Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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.
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.
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?
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.
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Here is a chance to play a version of the classic Countdown Game.
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.
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.
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 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. . . .
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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
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. . . .
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you find all the 4-ball shuffles?
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find out what a "fault-free" rectangle is and try to make some of
Exchange the positions of the two sets of counters in the least possible number of moves
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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. . . .
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?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?