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

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

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.

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

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 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.

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

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

An environment that enables you to investigate tessellations of regular polygons

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

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

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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

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?

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

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

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 draw on the dotty grid which each have one dot in the middle?

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

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

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

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.

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?

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2?

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.

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.

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

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

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

Calculate the fractional amounts of money to match pairs of cards with the same value.

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

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?

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

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

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!

An environment which simulates working with Cuisenaire rods.

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

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?

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