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?

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?

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?

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

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

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?

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

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?

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

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.

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.

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?

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?

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.

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

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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

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

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

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.

This task combines spatial awareness with addition and multiplication.

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.

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?

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

Number problems at primary level that may require determination.

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.

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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!

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

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

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

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?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

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!

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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?