Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

"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 ...?

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

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?

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!

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

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?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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?

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?

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.

A challenging activity focusing on finding all possible ways of stacking rods.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

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

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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.

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

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

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?