Vimeo is another contender for hosting videos. While not as well known as YouTube, it has the advantage of being pretty much ad free and provides better video quality.
Vimeo has a free version that will work well for most school projects. For a small yearly fee, you can upload as much video as you can create and get high quality, ad free playback on pretty much any device.
A good option if you already have an audience/following, or are looking for a quality experience.