I do ...but I don't make it a battle...
I have a 7 YO ina 2/3 class and two 6 YOs in 1st class. They have a home reader (the whole school has a booklet to sign off reading once a night and teh kids can earn certificates) if my lot don't like their reader they can choose something else from the shelf.
Then they have a spelling sheet and a math sheet..it all comes home on a Monday and is to be handed in on a Friday, so they can do a little bit each day or a lot over a few days.
They also have a 'show and tell' type of activity that we get told about on the Monday and they present a quick chat to theirclass on teh Friday (for EG, this past week was they had to take a photo of their family and talk about who everyone was and what they do)
There are also little boxes on the Homework sheet that requires a parents signature (not just for the above) but for a physical actvity [eg rrun around your backyard 5 times, or ride your bike] and discuss "topic" with your parents - this past week was "Respect".
We manage to fit it all in, we might skip a reader here or there if we have swimming on or everyone is over tired and they'd prefer to listen to me read to them at bedtime. Or depending on my work commitments.
..but, I think it provides a good connection between parent and teacher and student.
We have all sorts of activity books at home anyway - but it is good to be able to see where they are up to as a class, and where they need help/support.
we usually squeeze spelling/maths sheets in whilst I'm cooking dinner - so the three of them are at the table and I can still be doing something and hovering around if they need me.
I'm kinda dreading Highschool though - my youngest sister is 14 and has HOURS of homework to do - no wonder there are so many kids burning out.