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?

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?

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!

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?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

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.

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?

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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?

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

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

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.

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?

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?

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?

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?

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.

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

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?

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

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

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

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?

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

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.

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.

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

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?

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.

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?

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

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

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

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

How many models can you find which obey these rules?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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

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

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

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

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

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?