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

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

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?

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

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

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

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

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

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

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

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

This activity challenges you to make collections of shapes. Can you give your collection a name?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

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

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?

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?

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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

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!

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

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

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?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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.

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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

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.

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

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

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

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

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

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

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....?

A game in which players take it in turns to choose a number. Can you block your opponent?

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