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

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?

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?

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

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?

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

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.

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

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?

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

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

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

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?

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?

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?

Here is a version of the game 'Happy Families' for you to make and play.

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?

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

Can you make the birds from the egg tangram?

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you split each of the shapes below in half so that the two parts are exactly the same?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Can you fit the tangram pieces into the outline of Mai Ling?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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

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

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

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 make five differently sized squares from the tangram pieces?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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 outlines of the chairs?

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?

Explore the triangles that can be made with seven sticks of the same length.

Can you fit the tangram pieces into the outline of Granma T?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?