In our area it depends on private all day vs. public 1/2 day option. DD went to a private K as a 4 year old and they were expected to complete weekly homework and daily reading. The homework packet was given on Monday and it was supposed to take 15min. per day. Reading requirement was 15 min. a day as well. DD usually did the homework in two evenings instead of Mon-Thurs.
Our public schools also give homework but it was much less. Our friends told us there was a suggestion to read every night and then a weekly sheet for the letter of the week. Our public school has a 10 min. rule for homework, meaning 10 min. is added each year to how much homework the kids should have. I would ask what the requirement in in your school district. Our schools have a family handbook posted online that explains their policy.
Jen