Slope is simple, but slope is hard. It’s a simple equation with elusive variables. And it doesn’t help that landscape architects toss around up to four different conventions for describing slope — not even counting the most obvious one, angle, which makes sense on paper but is close to useless in the field. It’s hard to blame students for feeling overwhelmed.
The bad news, and the good news, is that there’s always another way to explain and clarify, and you never know which one will click. Here’s my latest handy reference, showing three ways of representing the same (arbitrarily selected) slope:

20% is .2 is 5:1, no?
Next, I’m wondering if there’s some kind of “slope jig” (not a dance, though there’s an idea) that would help students draw slopes and see what they mean. A set of sheets or cards with x axes and y axes, one with x fixed at 1; one with x fixed at 100; and one with y fixed at 1.
There’s always another way to explain and clarify — but which ones stick and help, and which ones just confuse?
Hmm. Who’s the learner here?
. . . and that is why I teach. And write.
we had a “slope visualization diagram” handout for Grading and Drainage class, showing all the various buildable slopes, that helped me a lot. seems to me one could build a little 3d model of the same thing, sort of like an anatomical cutaway model that med students would use. I’m probably not describing that very clearly, but I can picture it.
I can still invert a curb with the best of them. fortunately for me, I also know the phone numbers of VERY good civil engineers!
One of the things I like about being able to visualize slope is that once I get it, I also become able to visualize ways of dealing with slope. I might decide to add steps, or a wall, or make a terrace by filling and retaining, or make a terrace by cutting and retaining. Slopes give us opportunities for sculptural intervention, whether it’s rectilinear, curvilinear, full-bore, or extremely minimal. And sometimes we don’t want to intervene at all, and if we have the space we can let the slope and its horizon define the place’s beauty.