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

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.

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

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?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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?

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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!

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

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.

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

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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.

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?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

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

How many models can you find which obey these rules?

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

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

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

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

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

"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 ...?

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.

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?

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

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?

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?

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?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Sort the houses in my street into different groups. Can you do it in any other ways?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.