7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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...
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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 1 person to play on screen. Practise your number bonds
whilst improving your memory
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
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...
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?
These interactive dominoes can be dragged around the screen.
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Here is a chance to play a version of the classic Countdown Game.
Use the interactivities to complete these Venn diagrams.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
An animation that helps you understand the game of Nim.
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?
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 be the first to complete a row of three?
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?
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.
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 explain the strategy for winning this game with any target?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you complete this jigsaw of the multiplication square?
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 locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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.
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.
Work out how to light up the single light. What's the rule?
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?