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.
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 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 numbers?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
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?
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.
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?
Match the cards of the same value.
Can you find all the 4-ball shuffles?
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?
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?
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.
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. . . .
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.
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 the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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?
A metal puzzle which led to some mathematical questions.
Can you discover whether this is a fair game?
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you explain the strategy for winning this game with any target?
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?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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 beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
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.
Train game for an adult and child. Who will be the first to make the train?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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. . . .
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 chairs?