What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and. . . .

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

What is the missing symbol? Can you decode this in a similar way?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

Can you place the blocks so that you see the relection in the picture?

Someone at the top of a hill sends a message in semaphore to a friend in the valley. A person in the valley behind also sees the same message. What is it?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

This problem explores the shapes and symmetries in some national flags.

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

This interactivity allows you to sort letters of the alphabet into two groups according to different properties.

Follow these instructions to make a five-pointed snowflake from a square of paper.

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Use the clues about the symmetrical properties of these letters to place them on the grid.

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Use the information on these cards to draw the shape that is being described.

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?

Can you deduce the pattern that has been used to lay out these bottle tops?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

This activity investigates how you might make squares and pentominoes from Polydron.

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?