earlier post, I described the way I set up our paper schedule to facilitate that independence.
Another help to us was blocking out our day into segments. Each segment fit into a certain part of the day and had its own assigned work. While planning the year, I listed all the work my Year 4 dd needed to complete each day, assigned each a rough time estimate, and then sat down with dd to decide which work should be done at which point in the day. We actually assigned times to the work for this exercise, although we knew those times were merely for scheduling purposes and would not actually be used when the schedule was implemented.
For our schedule, we put work for which she needed me in the morning. This was math and her readings (which need to be narrated) mostly. Her work that could be done entirely or almost entirely on her own went right after lunch. This was instrument practice, copywork and dictation, typing, and that sort of thing. We even saved a couple of subjects for the evening, after supper (and realistically usually after the little ones went to bed). Because we broke up our day so much, school lasted all day. But once the work for a particular segment was complete, dd was able to have free time until another segment began. This allowed her to have breaks during the day when the other children were free.
Dd was busy in the mornings, but busy with the type of work that can travel with us to the park or anywhere I choose to take the younger children. She often did her work outside in the backyard. It was not too hard to take a break to listen to a narration even with all the other kids around. Her work after lunch was done while I was sitting with my other dd, who was in Year 1. My Year 1 student did almost all her work in one sitting while the younger children were napping. My pre-K student sometimes did a little work right after lunch, before naptime or just after naptime began. We scheduled my oldest's after-lunch work to be the sort that needed to be done at home, since almost every day we would be home for naptime and for school for my Year 1 student.