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

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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.

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

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?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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?

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

Number problems at primary level to work on with others.

Number problems at primary level that require careful consideration.

Number problems at primary level that may require determination.

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

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

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?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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

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?

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 task combines spatial awareness with addition and multiplication.

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

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

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?

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?

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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? 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.

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.

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?