Teacher Guide: Circumference & Area of Circles

Learning Objective 5-10 min lesson

Students will: Calculate the circumference and area of circles using the formulas C = 2(pi)r or C = (pi)d and A = (pi)r squared, and solve real-world problems involving circles.

Why this matters for FAST: Circle problems appear frequently on FAST. Students must know both formulas, when to use each, and how to work with pi (both as 3.14 and as an exact answer).

Materials Needed

Whiteboard/projector
Student Concept Worksheet
Circular objects
String and rulers
Calculators
Compass (optional)

Common Misconceptions to Address

Misconception #1: Confusing Radius and Diameter

Students use diameter in the area formula or radius in C = (pi)d, getting answers that are off by a factor of 2 or 4.

How to Address:

"The RADIUS is halfway across - from center to edge. The DIAMETER is all the way across - edge to edge. d = 2r. For area, you ALWAYS need the radius. If given diameter, divide by 2 first!"

Misconception #2: Forgetting to Square the Radius

Students calculate A = (pi)r instead of A = (pi)r squared, essentially finding circumference instead of area.

How to Address:

"Area is measured in SQUARE units. The 'squared' reminds us we're measuring the space inside. Always square the radius FIRST, then multiply by pi. A = (pi) times r times r."

Misconception #3: Not Knowing When to Use Which Formula

Students mix up when to use circumference vs area formulas.

How to Address:

"Circumference is the distance AROUND (like a fence). Area is the space INSIDE (like the grass). If the question mentions perimeter, border, or going around, use circumference. If it mentions covering, filling, or painting the surface, use area."

Lesson Steps

1

Activate Prior Knowledge (1 min)

Draw a circle. Ask: "What do we call the distance across?" (diameter) "What about halfway across?" (radius) "What's the distance around called?" (circumference)

2

Introduce Pi (1 min)

SAY THIS:

"Pi is a special number - about 3.14159... It NEVER ends! We write it as the symbol (pi) or use 3.14. Pi is the ratio of every circle's circumference to its diameter. Amazingly, it's the same for ALL circles!"

3

Circumference Formulas (2 min)

Circumference = Distance AROUND the circle

C = (pi)d or C = 2(pi)r

Both formulas work! Use whichever matches what you're given.

Example: r = 5 cm

C = 2 x (pi) x 5 = 10(pi) cm = 31.4 cm

4

Area Formula (2 min)

Area = Space INSIDE the circle

A = (pi)r squared

MUST use radius! If given diameter, divide by 2 first.

Example: r = 5 cm

A = (pi) x 5 squared = (pi) x 25 = 25(pi) = 78.5 sq cm

5

Guided Practice (2-3 min)

A circle has diameter 12 in. Find C. (C = (pi) x 12 = 12(pi) = 37.68 in)
A circle has radius 7 m. Find A. (A = (pi) x 49 = 49(pi) = 153.86 sq m)
A circular pool has diameter 20 ft. How much fencing is needed? (C = 20(pi) = 62.8 ft)

Check for Understanding

Quick Exit Ticket:

"A circle has a radius of 6 cm. What is its area?"

A) 12(pi) sq cm B) 36(pi) sq cm C) 6(pi) sq cm D) 18(pi) sq cm

Answer: B) 36(pi) sq cm. A = (pi)r squared = (pi) x 36 = 36(pi)

IXL Skills to Assign

Recommended IXL Practice:

Circumference of circles Area of circles Circles: word problems Radius and diameter

Differentiation & Extension

For struggling students: Use color coding - red for radius, blue for diameter. Have them circle whether the problem gives r or d before starting.

For advanced students: Introduce semicircles and quarter circles. Challenge them to find area when given circumference.

For home: Send Parent Activity sheet. Families can measure circular objects around the house.