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?

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

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

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. . . .

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?

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?

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

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?

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.

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.

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. . . .

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

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?

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.

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

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?

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.

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. . . .

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

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

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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

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. . . .

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

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.

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

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

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.

Use Excel to explore multiplication of fractions.

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

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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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

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?

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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

Use an Excel spreadsheet to explore long multiplication.

An environment that enables you to investigate tessellations of regular polygons

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

Can you find the pairs that represent the same amount of money?

Can you beat the computer in the challenging strategy game?

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?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?