This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in Maths and get you ready for the exciting next step into Year 8!

Let's go for a spin!

In this guide, you will learn:

• the two main types of symmetry: line symmetry (a fold) vs. rotational symmetry (a turn)
• what rotational symmetry is and how to find it
• what the 'order' of rotational symmetry means and how to count it

We already know that a shape has line symmetry if you can fold it in half with a 'mirror line' and both sides match perfectly.

But there is a second type of symmetry: rotational symmetry.

A shape has rotational symmetry if it looks exactly the same after being turned (rotated) around its centre point, before it gets back to the start.

The number of times a shape fits perfectly onto itself during one full 360° spin is called its order of rotational symmetry.

If you spin a square, it fits perfectly…

After 90°

After 180°

After 270°

After 360° (back at the start)

It fits 4 times. So, a square has rotational symmetry of order 4.

If you spin a rectangle, it only fits perfectly…

• after 180° (it's upside down, but fits the space)

• after 360° (back at the start)

It fits two times. So, a rectangle has rotational symmetry of order 2.

What about order 1? If a shape only fits onto itself after one full 360° turn (ie when it's back where it started), we say it has order 1. This means it has NO rotational symmetry. An irregular scalene triangle or a kite has order 1.

Spin-tastic! You now know what makes a shape symmetrical.

It can have:

• line Symmetry (a mirror fold)
• rotational Symmetry (a turn)

The order of rotational symmetry is the number of times a shape fits perfectly onto itself in one full 360° turn.

Think about these questions to stretch your thinking and sharpen your skills!

• Can a shape have line symmetry but no rotational symmetry (order 1)? (Hint: Think of a kite or a capital 'A').

• Can a shape have rotational symmetry but no line symmetry? (Hint: Think of a parallelogram).

• What is the order of rotational symmetry for a perfect circle?

Have a chat about your answers with a parent, teacher or your class.