Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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 solitaire type environment for you to experiment with. Which targets can you reach?
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 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?
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
What is the greatest number of squares you can make by overlapping three squares?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you fit the tangram pieces into the outline of Little Ming?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Can you fit the tangram pieces into the outline of the rocket?
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this telephone?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
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.
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 area.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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 fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this junk?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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.
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
Can you explain the strategy for winning this game with any target?
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.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?