Homework Woes

OK, as we wind down this school year (only 18 schools days left) it is time to reflect on the year and start thinking about things I want to do differently and/or better next year. Considering this is the end of my 2nd year in 4th grade I still have quite a bit to reflect on but I feel like the area that I just can't figure out is homework. Actually checking homework to be specific. I have no problem assigning the homework its just finding an easy and quick way to check it and see who has their's completed and who doesn't.

I have had the kids turn it in daily and weekly but turning it in just doesn't seem to be working for me. I would like to figure out a routine to establish first thing in the morning that allows me to quickly do a homework check and then move on with the day. Also one of our "social Development" grades is "Completes homework" so I need to have a system that allows me to keep track long term.

Sooooo Here's what I am thinking - and I would LOVE some feedback or ideas.
1 - Get a small notebook
2 - Print off a weekly class list spread sheet with a daily column each for Spelling, Vocab, and Math
3 - Set up the routine that when the students enter the classroom in the morning they unpack and put their homework on their desk
4 - as they write their new homework assignment in their agenda I can walk around and check off who has their homework and who doesn't.

This sounds simple in writing but will it actually work? Please share how you check your homework I would love to have some ideas for next year!