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?

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?

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?

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?

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

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

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

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

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

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

Match pairs of cards so that they have equivalent ratios.

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.

A metal puzzle which led to some mathematical questions.

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?

Match the cards of the same value.

An Excel spreadsheet with an investigation.

Use Excel to explore multiplication of fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

Use an Excel spreadsheet to explore long multiplication.

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

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.

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

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

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.

Can you beat the computer in the challenging strategy game?

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.

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

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.

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.

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.

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. . . .

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?

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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!

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

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 weekly challenge concerning prime numbers.

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 tool for generating random integers.

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