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

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?

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!

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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.

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

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?

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

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?

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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.

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?

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

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

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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.

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

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?

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

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.