Challenge 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.

Challenge Level

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.

Challenge Level

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

Challenge Level

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...

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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.

Challenge Level

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

Challenge Level

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. . . .

Challenge Level

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. . . .

Challenge Level

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. . . .

Challenge Level

Prove Pythagoras' Theorem using enlargements and scale factors.

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Challenge Level

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

Challenge Level

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. . . .

Challenge Level

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?

Challenge Level

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

Challenge Level

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.

Challenge Level

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. . . .

Challenge Level

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

Challenge Level

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.

Challenge Level

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. . . .

Challenge Level

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

Challenge Level

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.

Challenge Level

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.

Challenge Level

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.

Challenge Level

Use Excel to explore multiplication of fractions.

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

An Excel spreadsheet with an investigation.

Challenge Level

Use Excel to practise adding and subtracting fractions.

Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Challenge Level

Use an interactive Excel spreadsheet to investigate factors and multiples.

Challenge Level

Use an Excel spreadsheet to explore long multiplication.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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