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?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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
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.
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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
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.
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. . . .
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 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you fit the tangram pieces into the outline of Little Ming?
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 find all the 4-ball shuffles?
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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Here is a chance to play a version of the classic Countdown Game.
An animation that helps you understand the game of Nim.
Find out what a "fault-free" rectangle is and try to make some of
What is the greatest number of squares you can make by overlapping
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.
Work out how to light up the single light. What's the rule?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Experiment with the interactivity of "rolling" regular polygons,
and explore how the different positions of the red dot affects its
speed at each stage.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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!
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
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?
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?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Can you fit the tangram pieces into the outlines of these people?