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

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

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

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?

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

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

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?

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

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 make the birds from the egg tangram?

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

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

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

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?

Can you lay out the pictures of the drinks in the way described by the clue cards?

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

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

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

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

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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

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

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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 recreate this Indian screen pattern? Can you make up similar patterns of your own?

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 this junk?

Make a cube out of straws and have a go at this practical challenge.

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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?

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

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

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

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?