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

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

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

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?

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

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

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?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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.

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.

Use the information to work out how many gifts there are in each pile.

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

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

This task combines spatial awareness with addition and multiplication.

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

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

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.

Number problems at primary level that require careful consideration.

Number problems at primary level that may require determination.

This number has 903 digits. What is the sum of all 903 digits?

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?

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

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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

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?

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?

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

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

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?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.