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?

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

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.

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

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.

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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

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

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?

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 can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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?

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

Exchange the positions of the two sets of counters in the least possible number of moves

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?

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

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

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

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

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?

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!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

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

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?

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?

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?

An interactive activity for one to experiment with a tricky tessellation

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?