Google Drive continues to get better and better and one of the additions that I recently found incredibly useful was the ability to upload video which can then be embedded in other web pages. If you're the type of school that doesn't want to use YouTube, Vimeo or other video hosting platforms then this could be the almost perfect tool. The only downside is that the video requires Flash to play so all those iOS devices will not play it.
If you require a more secure viewing of the video you can change the Share setting to 'Anyone with the link' or 'Private' which can be set so only those invited by email can view.
Note: If you use Blogger as a blogging platform you do not need to embed the video using this method as Blogger uploads and embeds any video directly into a blog post.