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

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

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

A tool for generating random integers.

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

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

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

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

A metal puzzle which led to some mathematical questions.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Use Excel to explore multiplication of fractions.

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

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

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

Use an Excel spreadsheet to explore long multiplication.

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

An Excel spreadsheet with an investigation.

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.

Use Excel to practise adding and subtracting fractions.

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

Which dilutions can you make using only 10ml pipettes?

Which exact dilution ratios can you make using only 2 dilutions?

Can you locate these values on this interactive logarithmic scale?

Can you fill in the mixed up numbers in this dilution calculation?

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum. . . .

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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?

Prove Pythagoras Theorem using enlargements and scale factors.

An environment that enables you to investigate tessellations of regular polygons

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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.

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

A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!