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

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

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .

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.

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

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.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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

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?

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.

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!

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

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?

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

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

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

This Sudoku requires you to do some working backwards before working forwards.

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?

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

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?

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

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?

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

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

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

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

Number problems at primary level that may require resilience.

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

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

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

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

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

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?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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. . . .

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Which set of numbers that add to 10 have the largest product?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?