A collection of our favourite pictorial problems, one for each day of Advent.

Match pairs of cards so that they have equivalent ratios.

Match the cards of the same value.

An Excel spreadsheet with an investigation.

An environment that enables you to investigate tessellations of regular polygons

Use an interactive Excel spreadsheet to explore number in this exciting game!

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use Excel to explore multiplication of fractions.

Use an Excel spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Use an interactive Excel spreadsheet to investigate factors and multiples.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

A tool for generating random integers.

Use Excel to investigate the effect of translations around a number grid.

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.

The classic vector racing game brought to a screen near you.

Here is a chance to play a fractions version of the classic Countdown Game.

A metal puzzle which led to some mathematical questions.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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?

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. . . .

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.

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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.

Can you beat the computer in the challenging strategy game?

A collection of resources to support work on Factors and Multiples at Secondary level.

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

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

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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.

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.

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. . . .

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

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. . . .

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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.

Cellular is an animation that helps you make geometric sequences composed of square cells.