I tend to work on landings with my students before takeoffs as well. Mostly because it's easier to teach that way, believe it or not.

First, I usually have the student doing the taxiing a bit, but I do the takeoff. The we start shooting approaches, working the throttle, and learning proper technique for not just the approach, but the abort and go-around and climb away.

Once they have that down, it's usually time to land anyway, so I get them to land it. Then I get to tell them that a fast taxi followed by the "go around" from an approach is basically a take off, with just the elevator work to avoid leaping off the ground too soon. So I get them to take off from that point. So I kind of get to teach them two things at once, .

As a side note, I've seen more "close calls" on bad take-offs at my field than on bad landings. Guys yanking it off the ground too soon and doing that classic stalling arc to the side and in to the ground. And it seems 9 times out of 10 the arc is towards the pits. Planes hitting potholes or ground looping and coming out facing the pits at full throttle seems to be all too common as well. And that's all amoung "experienced" pilots.

I think a typical student at a typical flying field is more likely to crash their own plane on landing, but more likely to hurt someone else on takeoff.