The way I decided to do it, because the suggestion to use separate installations was just not feasible due to our resources available, was to use one installation.
-each school and top level department is a section
-each section (school/department) has the same generic categories of news, events, and library/resource center
-using JACL I can allow individual school editors to edit their sections, and individual category editors to edit their content.
-I have pretty much been able to have templates applied by section and category because they are already menu links. There are some kinks to work out with this.
-each teacher has their own profile where they have a blog for posting their own curriculum/news and events using community builder.
I think the hardest part of the experience of setting this up was getting the structure and information flow visualized and the JACL set up. Also you have to spend the time to figure out how to do what you need to do in the simplest way possible with the least amount of extensions. The simpler the better to start with, you can always expand and enrich as you go along, but simple is best, especially if a number of people with various degrees of computer expertise are going to be involved in putting in content.
Hope that helps.
Co-author of the Official Joomla! Book http://officialjoomlabook.com
Marpo Multimedia http://marpomultimedia.com