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. . . .

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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?

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

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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.

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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?

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

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

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!

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

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

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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?

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

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

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?

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?

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.

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?

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.

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