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

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

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

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

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

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?

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?

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.

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

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

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

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?

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

Can you complete this jigsaw of the multiplication square?

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?

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?

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?

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?

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

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?

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

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

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?

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

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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?

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

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.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Can you work out some different ways to balance this equation?

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?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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 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?

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

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

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

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?

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?