Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

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

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

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

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?

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?

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

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

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

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

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

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?

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?

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

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

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 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?

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?

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.

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

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

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?

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

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.

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 chance to play a version of the classic Countdown Game.

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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