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

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?

Match pairs of cards so that they have equivalent ratios.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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 find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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. . . .

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

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

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

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

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.

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

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. . . .

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?

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.

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.

An environment that enables you to investigate tessellations of regular polygons

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

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

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

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 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.

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

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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A tool for generating random integers.

A collection of our favourite pictorial problems, one for each day of Advent.

Here is a chance to play a fractions version of the classic Countdown Game.

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

The classic vector racing game brought to a screen near you.

Square It game for an adult and child. Can you come up with a way of always winning this game?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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. . . .

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

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

Can you beat the computer in the challenging strategy game?

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.

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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 metal puzzle which led to some mathematical questions.

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

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. . . .