Take a look at the image below. How do you think it was created?

Did you notice any symmetry in the image?

Does this help you to imagine how the image was made?

Here is a diagram which shows how we created the image. We started with a triangle (shaded) and then used the coordinate grid to help us to rotate it through multiples of $90^{\circ}$ around the point $(0,0)$.

Create some images of your own by rotating a shape through
multiples of $90^{\circ}$.

You might like to start with a triangle as we did, or you
might want to use other shapes.

How can you use a coordinate grid to help you to rotate each
point around $(0,0)$?

What is the relationship between the coordinates of the points
as they rotate through multiples of $90^{\circ}$?

Here are some more ideas to
explore:

Can you use an isometric grid to rotate a shape through
multiples of $60^{\circ}$?

Try creating some images based on other rotations, such as
$30^{\circ}$ or $72^{\circ}$ or... (you will need to use a
protractor for these). What do you notice about the rotational
symmetry of your images?

What is the rotational symmetry of your final image if you
rotate through multiples of $80^{\circ}$ or $135^{\circ}$? Can you
explain why?

Here is the kind of image you could
try to create:

Send us pictures of your rotation
patterns along with your interesting mathematical
discoveries.