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

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

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

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

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

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

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?

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.

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.

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

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

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?

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

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?

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. . . .

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?

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?

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

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

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?

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.

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

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?

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

This task combines spatial awareness with addition and multiplication.

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?

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.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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

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

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

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?