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

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

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

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?

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

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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.

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

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.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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

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

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?

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

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?

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?

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.

This problem is designed to help children to learn, and to use, the two and three times tables.

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

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

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!

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.

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.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?