Which dilutions can you make using only 10ml pipettes?

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. . . .

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

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

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 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?

Can you locate these values on this interactive logarithmic scale?

Prove Pythagoras' Theorem using enlargements and scale factors.

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

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

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

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

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?

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

How do scores on dice and factors of polynomials relate to each other?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

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?

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

An environment that enables you to investigate tessellations of regular polygons

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

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

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!

Have you seen this way of doing multiplication ?

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.

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. . . .

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.

Can you correctly order the steps in the proof of the formula for the sum of a geometric series?

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?

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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. . . .

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.

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 explore multiplication of fractions.

How good are you at finding the formula for a number pattern ?

Can you beat the computer in the challenging strategy game?

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

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?

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

Can you work out which spinners were used to generate the frequency charts?

Can you work through these direct proofs, using our interactive proof sorters?