Grade 3 (age 8-9)

grade 3 Introduction to Circles

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?

🎯 Are all round shapes circles?

①Coins, clocks, pizzas — round things

②A circle = points all at equal distance from a center

③Squashed round = NOT a circle (distances differ from center)

Parts of a Circle

Radius (cm)8

💡 Three Parts of a Circle

①Center (O): the middle point

②Radius (r): distance from center to circle — same anywhere

③Diameter (d): longest line across — must pass center

④A chord that misses the center is shorter than the diameter

⑤Diameter = 2 × radius!

Drawing with a Compass

📐 How to Use a Compass

①Compass point = will become the center

②Distance between point and pencil = radius

③Spin without changing distance!

④Wider opening = bigger circle, smaller = smaller circle

Summary

Diameter & Radius

d = 2r (Diameter = Radius × 2)

Diameter is always 2× radius

Radius & Diameter

r = d2 (Radius = Diameter ÷ 2)

Half the diameter is the radius

Circle Property

All points on circle have equal distance from center (= radius)

This is what makes a circle a circle

🎯 Key Points

①Center = middle of circle

②Radius = center-to-circle distance (always equal)

③Diameter = 2 × radius (longest line)

④Compass opening = radius

⑤Same center + same radius = same circle!

Examples and Unit Test

Example 1

A circle has a radius of 5 cm. What is its diameter?

The diameter is twice the radius (d = 2r).

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?

The radius is half the diameter (r = diameter ÷ 2).

14 ÷ 2 = 7, so the radius is 7 cm.

▸ 7 cm

The radius is the diameter divided by 2.

Unit Test

A compass is opened to 6 cm to draw a circle. What is the diameter?

①3 cm

②6 cm

③12 cm

④36 cm

▸ ③ 12 cm

The compass opening is the radius, so the radius is 6 cm.

Diameter = radius × 2 = 6 × 2 = 12 cm.

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Plane Figures

Length & Time