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:
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?