I am teaching an introductory course in algebraic geometry for masters and it turns out that many of them are not at all familiar with the notion of projective space. So it is necessary to spend two-three hours on explaining what this notion. I would like to know if there is a short (say 5-10 pages) carefully written note with a nice explanation of what is projective space containing some non-tautological statements (like Desargues theorem) that would help to students to get a feeling.
Miles Reid has a nice introductory book called Undergraduate Algebraic Geometry, which has the goal of providing motivation for algebraic geometry to undergrads (& beginning masters students). I highly recommend it, along with his book Undergraduate Commutative Algebra. These don't satisfy your condition of being 5-10 pages, but they are certainly at the right level.