Many computer users are familiar with compressed formats such as zip, gzip, or gif images. These are based on a method called Ziv-Lempel coding, which turns out to be an interesting exercise in finding patterns in text.
Children's rhymes and stories are good examples for text compression, because they often involve repeated words and sequences.
Mordechai (Moti) Ben-Ari from the Weizmann Institute of Science, Israel has programmed the Text Compression Unplugged activity in Scratch which can be downloaded in a zip file of the complete set of activities .
Computing Science Inside Workshop has an activity Zipping it Up which is a nice extension activity to this topic. This workshop questions why it has taken so long to introduce 3G mobile phones, identifying lack of bandwidth as a key issue. It explores the area of data compression and decompression - essential in any application where the bandwidth is low or storage is limited - and gets pupils working with the kinds of algorithms that underlie the Zip utility found on a PC.
Note: You will need to apply and register in order to recieve the Workshop Pack for this activity.
Centre for Innovation in Mathematics Teaching has the following teaching packages in compression related topics developed to teach Codes and Ciphers in their Maths Curriculum:
The Royal Institution UK and Microsoft Research together have produced an activity in Information Theory explaining the concept of compression for the classroom called Information Salvation.
An older version of this activity can be downloaded in PDF format here. The content is similar to the current version, but there's some extra technical information.
The Mathmaniacs web site has a similar activity (lesson 2).
CSFN has the following articles that demonstrate compression:
Wolfram Demonstrations Project has the following demonstration activities. Note: You will need to install the Wolfram CDF Player in order to use these activities. You can either download each demonstration or use your browser to run it.