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 distance. . . .

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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.

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

Can you break down this conversion process into logical steps?

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

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 only 10ml pipettes?

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

Match pairs of cards so that they have equivalent ratios.

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

Use Excel to explore multiplication of fractions.

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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.

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

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

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

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

An environment that enables you to investigate tessellations of regular polygons

A metal puzzle which led to some mathematical questions.

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.

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?

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

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

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

Use an Excel spreadsheet to explore long multiplication.

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

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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

To avoid losing think of another very well known game where the patterns of play are similar.

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

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.

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

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...

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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?

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.

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

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?

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.