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?

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?

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?

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

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.

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

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?

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.

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?

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

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?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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.

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

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

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?

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

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

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?

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

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?

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?

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.

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

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

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

"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 ...?

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

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

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

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

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

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

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.

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Can you find what the last two digits of the number $4^{1999}$ are?

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

Given the products of adjacent cells, can you complete this Sudoku?

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

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!