This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

Can you find different ways of creating paths using these paving slabs?

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.

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

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

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!

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

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?

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?

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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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?

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

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.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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

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

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?

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

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

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

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?

How would you count the number of fingers in these pictures?

Find the next number in this pattern: 3, 7, 19, 55 ...

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

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

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?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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.

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.