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?

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

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

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?

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?

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?

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

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?

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

"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?

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?

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.

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.

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

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 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?

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?

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

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

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?

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?

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

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

How many different rectangles can you make using this set of rods?

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.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

An environment which simulates working with Cuisenaire rods.

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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?

Number problems at primary level that may require resilience.

Number problems at primary level to work on with others.

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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

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?

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?

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

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