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

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

Can you replace the letters with numbers? Is there only one solution in each case?

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.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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.

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

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

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

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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?

Number problems at primary level that may require determination.

Number problems at primary level that require careful consideration.

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?

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

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

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?

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.

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. . . .

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?

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

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?

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?

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

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.

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

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?

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

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

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

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.

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

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

This task combines spatial awareness with addition and multiplication.

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

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?

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?

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?

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.

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?

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.

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?

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?