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

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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.

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?

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?

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.

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

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

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?

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

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

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

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

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!

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

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?

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?

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?

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

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

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?

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?

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

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?

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Are you resilient enough to solve these number problems?

This task combines spatial awareness with addition and 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.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.