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?

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?

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

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

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

A tool for generating random integers.

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

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

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

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?

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

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

Use Excel to explore multiplication of fractions.

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

An environment that enables you to investigate tessellations of regular polygons

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.

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.

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

An Excel spreadsheet with an investigation.

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

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

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?

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.

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. . . .

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?

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?

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. . . .

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.

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.

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.

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.

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. . . .

Match the cards of the same value.

A metal puzzle which led to some mathematical questions.

Can you locate these values on this interactive logarithmic scale?

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