Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Move just three of the circles so that the triangle faces in the opposite direction.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

An activity centred around observations of dots and how we visualise number arrangement patterns.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

What happens when you try and fit the triomino pieces into these two grids?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Can you find a way of counting the spheres in these arrangements?

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

Can you work out what is wrong with the cogs on a UK 2 pound coin?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you fit the tangram pieces into the outlines of the convex shapes?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Which of these dice are right-handed and which are left-handed?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Make one big triangle so the numbers that touch on the small triangles add to 10.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Watch this animation. What do you see? Can you explain why this happens?

Can you fit the tangram pieces into the outline of the plaque design?

Can you fit the tangram pieces into the silhouette of the junk?

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

Can you fit the tangram pieces into the outline of the playing piece?

Can you fit the tangram pieces into the outline of the clock?

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outlines of the rabbits?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of the dragon?

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?