Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

What is the greatest number of squares you can make by overlapping three squares?

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?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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

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

Can you make five differently sized squares from the tangram pieces?

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

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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

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

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?

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

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Can you deduce the pattern that has been used to lay out these bottle tops?

Can you put these shapes in order of size? Start with the smallest.

What shape is made when you fold using this crease pattern? Can you make a ring design?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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?

What do these two triangles have in common? How are they related?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Exploring and predicting folding, cutting and punching holes and making spirals.

Can you make the birds from the egg tangram?

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

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?

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

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?

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?

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

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?

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

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

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

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?

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?

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?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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