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.
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?
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?
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. . . .
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.
Can you beat the computer in the challenging strategy game?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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.
Match the cards of the same value.
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.
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. . . .
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?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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 explore multiplication of fractions.
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.
To avoid losing think of another very well known game where the patterns of play are similar.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
A metal puzzle which led to some mathematical questions.
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?
Play a more cerebral countdown using complex numbers.
A weekly challenge concerning prime numbers.
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
Play countdown with vectors.
Play countdown with matrices
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. . . .
The classic vector racing game brought to a screen near you.
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!
Practise your skills of proportional reasoning with this interactive haemocytometer.
Can you locate these values on this interactive logarithmic scale?
How good are you at finding the formula for a number pattern ?
Cellular is an animation that helps you make geometric sequences composed of square cells.
Here is a chance to play a fractions version of the classic Countdown Game.
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 collection of our favourite pictorial problems, one for each day of Advent.
Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
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.
A group of interactive resources to support work on percentages Key Stage 4.
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.
Can you be the first to complete a row of three?
A collection of resources to support work on Factors and Multiples at Secondary level.
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.
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?