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

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

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?

Can you make the birds from the egg tangram?

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

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.

Can you fit the tangram pieces into the outline of the rocket?

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

Can you fit the tangram pieces into the outline of this telephone?

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

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of this sports car?

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?

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

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 outline of Little Ming playing the board game?

Can you cut up a square in the way shown and make the pieces into a triangle?

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

A game to make and play based on the number line.

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?

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

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?

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?

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

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 clocks?

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.

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

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

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

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

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

Can you fit the tangram pieces into the outline of these convex shapes?

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

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

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

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

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

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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

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

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

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

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

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

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?

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?