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

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?

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

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

Number problems at primary level that may require determination.

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

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

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?

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

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

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.

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?

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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?

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

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.

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

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

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?

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

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

Number problems at primary level that require careful consideration.

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

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

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

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

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

Can you work out some different ways to balance this equation?

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?

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

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?

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?

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?

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?

This task combines spatial awareness with addition and multiplication.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?