FWIW, if you start with "The view frustum is a 90 degree pyramid with the tip cut off at z = 1 and the 'end' at infinity", you can then work out how to map that to a NDC using a matrix and perspective divide.

I've used that when teaching short "Graphics 101" (not in the first session though) and the math comes out more intuitive than the usual "here's how to calculate a perspective matrix, don't ask where these numbers come from" version.