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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
How good are you at finding the formula for a number pattern ?
Can you beat the computer in the challenging strategy game?
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
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
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 hit?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
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 discover whether this is a fair game?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Have you seen this way of doing multiplication ?
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 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?
Discover a handy way to describe reorderings and solve our anagram in the process.
To avoid losing think of another very well known game where the patterns of play are similar.
An environment that enables you to investigate tessellations of regular polygons
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.
A metal puzzle which led to some mathematical questions.
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.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Match pairs of cards so that they have equivalent ratios.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Use Excel to explore multiplication of fractions.
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. . . .
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?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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?
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.
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 total.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
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.
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.
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.
A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
An Excel spreadsheet with an investigation.