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

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.

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?

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

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?

Can you find triangles on a 9-point circle? Can you work out their angles?

An environment that enables you to investigate tessellations of regular polygons

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. . . .

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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 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. . . .

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

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. . . .

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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

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?

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

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

A collection of resources to support work on Factors and Multiples at Secondary level.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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?

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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.

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 Excel to explore multiplication of fractions.

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.

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

A game in which players take it in turns to choose a number. Can you block your opponent?

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.

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.

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.

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

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

An Excel spreadsheet with an investigation.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Use Excel to practise adding and subtracting fractions.

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

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.

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