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?

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?

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?

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.

Number problems at primary level that may require resilience.

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

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

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

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?

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

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?

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?

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?

Number problems at primary level to work on with others.

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

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?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

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

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?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

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?

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

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

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?

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

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.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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?

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?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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

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

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?