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?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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 find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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.

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.

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?

Here is a chance to play a version of the classic Countdown Game.

Can you complete this jigsaw of the multiplication square?

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?

Can you find all the different triangles on these peg boards, and find their angles?

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?

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 make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

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!

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?

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?

Work out how to light up the single light. What's the rule?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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!

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.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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 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?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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?

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

Work out the fractions to match the cards with the same amount of money.

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you find all the different ways of lining up these Cuisenaire rods?

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.