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.
This is an interactivity in which you have to sort into the correct
order the steps in the proof of the formula for the sum of a
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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Can you discover whether this is a fair game?
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?
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
Can you work through these direct proofs, using our interactive
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.
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?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Find the vertices of a pentagon given the midpoints of its sides.
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?
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
Play countdown with matrices
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?
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?
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.
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.
Have you seen this way of doing multiplication ?
A collection of our favourite pictorial problems, one for each day
Use Excel to explore multiplication of fractions.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Use an interactive Excel spreadsheet to investigate factors and
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
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. . . .
Play countdown with vectors.
Can you beat the computer in the challenging strategy game?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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!
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.
Practise your skills of proportional reasoning with this interactive haemocytometer.
A tool for generating random integers.
Here is a chance to play a fractions version of the classic
Cellular is an animation that helps you make geometric sequences composed of square cells.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
A weekly challenge concerning prime numbers.
Can you locate these values on this interactive logarithmic scale?
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.
Match the cards of the same value.
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?