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

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

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

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?

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my 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?

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.

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?

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

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

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

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

This task combines spatial awareness with addition and multiplication.

Number problems at primary level that may require resilience.

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 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?

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?

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

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.

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

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.

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?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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?

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?

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?

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

Can you find different ways of creating paths using these paving slabs?

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

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

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

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?

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

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

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?

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

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?

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?

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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?

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

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