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

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

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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

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?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

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

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.

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

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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.

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

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?

A game that tests your understanding of remainders.

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?

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

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?

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

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.

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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.

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?

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

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.

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?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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?

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

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?

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

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

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?

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.

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

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

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

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.

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?