What is the quickest route across a ploughed field when your speed around the edge is greater?
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.
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.
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.
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?
Can you beat the computer in the challenging strategy game?
To avoid losing think of another very well known game where the patterns of play are similar.
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 Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
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. . . .
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?
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.
Use Excel to explore multiplication of fractions.
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.
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
A weekly challenge concerning prime numbers.
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!
Play a more cerebral countdown using complex numbers.
Play countdown with vectors.
How good are you at estimating angles?
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. . . .
Play countdown with matrices
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.
Balancing interactivity with springs and weights.
How good are you at finding the formula for a number pattern ?
A metal puzzle which led to some mathematical questions.
Can you locate these values on this interactive logarithmic scale?
Practise your skills of proportional reasoning with this interactive haemocytometer.
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.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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?
Use Excel to investigate the effect of translations around a number grid.
Use an interactive Excel spreadsheet to explore number in this exciting game!
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
A group of interactive resources to support work on percentages Key Stage 4.
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?
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
A collection of resources to support work on Factors and Multiples at Secondary level.
Use an interactive Excel spreadsheet to investigate factors and multiples.