Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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 outline of Granma T?

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

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

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

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 outline of these convex shapes?

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?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

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

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

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?

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

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?

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

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 fit the tangram pieces into the outline of this sports car?

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 outlines of the lobster, yacht and cyclist?

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 the child walking home from school?

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

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

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

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

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

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

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

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

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

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 Little Fung at the table?

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

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.

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