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

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

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

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?

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

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?

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

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?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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?

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

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

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?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

There were 22 legs creeping across the web. How many flies? How many spiders?

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. . . .

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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

How would you count the number of fingers in these pictures?

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?

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

This task combines spatial awareness with addition and multiplication.

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

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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.

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?

Number problems at primary level that may require determination.

Number problems at primary level that require careful consideration.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

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?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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!

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?