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

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?

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

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?

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

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?

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

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?

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?

Number problems at primary level that may require determination.

Got It game for an adult and child. How can you play so that you know you will always win?

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?

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?

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 find the chosen number from the grid using the clues?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

This package will help introduce children to, and encourage a deep exploration of, multiples.

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Number problems at primary level to work on with others.

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

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

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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 make square numbers by adding two prime numbers together?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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?

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.

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?

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

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

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?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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

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

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?