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
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Can you explain the strategy for winning this game with any target?
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?
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 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. . . .
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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 game in which players take it in turns to choose a number. Can you block your opponent?
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 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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
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.
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...
Work out how to light up the single light. What's the rule?
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.
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.
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?
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.
An animation that helps you understand the game of Nim.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
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?
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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 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?