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?

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. . . .

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

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.

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Use Excel to explore multiplication of fractions.

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?

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. . . .

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

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. . . .

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

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?

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. . . .

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?

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 problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

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

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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

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

An Excel spreadsheet with an investigation.

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

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

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

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 of P?

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

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

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

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

Can you explain the strategy for winning this game with any target?

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. . . .

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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.

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

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

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...

Can you fill in the mixed up numbers in this dilution calculation?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.