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.
How good are you at finding the formula for a number pattern ?
Can you beat the computer in the challenging strategy game?
Can you discover whether this is a fair game?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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. . . .
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.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Discover a handy way to describe reorderings and solve our anagram
in the process.
An environment that enables you to investigate tessellations of
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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?
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
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?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A collection of our favourite pictorial problems, one for each day
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.
Practise your skills of proportional reasoning with this interactive haemocytometer.
A tool for generating random integers.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
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.
Can you work out which spinners were used to generate the frequency charts?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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?
Match the cards of the same value.