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

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

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 remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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

Exchange the positions of the two sets of counters in the least possible number of moves

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?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

Can you fit the tangram pieces into the outline of these convex shapes?

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

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

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?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

How many loops of string have been used to make these patterns?

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

Can you fit the tangram pieces into the outline of Little Ming?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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

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!

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

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.

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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.

Can you fit the tangram pieces into the outlines of these clocks?

How many pieces of string have been used in these patterns? Can you describe how you know?

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

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 the child walking home from school?