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?

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

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?

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?

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.

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

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

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.

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?

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

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.

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 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.

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?

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?

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

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?

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?

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?

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

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

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?

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?

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?

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

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

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?

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

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

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

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

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

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

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?