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

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

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.

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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?

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

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?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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

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

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?

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?

This task combines spatial awareness with addition and multiplication.

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

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.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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?

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?

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

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?

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

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

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?

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!

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

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?

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.

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

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

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

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