WP as CMS: Multiple templates for single.php?

Greetings! Firstly, I want to thank everyone who has contributed to WordPress’ development. Not being a PHP expert by any means, I struggled for weeks with Joomla — never getting it to work as I hoped. Yet I was able to replicate all I had accomplished with WordPress in only a day or so. Bravo, God bless you, my sincere thanks, & the next round is on me!

Background: I am re-designing the default theme in WP 2.2 as a CMS for a new learning archive site. It has 9 primary categories (e.g., Math, Science, etc.) and over 200 (sub-)categories (e.g., Addition, Algebra, etc.).

To aid in navigation (especially since users will include very young children), each primary category has its own, color-coordinated, header.php and sidebar.php. Consequently, I have 9 header.php files and 9 sidebar.php files. Site thus far is available at: https://www.growandknow.com .

Based on this post (“using as cms: page or post?”), I have decided that we will need a few static Pages (home page, About Us, etc.), but the bulk of the content will be Posts, due to the need of the categories (at least, I think that is the proper decision… any thoughts?).

Question: So now, a problem arises with the single-post pages… I would like single.php to include the sidebar and for single.php to instead divert to the proper category’s template — that is, so a single post page would display the appropriate header and sidebar from one of the eight primary categories.

It wasn’t too difficult to figure out how to divert users to 1-of-the-9 category.php files, but I have no clue on where/how the single.php files are called for, and how to tie the various category themes to single.php.

Please help? Such as it is worth, my undying gratitude will be yours.