She needs you most of all to be with her and do things with her, but I see that you have to work. But this is what she really needs and wants. Children really don't need the social stuff half as much as society thinks they do, this comes much later. She's just use to all the other students and the activities and thinks it's the way it is since this is what she knows.(Besides, it's not the quanity of social activity, it's the quality that is imperative.) She needs to know how to be independent in her play. Imaginational play is paramount now and so let her make things up and play with dolls and such -- set the stage for her, so to speak. Give her the "right" environment and the rest will take care of itself.
I think I would tell her that she can help you make supper when it's time. This gives her something to look forward to and most kids love to cook with mom/dad, plus it's good for them. When this becomes old or not to work so well, time to change it up. Figure out something else you can do together, washing/folding clothes, playing cards, board games etc. Simple and useful things that children actually enjoy doing.
Also, I would get a basket and fill it with small toys and crayons and paper, clay, small dolls with fabric pieces, etc. Things that take a bit more imagination to play with. Keep it to just a few things and tell her the only time she plays with these things is while mama is working. Let her play along side you. When work is done, put it all up and away for the next time. Then change it up every few weeks. Also, if you know how to knit or know someone that does this is a good thing for her to learn at this age and she can knit while you work. Also she can sew with thick needle and thread with felt -- cut out simple shapes such as doll or animals to sew and fill, make bean bags with felt, she can make some to toss for you two to play with and make some for friends or relatives.
Keep things simple and charming and warm and let her know you're there for her as best as you can be and give her lots of hugs and kisses and reassurance. If you don't make a big deal of this she won't either. Let her know she is expected to work/play quietly and happily. Remember she's coming down after school from all the hoopla and hollering and hustle and bustle. She needs to regroup and breath.
Also there are all kinds of sites that have craft ideas for kids. A lot sound better than they really are but there are some good ideas out there. Keep it simple.
The best to you and your little girl.