Can you make a 3x3 cube with these shapes made from small cubes?

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

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?

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

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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

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.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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 shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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

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

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Can you cut up a square in the way shown and make the pieces into a triangle?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

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 Little Ming?

Make a flower design using the same shape made out of different sizes of paper.

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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!

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?

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

Make a cube out of straws and have a go at this practical challenge.

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 outlines of the lobster, yacht and cyclist?

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.

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

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

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

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

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