In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outline of these rabbits?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Here's a simple way to make a Tangram without any measuring or ruling lines.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Can you make the birds from the egg tangram?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

Use the tangram pieces to make our pictures, or to design some of your own!

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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?

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?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

These pictures show squares split into halves. Can you find other ways?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of the child walking home from school?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Can you fit the tangram pieces into the outlines of the chairs?