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

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

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

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

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

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

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 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?

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.

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!

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

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

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

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

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?

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....?

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?

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

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.

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

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

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

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?

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

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?

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?

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

Can you find all the different ways of lining up these Cuisenaire rods?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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

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

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.

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

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?

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Train game for an adult and child. Who will be the first to make the train?