Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

"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?

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

Can you find a way to identify times tables after they have been shifted up?

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

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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?

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?

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

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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.

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

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

Is there an efficient way to work out how many factors a large number has?

Number problems at primary level to work on with others.

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

Number problems at primary level that may require determination.

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?

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

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

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?

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

A game that tests your understanding of remainders.

Find the highest power of 11 that will divide into 1000! exactly.

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?

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?

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?"

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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

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

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?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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