**What is rotational symmetry?**

A shape has rotational symmetry when it still **looks the same** after some rotation of less than one full turn through 360°.

A shape's degree of rotational symmetry is the number of **distinct orientations** in which it looks exactly the same **within one rotation**.

**Applied in geometric shapes**

If we take **a square **and rotate it through a full turn, it will look **exactly the same on four occasions**: after a quarter turn, half turn, three-quarters of a turn and a full turn.

We call this rotational symmetry of **order 4**.

If we take **a rectangle **and rotate it through a full turn, it will look the **same twice**: after half a turn and a full turn.

We call this rotational symmetry of **order 2**.

If we take **an isosceles triangle** and rotate it through a full turn, it will look the **same only once**: after a full turn.

We call this rotational symmetry of **order 1**.

**e.g. What order of rotational symmetry does this shape have?**

If we rotated this shape through a full turn, we would reach this **same image on three occasions**: 1/3 of a turn, 2/3 of a turn and a full turn.

So this shape has rotation symmetry of **order 3**.

**e.g. Which squares would we have to shade for this shape to have rotational symmetry of order 2?**

'Order 2' means it would look the same** twice** within one full rotation of 360°.

If we divide the full turn (360°) by this, we find that it looks the same every **180°**.

If we rotated the shape 180°, the shaded trio of squares would be in the **bottom left corner **instead, like this:

So this version of the square will have rotational symmetry to the **order of 2**.

**e.g. Which squares would we have to shade for this shape to have rotation symmetry of order 4?**

'Order 4' means it would look the same** four times** within a full rotation.

If we divide the full turn (360°) by this, we find that it looks the same every **90°**.

If we rotated the shape 90°, the shaded pair of squares would be in the **bottom right corner**.

If we rotated the shape another 90°, the shaded pair of squares would be in the **bottom left corner**.

If we rotated the shape a final 90°, the shaded pair of squares would be in the** top left corner**.

If we colour all these squares, our final image will look like this:

In this activity, we will recall and identify the rotational symmetry of common 2D shapes, plus locate squares in a grid to colour to create rotational symmetry to a specified order.