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.

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?

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?

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

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

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?

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

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.

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?

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

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 many models can you find which obey these rules?

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?

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.

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

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?

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

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

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

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?

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?

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

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?

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?

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

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.

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.

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

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?

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?

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?

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

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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

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

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

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?

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?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?