Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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.

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?

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?

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

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

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

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.

This task combines spatial awareness with addition and multiplication.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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?

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?

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

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?

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?

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

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

Are these statements always true, sometimes true or never true?

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?

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

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

Number problems at primary level that may require determination.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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

Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.

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?

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.

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

This problem is designed to help children to learn, and to use, the two and three times tables.

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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

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

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