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?

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

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. . . .

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

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

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

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

Can you complete this jigsaw of the multiplication square?

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?

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?

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

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.

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

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?

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

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?

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.

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

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

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?

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

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

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 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?

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

This task combines spatial awareness with addition and multiplication.

Have a go at balancing this equation. Can you find different ways of doing it?

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

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.

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?

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

Number problems at primary level that may require determination.

Number problems at primary level that require careful consideration.

Here is a chance to play a version of the classic Countdown Game.

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?

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 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.