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

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?

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

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?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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

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.

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?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

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.

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

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?

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

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.

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?

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

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.

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Can you find what the last two digits of the number $4^{1999}$ are?

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Find a great variety of ways of asking questions which make 8.

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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