seegongsik
Grade 3 (age 8-9)

grade 3 Introduction to Circles

A circle is a round shape made of all the points that sit the same distance from one center. Round things like coins, clocks, and pizzas are circles you meet every day. The middle is the center, the distance out to the edge is the radius, and the longest line through the center is the diameter, always twice the radius. Slide the radius and the circle grows; on the compass picture the opening between the pin and the pencil is that radius.

What is a circle?

🎯 Is every round shape a circle?
①Coins, clocks, and pizzas are round like circles
②A circle is made of all the points that are the same distance from a point in the middle (the center)
③A squashed round shape is not a circle, because its edge is not the same distance from the center all the way around

Parts of a circle

8
💡 Three parts of a circle
①The center (O) is the point in the middle of the circle
②The radius (r) is the distance from the center to a point on the circle, and it is the same in every direction
③The diameter (d) is a line segment through the center joining two points on the circle
④Any segment joining two points on the circle without passing through the center is shorter, so the diameter is the longest segment in the circle
⑤The radius and the diameter are written together under the picture

Drawing a circle with a compass

📐 Using a compass
①Where you press the point of the compass becomes the center
②The distance between the point and the pencil tip is the radius
③Keep that distance the same and turn the compass once to draw a circle
④Open it wide for a big circle and a little for a small one

Wrap-up

Diameter and radius
diameter = radius × 2 → d = 2r
The diameter is always twice the radius
Radius and diameter
radius = diameter ÷ 2 → r = d2
Half of the diameter is the radius
What makes a circle
distance from the center to every point on the circle = the same (= radius)
This is the key property that makes a circle a circle
🎯 Remember
①The center is the point in the middle of the circle
②The radius is the distance from the center to the circle, the same everywhere
③The diameter is twice the radius and the longest segment in the circle
④How wide the compass is open is the radius
⑤Same center and same radius means the same circle

Examples and unit check

Example 1
A circle has a radius of 5 cm. What is its diameter?
1
The diameter is twice the radius (d = 2r).
2
5 × 2 = 10, so the diameter is 10 cm.
▸ 10 cm
The diameter is always twice the radius.
Example 2
A circle has a diameter of 14 cm. What is its radius?
1
The radius is half of the diameter (r = diameter ÷ 2).
2
14 ÷ 2 = 7, so the radius is 7 cm.
▸ 7 cm
The radius is the diameter divided by 2.
Unit check
You open a compass to 6 cm and draw a circle. What is the diameter of the circle?
①3 cm
②6 cm
③12 cm
④36 cm
▸ ③ 12 cm
1
How wide the compass is open is the radius, so the radius is 6 cm.
2
diameter = radius × 2 = 6 × 2 = 12 cm.
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