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...
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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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
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.
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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 explain the strategy for winning this game with any target?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Meg and Mo still need to hang their marbles so that they balance,
but this time the constraints are different. Use the interactivity
to experiment and find out what they need to do.
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. . . .
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
An animation that helps you understand the game of Nim.
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
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.
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...
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can you find all the 4-ball shuffles?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?