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?

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.

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 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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?

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?

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

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

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.

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

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?

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 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?

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?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Can you complete this jigsaw of the multiplication square?

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

An interactive activity for one to experiment with a tricky tessellation

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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....?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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?

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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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?

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

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

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?

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?

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

Use the interactivity or play this dice game yourself. How could you make it fair?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!