- The most obvious kind is practice. This is an easy type of HW to give, but the tricky part is making kids see that they need it. Assessments should be framed as an opportunity for the students to find out what they need to work on - as formative, rather than summative, and HW is then the second step in a lot of cases. This is a difficult thing to do, and it requires a lot of frank talking with students in class, particularly at the beginning. I get better at selling this every year, but you'll never have every kid on board. Those kids that you can't ever get probably weren't getting much out of "completing" mandatory HW anyway.
- Deeper applications of concepts that you already know can work, but they can be difficult to pull off. Because of their nature, lots of kids are going to miss a subtle concept in there, and you'll have a few successful solutions waiting around for everyone to catch up in class. Depending on the kids and the culture, you may have a large percentage shut down and come in with something blank. It takes good scaffolding for these, and I'd use them sparingly - this is exactly the sort of thing that class is good for.
- Simulations or calculations can take some of the time-consuming, but not super-difficult bits of lab work outside of class. If kids are following up on a collision lab by calculating the center of mass velocity or change in kinetic energy for each system, that's something pretty easy for them to do, and they won't mind doing it (because it's not mentally taxing), but it'll save you class time. If they're at the point where they're pretty comfortable modeling, you can give them a simulation and have them model the relationship. I do this with universal gravitation (since we can't do the experiment in class anyway) and sometimes with circular motion, depending on how I'm feeling about experimental setup. At this point in the year (early second trimester), they're mostly ready to do that - certainly the design, data-taking, and graphical modeling, and most can do the algebraic modeling as well. We can then wrap up the relationship together and have a good discussion when they're 'fresh,' rather than after they've spent an hour taking data and running fits, etc.
- Another useful kind is new explorations. If they're framed well and have a low barrier to entry, they can be really productive. The first one where some kids obviously didn't do it should bring some helpful peer pressure as well. If you have one where nearly everybody doesn't do it and there's a frustrating day, that's a good candid conversation to have with them (and to remind them of the next time).
In this last vein, I have an example, using this gravity simulator (I just got sidetracked for 10 minutes playing with it while finding the link):
This is basically a way to get the conversation started on elliptical orbits, while reviewing a bit about circular orbits and Newton's laws. The kids come in with all sorts of observations and ideas, and it is a great springboard into the topic. If you do this in class, you end up having to curtail their investigation in the hopes of getting the discussion started, which isn't super fun for anybody.
Not every assignment worth doing looks like this, but it's a way to start to think about meaningful HW outside of class that isn't practice on old topics.