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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

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?

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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.

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

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

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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. . . .

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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.

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.

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.