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

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

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

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?

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

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?

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

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...?

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

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.

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.

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

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

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

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

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

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

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

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

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

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?

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

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

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

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 fit the tangram pieces into the outline of this junk?

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

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

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

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

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 Little Ming playing the board game?

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?

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

Can you make the birds from the egg tangram?

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

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

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?

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

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?

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...