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 explain the strategy for winning this game with any target?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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. . . .
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.
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.
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
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?
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.
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 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. . . .
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Can you discover whether this is a fair game?
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 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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Work out how to light up the single light. What's the rule?
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?
Here is a chance to play a version of the classic Countdown Game.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you find all the 4-ball shuffles?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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. . . .
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
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?
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.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
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?
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
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
Meg and Mo need to hang their marbles so that they balance. Use the
interactivity to experiment and find out what they need to do.
An animation that helps you understand the game of Nim.
Square It game for an adult and child. Can you come up with a way of always winning this game?
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.
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?