I've read most of Julie's responses.
I'm in my 5th year. I'm doing CtG. I have 6 kids who are in 4th grade, twin 2nd graders (not fluent readers yet), twins in K and a 3 year old. And yup, I have a couple of children with character flaws.
My oldest is really tough when it comes to being independent because he has such a hard time staying focused. He also has an aversion to doing anything challenging, though it is getting better this year. One of my 5 year old twins gets into things. A few months ago, I sent him to his room to play (with his twin). His twin came down to tell me he was getting the room wet. He was filling the bins from his toy shelf with water and then dumping it on the floor of his room. His twin brother's mattress was so wet I had to sit it upright outside in the sun to let it dry. My other 5 year old can't get enough school. He begs me to "do school" with him all the time. So, that can be stressful for me because I prioritize my older children's formal education....I'm relaxed in K and have a "better late than early" type philosophy. My 3 year old wants to be on me a lot of the time, but he does not have a quiet mode, even when he is behaving. It's a crazy life with lots of littles.
For me, I think of this as a season. I also remind myself often of why I'm doing this. I had a very rough year last year. I got burnt out and basically, I quit....for a time. We usually school year round, but I was so burnt out and tired of struggling through every day that we took a very long summer break, 8-9 weeks. We never finished ECC.
I wanted to get back to it, but we needed a fresh start. I prayed about it and we moved to CtG as scheduled this fall. It's been going much better this year. I feel God has intervened on our behalf and really shown Himself in our school this year. I'm really learning to lean on Him for my strength and patience.
But, as for your question, I think the independent work for a 4th grader is more about maturity and what you want for your student than about reading ability. My 4th grader reads on a very high level and really loves to read. He is an avid reader both of fiction and non-fiction books. But, for us, one of the reasons I homeschool is so that I can guide his learning in some of subjects that are more interpretive. We use these subjects as a jumping off point to have lots of discussions. I want to guide his understanding of the world and point him toward the right path, God's.
For us, anyone who is in 1st or higher does the cycle year. So, last year, my 1st graders did ECC with us. I just adjusted to their level and they did great. They did MFW 1st LA and their own math. Same thing this year for my 2nd graders. My K'ers get LA and math and maybe a book and possibly 1 activity from MFW K topic of the unit and the rest they can sit with us...or not. I'm relaxed about K. Oh, they get the Bible from K, but a simplified version and not necessarily every morning/day. This cuts down on the amount of work I'm doing with each child.
So, we all do Bible, history, science, art/music together. We don't always get to music and art. We do it when it fits in the day, which is only 1-2 times per week. I don't sweat it because we have plenty of time for that as they grow and mature.
My 4th grader does several things without me. He does spelling independently except for testing on Thursday and the random times he needs help. He does writing independently except the random explanation from me. He does his math drills independently and his workbook exercises. I do teach him the lessons. My goal is to teach him the lesson and then have him do the workbook page for it the next day, so he can do his math in the morning while I am teaching the younger children. Any notebooking page for history or science, I let him do while I'm working with someone else. Copywork is independent. I work with him on Language Lessons, but it's very quick, maybe 5 minutes. Any work to be done from it, he does independently. Oh, I teach the Greek vocab word in about 3 minutes to all of them on Monday. But, he does the rest of week's vocab work by himself. I put it on our whiteboard and I mention at least once a day, "What's our Greek vocab root of the week, Kids?" I point, they answer and we move on. My 4th grader tests on them while he is taking his spelling test for the week.
Basically, I have him do anything he can independently, even if I have to get him started first, except the reading/teaching portion of Bible, history and science. We do Bible first, but after that he works on his independent stuff in the morning while I'm working with the younger kids. I usually am able to do his Language Lessons too because it's so fast. After lunch, we do our CtG work together. Whatever gets done first, gets done. So, we start with LA and math.
He has a composition book that we use as an "assignment book." Each night, I write down all the things he can do independently. He checks them off as he goes. He gets tickets for completing his work each day. He gets 5 for doing it and 1 for having a good attitude. Anything not done that was through no fault of mine (he can't do a notebooking page on something I haven't gotten to teach him) or any complaining/dilly dallying results in lost tickets for the day. The tickets = $.05 each or we have prizes they can choose from. Most days, I do have to keep him on track. I'm constantly saying, "Do the next thing." If I remind once (or twice) and he gets to it, he doesn't lose. I know he struggles with focus and I make concessions for that, but don't let it get excessive either. I usually let him choose the order, but I require something written before reading/book basket. (Again, whatever you do first, gets done.)
So, while my 4th grader does have a lot of time with me, he also does have a lot of independent work too. I can't stress enough to remember that this time with your family this age is a season. It won't last. I feel like at my house, we are already starting to get over the hump of it. But, I have twin 7 year olds. So, with finally having 3 who are getting a little older and not 6 who are 7 and under type of thing, my life is less crazy than it was. It's still crazy! LOL! My toughest season was last year....so far...with 6 kids 9 and under, a 3rd grader still needing a lot more direction than this year, twin 1st graders in the thick of learning phonics and reading and twin 4 year olds and a 2 year old. It was tough year. This may be that year for you. It's different for all of us. Take a break if you need it. Pray without ceasing. Prayer is my lifeline. I never thought of myself as a prayer warrior. I am now! If God has called your family to homeschooling, He will give you the grace to see it through. Trust Him and call on Him. He who began a good work in you will be faithful to complete it. Take each day as it comes. Teach and raise your children one day at a time, one hour, one minute if you need to. Hang in there. I'll say a prayer for you and your family.
Wow...this is long...I'm always long winded. Maybe something I said will help a little. LOL!!