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?
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.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you complete this jigsaw of the multiplication square?
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
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.
Here is a chance to play a version of the classic Countdown Game.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Can you find all the different triangles on these peg boards, and
find their angles?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
These interactive dominoes can be dragged around the screen.
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
A card pairing game involving knowledge of simple ratio.
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.
Choose a symbol to put into the number sentence.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
A train building game for 2 players.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 the fractions to match the cards with the same amount of
Find out what a "fault-free" rectangle is and try to make some of
Can you find all the different ways of lining up these Cuisenaire
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.