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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

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

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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 these convex shapes?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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

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

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

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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.

What is the best way to shunt these carriages so that each train can continue its journey?

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

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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 outlines of Mai Ling and Chi Wing?

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

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 outline of this goat and giraffe?

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

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

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

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

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?

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

Can you find ways of joining cubes together so that 28 faces are visible?

Exploring and predicting folding, cutting and punching holes and making spirals.

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?