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?

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.

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

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.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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?

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.

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

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

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.

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?

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?

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?

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

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?

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

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?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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

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.

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.

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

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?

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?

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?

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

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

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

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

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

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?

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!

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

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

How many models can you find which obey these rules?

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

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

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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?

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?

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

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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?

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?

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?