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...

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.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

To avoid losing think of another very well known game where the patterns of play are similar.

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.

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?

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?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Cellular is an animation that helps you make geometric sequences composed of square cells.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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 moves.

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Work out how to light up the single light. What's the rule?

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. . . .

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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. . . .

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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 make a right-angled triangle on this peg-board by joining up three points round the edge?

Prove Pythagoras' Theorem using enlargements and scale factors.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

How good are you at finding the formula for a number pattern ?

Use Excel to explore multiplication of fractions.

A metal puzzle which led to some mathematical questions.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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. . . .

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.

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.