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?

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

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

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.

Number problems at primary level that require careful consideration.

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?

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?

Play this game and see if you can figure out the computer's chosen 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?

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

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

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

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?

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?

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

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

Number problems at primary level that may require resilience.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

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 this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

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

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

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

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.

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

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

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

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?

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 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,. . . .

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?

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

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

This task combines spatial awareness with addition and multiplication.

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

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?

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

Resources to support understanding of multiplication and division through playing with number.

More resources to support understanding multiplication and division through playing with numbers

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

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

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

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