Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
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?
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?
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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
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?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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?
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
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.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
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
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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...
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
Here is a chance to play a version of the classic Countdown Game.
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
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?
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?
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?
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?
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.