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

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

Number problems at primary level that require careful consideration.

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.

Ben’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?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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

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?

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.

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

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?

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

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

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,. . . .

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

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.

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

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Can you put these four calculations into order of difficulty? How did you decide?

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?

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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?

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

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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

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

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.

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

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

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

This task combines spatial awareness with addition and multiplication.

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

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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.