Alternative ways to use lecture time when only one quarter of the students can attend?
I would offer an answer which actually works under the assumption that your restriction may not be as hard as you think (should be a comment, but too long).

Live streaming is possible! I can't see under what circumstances it is not possible to do live streaming. Bring a laptop to the lecture (you probably do that anyway) and point the webcam to where you are lecturing and do live-streaming with some platform of your choice (in addition to the recording of the lecture). It's very simple to do, the quality will probably be much worse than the official recording, but some students will still appreciate the live stream (especially if they can watch a high quality recording afterwards).

What is the benefit for students? The students have to rewatch 3 hours of lecture per week! That's a lot of stuff and a lot of time lonely in front of a screen. If they attended a live lecture it's more engaging. If they did not get something in the live stream (e.g. due to low video or audio quality), the can specifically jump to the time in the lecture which is huge time-saver.

Interaction is possible! Create a chat room for the lecture and include a chat window in the live-stream. (You may use a chat where the students may choose to anonymous to lower the bar for questions.) This is also beneficial for student who are present: What can happen is that students ask questions in the chat and other students chime in and answer the question before the lecturer even notice the question.


I have to add: All this above is based on a lecture I held last semester. The benefits have be reported by the students exactly as I described them. The chat worked out perfectly! Student where pretty active there - they did not only ask questions and answer them, but also posted memes they created for the lecture. I was impressed.

Why could live streaming be a problem? I don't know. I would be very surprised if there would be no internet connection (I used our eduroam and this worked fine for streaming in HD).

What about privacy? My university does not offer a streaming server and I would have to use a commercial streaming service. I don't an issue here: The only one recorded would be lecturer, the students in the lecture hall will not be on the video and it should be the case that even the audio of students would not be part of the recording. The chat if both anonymous and also optional. The only thing I could imagine is that some bureaucrat would say that this is forbidden. Frankly, I didn't ask for permission and if somebody would argue I would simply state that this is needed for my concept and I would gladly change to a similar service which is offered by the university.

Other issues? Low quality video was not a big issue. On some days I had problems and had to use a bad webcam (just 720p, weird colors), but no complaints. (Btw. I had lecture note prepared and distributed in advance and I also included in the live stream; so the students knew what I was talking about even if the video was no that great). Bad audio was bigger problem! The mic of the laptop was way too bad and students complained. I ended up using the mic of the lecture hall through the speakers of the lecture hall (which was already an improvement) and recorded this with an external USB mic.