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?

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?

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 hit?

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

Match pairs of cards so that they have equivalent ratios.

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?

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

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

Can you work out which spinners were used to generate the frequency charts?

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?

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

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"

An environment that enables you to investigate tessellations of regular polygons

Match the cards of the same value.

A metal puzzle which led to some mathematical questions.

Discover a handy way to describe reorderings and solve our anagram in the process.

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 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?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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 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?

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

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.

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

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?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Which exact dilution ratios can you make using only 2 dilutions?

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.

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. . . .

Can you beat the computer in the challenging strategy game?

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

Use an Excel spreadsheet to explore long multiplication.

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use an interactive Excel spreadsheet to explore number in this exciting game!

Use Excel to investigate the effect of translations around a number grid.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Use an interactive Excel spreadsheet to investigate factors and multiples.

A tool for generating random integers.

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.