Homework Help

I need some advice. Other than sharpening pencils, homework is probably the source of most of my headaches before 10 AM. I don't know about the rest of you, but I don't grade homework. I'm a little embarrassed to admit this...but I check in the homework every morning to make sure it's getting done (I try to glance at a few kids key kids' work to make sure they're getting it), but at the end of the day....I throw it away! What ends up giving me my headaches though is that it's the same 3-5 kids and then another random 1 or 2 who don't turn in homework consistently on a daily basis. What makes me so upset is that those 3-5 kids who don't turn in their homework most days are the same 3-5 kids with failing grades. I try reaching out to parents, offering positive incentives for turning in homework, and taking away privileges for not turning in homework. Nothing seems to make a difference.

One of my goals for this year is to make homework more meaningful and in turn hopefully I will have 100% (or close to it) homework completion each day. I have read other bloggers' ideas and teacher websites and have found a few different possibilities.
1. Weekly schedule for homework (different activity for each day of the week)
2. Weekly packet (due Friday)
3. "Speller's Choice" activities to choose from

Here are my questions:
1. How important is it to go over the homework in class?
2. How much do phonics worksheets help students? Are they worth it?
3. Do you send homework home graded? If so, what are the benefits that you've seen?

I would love to hear what works for you!! I welcome any and all ideas!