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?

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

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?

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

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

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

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

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?

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.

Can you find the chosen number from the grid using the clues?

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

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

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?

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

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?

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?

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?

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

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.

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

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?

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

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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?

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.

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

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

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?

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

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

Can you complete this jigsaw of the multiplication square?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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 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.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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?

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

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?

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

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

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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