Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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

If you have only four weights, where could you place them in order to balance this equaliser?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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....?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Can you complete this jigsaw of the multiplication square?

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

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

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 this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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?

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

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?

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

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?

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.

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 two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

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?

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?

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

An interactive activity for one to experiment with a tricky tessellation

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?

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.

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

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

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

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

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?