My DSS is Y2 (and I have worked in primary school), he has regular reading (no set amount, but I'm sure the teacher would grumble if he didn't do any) and has class access to this online 'matheletics' thing which he progresses through at home and gets certificates for, again he is supposed to do that a few nights a week but it's not really checked up on.
Also every weekend he gets a slip with a vague sentence on it like "this week we have been learning about Italy, please find out three things about Italy and write them down/draw pictures. Not everyone actually does this homework.
We could, technically, spend a couple of hours a night doing this lot so it is quite a lot.
For me, when my DC is in school, I don't think I'll mind either way. It doesn't necessarily matter if they get set your DCs 'learning log' thing, the load my DSS gets or nothing - if you care about their education and encourage them to learn at home as well as school, they are likely to get ahead, or if you do the bare minimum and don't encourage them to learn, then they are likely to fall behind.
IMHO my DSS learns far more from spending an hour visiting a museum with us or by reading one of the non-fiction books he likes than by doing his homework. If he were, for example, behind with his writing, then we could get him to work on his specific problem rather than doing a blanket exercise that the whole class had been set.