There are lots of amazing dissections; I really like wooden ones; the picture below shows a nice wooden dissection puzzle available from education-interactive.  The pieces fit together to make a T. This is part of a range of similar puzzles.

I gave this to my year 8 students to have a go at (see video on the right).  The solution to this puzzle is here if you are interested.

There are some lovely ones on the website 'how round is your circle'; watch the video on the right.

It was discovered over 100 years ago by Henry Dudeney.  His book Amusements in Mathematics can be read here.  I personally like his dissection puzzles the most, especially the Greek Cross ones:

Here is an example of another dissection puzzle from this book:

The diagram shows how to cut a strip, 5 inches by 1 inch, into 5 pieces to make a square.  How could you cut it into only four pieces to make a square?

Answers on a postcard please (or on the blog).

This would be a good way to investigate area (and perimeter) with students.

For example, you could present the very simple dissection problem on the right (click to enlarge). An extension to this might be how to dissect this triangle into a square.

It is actually possible to create any other polygon from any other polygon, but the interesting thing lies in doing it in as few cuts as possible.

So you could extend this to different shapes such as trapeziums, rhombuses and kites; I think this would be a good way of exploring the area and characteristics of 2D shapes.

Below are some more dissection tasks from SMILE (click to enlarge):