Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Sort the houses in my street into different groups. Can you do it in any other ways?

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!

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

What happens when you try and fit the triomino pieces into these two grids?

Move just three of the circles so that the triangle faces in the opposite direction.

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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?

Can you find all the different triangles on these peg boards, and find their angles?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

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

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

How many trains can you make which are the same length as Matt's, using rods that are identical?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Make one big triangle so the numbers that touch on the small triangles add to 10.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

Can you sort these triangles into three different families and explain how you did it?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Try out the lottery that is played in a far-away land. What is the chance of winning?