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

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

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

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

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

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

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

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

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?

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

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 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?

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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?

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

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

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?

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

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

Move just three of the circles so that the triangle faces in the opposite direction.

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?

Complete the squares - but be warned some are trickier than they look!

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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?

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