Are these statements always true, sometimes true or never true?

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

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

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

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

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

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

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

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.

How many different symmetrical shapes can you make by shading triangles or squares?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

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

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

Can you devise a fair scoring system when dice land edge-up or corner-up?

When dice land edge-up, we usually roll again. But what if we didn't...?

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

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

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. . . .

Here is a chance to create some Celtic knots and explore the mathematics behind them.

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?

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

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

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

Look carefully at the video of a tangle and explain what's happening.

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?

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

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

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

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

Points off a rolling wheel make traces. What makes those traces have symmetry?

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

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

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

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

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?