On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

How will you work out which numbers have been used to create this multiplication square?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

Can you sort numbers into sets? Can you give each set a name?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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?

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.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

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?

Can you find different ways of creating paths using these paving slabs?

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Can you make square numbers by adding two prime numbers together?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

This article for teachers describes how number arrays can be a useful representation for many number concepts.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

An investigation that gives you the opportunity to make and justify predictions.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?