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 beat the computer in the challenging strategy game?
How good are you at finding the formula for a number pattern ?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Can you discover whether this is a fair game?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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
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 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?
An environment that enables you to investigate tessellations of
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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?
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 give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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?
Use Excel to explore multiplication of fractions.
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?
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A tool for generating random integers.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
Practise your skills of proportional reasoning with this interactive haemocytometer.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
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.
Can you work out which spinners were used to generate the frequency charts?
Balancing interactivity with springs and weights.
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 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. . . .
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.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.