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

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?

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

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

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

What is the best way to shunt these carriages so that each train can continue its journey?

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.

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?

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

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?

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

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

Can you fit the tangram pieces into the outline of the sports car?

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

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

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.

Here are shadows of some 3D shapes. What shapes could have made them?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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.

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

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Can you fit the tangram pieces into the outline of this teacup?

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

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of Mah Ling?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

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