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

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

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" .

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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. . . .

What is the remainder when 2^{164}is divided by 7?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

What is the least square number which commences with six two's?

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.

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.

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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.

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

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

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?

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

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

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

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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

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?

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

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.

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.

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?

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?

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?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Use the information to work out how many gifts there are in each pile.

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

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?

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

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?

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

This number has 903 digits. What is the sum of all 903 digits?

Number problems at primary level that require careful consideration.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.