Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

Can you find triangles on a 9-point circle? Can you work out their angles?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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.

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

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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!

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

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway 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.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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?

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?

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?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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.

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

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?

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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.

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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.

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?

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

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

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

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

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?

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.

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

Can you explain the strategy for winning this game with any target?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

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?

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

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4