Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
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
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?
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 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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Work out how to light up the single light. What's the rule?
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.
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best 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.
Can you discover whether this is a fair game?
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
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.
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. . . .
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?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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 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.
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?
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 all the 4-ball shuffles?
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...
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.
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
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
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?
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.
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?
Here is a chance to play a version of the classic Countdown Game.
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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 work out which spinners were used to generate the frequency charts?