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 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?

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

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?

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

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?

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?

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

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.

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

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 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.

Number problems at primary level that may require determination.

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

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

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

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

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

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 complete this calculation by filling in the missing numbers? In how many different ways can you do 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?

Can you work out some different ways to balance this equation?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

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

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?

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?

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.

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

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?

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.

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?

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

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

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

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?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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!

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

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

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