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

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?

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.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Can you break down this conversion process into logical steps?

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

Which dilutions can you make using only 10ml pipettes?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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

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 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. . . .

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.

Can you find a way to turn a rectangle into a square?

Match pairs of cards so that they have equivalent ratios.

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

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

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?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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?

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you explain the strategy for winning this game with any target?

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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

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?

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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

Prove Pythagoras' Theorem using enlargements and scale factors.

An Excel spreadsheet with an investigation.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Use an Excel spreadsheet to explore long multiplication.

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?