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

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

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?

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?

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

"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 ...?

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Investigate what happens when you add house numbers along a street in different ways.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Investigate the different ways you could split up these rooms so that you have double the number.

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

An activity making various patterns with 2 x 1 rectangular tiles.

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

A follow-up activity to Tiles in the Garden.

In how many ways can you stack these rods, following the rules?

Why does the tower look a different size in each of these pictures?

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.