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

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

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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

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.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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?

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

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

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?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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

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?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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

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

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

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

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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

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

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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?

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.

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

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

How would you count the number of fingers in these pictures?