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

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

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

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

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

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?

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

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

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 sports car?

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

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 outline of Little Ming playing the board game?

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 rabbits?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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

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

Can you fit the tangram pieces into the outline of these convex shapes?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

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

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

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

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

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?

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 Mai Ling and Chi Wing?

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

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.

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 Mai Ling?

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 workmen?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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?

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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

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?