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

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

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?

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

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?

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

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.

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.

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. . . .

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

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?

Can you beat the computer in the challenging strategy game?

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 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?

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.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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?

Use Excel to explore multiplication of fractions.

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?

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. . . .

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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 Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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.

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.

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.

A tool for generating random integers.

A weekly challenge concerning prime numbers.

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

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 classic vector racing game brought to a screen near you.

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

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

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

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

A metal puzzle which led to some mathematical questions.

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

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

Cellular is an animation that helps you make geometric sequences composed of square cells.

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