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
Can you discover whether this is a fair game?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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
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.
Match pairs of cards so that they have equivalent ratios.
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
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?
A collection of our favourite pictorial problems, one for each day
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to investigate factors and
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.
Use an Excel spreadsheet to explore long multiplication.
Match the cards of the same value.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
An Excel spreadsheet with an investigation.
Use Excel to investigate the effect of translations around a number
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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. . . .
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Use Excel to explore multiplication of fractions.
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Can you be the first to complete a row of three?
Use an interactive Excel spreadsheet to explore number in this
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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. . . .
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
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.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
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.
An environment that enables you to investigate tessellations of
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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 beat the computer in the challenging strategy game?
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
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you find all the 4-ball shuffles?
What is the greatest number of squares you can make by overlapping
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?