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

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

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?

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?

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

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?

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 draw on the dotty grid which each have one dot in the middle?

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

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

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?

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

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

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

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

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

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?

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?

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

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

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

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

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

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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

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

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?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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!