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 ?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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 make a right-angled triangle on this peg-board by joining
up three points round the edge?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Discover a handy way to describe reorderings and solve our anagram
in the process.
The classic vector racing game brought to a screen near you.
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. . . .
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
A metal puzzle which led to some mathematical questions.
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.
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
An environment that enables you to investigate tessellations of
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Match the cards of the same value.
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?
Use Excel to explore multiplication of fractions.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .
Square It game for an adult and child. Can you come up with a way of always winning this game?
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.
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
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
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?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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.
Use an interactive Excel spreadsheet to explore number in this