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

Use an interactive Excel spreadsheet to investigate factors and multiples.

Match pairs of cards so that they have equivalent ratios.

An Excel spreadsheet with an investigation.

Use Excel to explore multiplication of fractions.

Use Excel to practise adding and subtracting fractions.

Use an Excel spreadsheet to explore long multiplication.

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

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

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

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

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

An environment that enables you to investigate tessellations of regular polygons

A tool for generating random integers.

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

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

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

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?

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

Can you beat the computer in the challenging strategy game?

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.

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

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.

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

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. . . .

A metal puzzle which led to some mathematical questions.

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.

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.

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?

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?

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

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

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.

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

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 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 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?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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 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.

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?

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. . . .

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