Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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?

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

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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.

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

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.

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?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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,. . . .

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

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?

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

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

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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

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?

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

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

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?

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 find different ways of creating paths using these paving slabs?

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

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

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!

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?

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?

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.

This task combines spatial awareness with addition and multiplication.

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

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.

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

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?

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?

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?