How will you work out which numbers have been used to create this multiplication square?

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.

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

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?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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 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?

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

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

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

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

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?

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

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

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?

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

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?

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?

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?

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?

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

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

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?

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

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.

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

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

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?

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

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

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

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

This task combines spatial awareness with addition and multiplication.

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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.

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.