Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

How many different rhythms can you make by putting two drums on the wheel?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

What happens when you try and fit the triomino pieces into these two grids?

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

Can you hang weights in the right place to make the equaliser balance?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

How many different triangles can you make on a circular pegboard that has nine pegs?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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?

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 put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Use the interactivity or play this dice game yourself. How could you make it fair?

How many trains can you make which are the same length as Matt's, using rods that are identical?

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?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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. . . .

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

An interactive activity for one to experiment with a tricky tessellation

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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!

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Take it in turns to make a triangle on the pegboard. Can you 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?

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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