Can you explain the strategy for winning this game with any target?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 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.
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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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 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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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. . . .
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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!
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Work out the fractions to match the cards with the same amount of money.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you find all the 4-ball shuffles?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Find out what a "fault-free" rectangle is and try to make some of your own.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Here is a chance to play a fractions version of the classic Countdown Game.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Exchange the positions of the two sets of counters in the least possible number of moves
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Here is a chance to play a version of the classic Countdown Game.
Can you fit the tangram pieces into the outlines of these clocks?
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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 outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
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. . . .