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?

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?

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

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?

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?

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.

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

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?

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?

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

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?

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

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

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

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

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?

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?

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

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.

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

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

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

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

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....?

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

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?

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?

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

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?

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

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

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

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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?

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