I am a fourth-grade teacher. This year we are back in person, but I spent the entire last school year teaching virtually. For me monitoring students and keeping them on task started with keeping them engaged. When kids are in our classroom we have total control of their learning environment their only distraction is typically other students. When our students are learning from home their list of possible distractions is endless. I combated that by mandating that each child had to have a quiet learning space in their home where they did their learning every day. For some kids, this was just sitting at the kitchen table for others they cleaned out a corner in their playroom or living room. I even had a few setup shop in the closet of their bedrooms. It didn't matter where they were as long as they had a spot to sit that wasn't curled up in bed or on the couch. After ensuring everyone had a space to learn we set our schedule and routine.
I began the school year with 48 kiddos in my virtual classroom. First, I split my kiddos into two groups so my actual live sessions were smaller. My day was basically split into two parts. One group would be asynchronous while the other was in a Google Meet class with me. We had the same schedule starting the first week of school until the end of school. I made sure that their schedule was posted EVERYWHERE. I sent a digital and physical copy of their schedule to their parents and scheduled reminders to go out via Remind the first few weeks. I made sure all my students and all my parents knew when their kids were supposed to be online and when they were supposed to be doing work. This helped ensure that all of my kids were actually online when they needed to be making it easier to monitor them.
The next thing I did was increase my formative assessments. Every assignment we did had some sort of exit slip. I traded in my Google Slides for Peardecks, created oodles of Kahoots, and fashioned hundreds of Google Forms. Every time we finished something asynchronous or synchronous we did a formative. All of these tools provided me with instant feedback, this allowed me to know as soon as one part of my lesson was done who was and was not paying attention.
My school also uses a Dyknow, a Chromebook monitoring application, so that I could block any student activity that wasn't their classwork. This was major! If the school doesn't have a program like this DyKnow has a free trial offer you can apply for.