Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

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

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

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

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 these people?

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

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 this telephone?

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?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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 Little Ming playing the board game?

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

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?

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

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

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 ...

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

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

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

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

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

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

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

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 Wai Ping, Wah Ming and Chi Wing?

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

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.

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

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

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

Reasoning about the number of matches needed to build squares that share their sides.

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

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

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

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 Mai Ling and Chi Wing?