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

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

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

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

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

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

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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?

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?

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.

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?

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?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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

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

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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?

Can you find what the last two digits of the number $4^{1999}$ are?

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.

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

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

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

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

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?

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

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

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

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

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

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

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!

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

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

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?

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?