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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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

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?

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

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

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.

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.

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

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.

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.

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?

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

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 each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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

Number problems at primary level that may require resilience.

Find the next number in this pattern: 3, 7, 19, 55 ...

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?

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

Investigate the different distances of these car journeys and find out how long they take.

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

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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

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.

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Number problems at primary level to work on with others.

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.