1. Symmetry in a circular motion
Rotational Symmetry
Symmetry in a circular motion

2. Defining Rotational Symmetry
Rotational Symmetry happens when a shape or a design can be turned around its centre of rotation so that it actually fits onto its outline more than once in a complete turn
Now, a centre of rotation is the point around which you turn the object or the design
Usually, the centre of rotation is the exact centre of the design.
However, a centre of rotation can also be “off center”
Don’t forget: a design can have BOTH line symmetry and rotation symmetry.

3. Examples:
The centre of rotation is noted with a red dot in the following designs or shapes:

4. Examples of “off centre” rotations
These designs have a centre of rotation that is considered “off centre”

5. Order of Rotation
The order of rotation is the number of times which a shape or design fits into itself in one, complete turn of 360°.
The first design shown has an order of 8.
The order of rotation in the second design is 10.

6. Order and Angle of Rotation
The angle of rotation actually measures the minimum angle required in order to turn the shape onto itself. It can also be stated as a fraction of a turn.
This picture has an order of rotation of 4
its angle of rotation is 360 ÷ 4 = 90°
The fraction of turn is ¼

7. Order and Angle of Rotation
This picture has an order of rotation of 3.
its angle of rotation is 360 ÷ 3 = 120°
The fraction of turn is 1/3

8. Time to play
This website is AWESOME for playing with rotational symmetry. It has basic explanations, interactive examples, a symmetry artist activity and much more!
Check it out – what could be better than a website called “Math is fun”?

9. Time to practice:
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