grade 7 Math · Chapter 7 · Lesson 1
Measuring a Circle
Where π actually comes from.
10 problems · about 18 minutes · 7.G.B.4
What this lesson teaches
The child discovers π as the ratio of circumference to diameter and computes circumference.
- Circumference divided by diameter is the same for every circle.
- That ratio is π, about 3.14.
- C = πd is a proportional relationship.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Solving Inequalities: 4x > 20. Smallest whole number x?
Answer 6
Why 6.
Review — Solving p(x + q) = r: 6(x + 2) = 42. What is x?
Answer 5
Why x = 5.
Warm Up
Straightforward practice. Get the method working first.
4 problemsDiameter 50, using π = 3.14. Circumference?
Answer 157
Why 157.
What is π?
Answer Circumference divided by diameter.
Why π is a measured ratio, the same for every circle.
Diameter 10, using π = 3.14. Circumference?
Answer 31.4
Why 3.14 × 10.
Radius 4. What is the diameter?
Answer 8
Why Double it.
Build It Up
The same ideas with more to keep track of.
2 problemsDiameter 100, using π = 3.14. Circumference?
Answer 314
Why 3.14 × 100.
Circumference divided by diameter is about what?
Answer 3.14
Why It never changes.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Wheel: A wheel has diameter 20 cm. What is its circumference, using 3.14 for π?
Answer 62.8 cm
Why 62.8 cm.
The Radius: A circle has radius 5 cm. What is its diameter?
Answer 10 cm
Why 10 cm.