Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

56 406 is the product of two consecutive numbers. What are these two numbers?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Can you complete this jigsaw of the multiplication square?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

A game that tests your understanding of remainders.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

There were 22 legs creeping across the web. How many flies? How many spiders?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Resources to support understanding of multiplication and division through playing with number.

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

This problem is designed to help children to learn, and to use, the two and three times tables.

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

Are these statements always true, sometimes true or never true?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?