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?

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

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.

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

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?

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?

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?

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

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.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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?

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

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

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

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.

"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 ...?

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

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?

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?

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

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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

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?

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.

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?

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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.

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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?

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?

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?

Can you find ways of joining cubes together so that 28 faces are visible?

Investigate the number of faces you can see when you arrange three cubes in different ways.

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.