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

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?

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.

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?

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

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.

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

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

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

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?

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?

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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.

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

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

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

Given the products of adjacent cells, can you complete this Sudoku?

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. . . .

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?

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Are these statements always true, sometimes true or never true?

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?

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?

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?

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

Here is a chance to play a version of the classic Countdown Game.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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 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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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?

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 article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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