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?

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?

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?

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.

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

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

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

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?

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’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?

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?

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?

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

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?

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?

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.

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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?

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

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?

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

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

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

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. . . .

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

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

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

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?"

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

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?

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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

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" .

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

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?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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!