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?

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.

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?

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

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

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

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

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?

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?

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

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

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

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

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.

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

Number problems at primary level that may require determination.

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.

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

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?

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

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 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?

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

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?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

This task combines spatial awareness with addition and multiplication.

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

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?

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

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

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?

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?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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

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

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

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?

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?

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?

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