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

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!

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

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 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?

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

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 visualise what shape this piece of paper will make when it is folded?

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

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

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

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

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

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 these rabbits?

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

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.

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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?

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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

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

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?

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

What is the greatest number of squares you can make by overlapping three squares?

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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

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

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

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

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

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

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 the rocket?

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

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

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