Magnitudes are intuitionally directionless (hence why norms and measures are nonnegative reals). Of course, you can extend notions suitably and make it work, but I really don't think that this is terribly intuitive. (Of course, different people will find different things intuitive.)
The idea of negative measurements (meaning "opposite direction along a line") as is well understood before children study geometry. Kindergarteners learn "left" vs "right" and "forward" vs "backward".
I agree with other poster about the value of showing negative and positive lengths visually in the same diagram.