Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Here is a chance to play a version of the classic Countdown Game.
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
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.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you complete this jigsaw of the multiplication square?
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?
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.
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!
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
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?
Choose a symbol to put into the number sentence.
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?
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?
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 triangle.
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.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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 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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
An interactive activity for one to experiment with a tricky tessellation
Work out the fractions to match the cards with the same amount of
If you have only four weights, where could you place them in order
to balance this equaliser?
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....?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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 train building game for 2 players.
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
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.
Can you find all the different ways of lining up these Cuisenaire
An animation that helps you understand the game of Nim.