It is odd that the team of teachers do not have the same plan. At our school, the team follows a weekly lesson plan which includes homework. This is every grade level in the elementary.. K-5.
A typical first grade week at our schools...
Monday... brainstorm with the teacher in class on spelling patterns for the week and come up with words to review all week. No "set" homework on this except to review spelling. Most Language Arts work in class will focus on the spelling of the week so the children are exposed every day.
Monday... each student is given a small book assigned to their specific reading group to take home, read every night, have parents sign the book and return on Friday. This is to practice fluency and comprehension. Students receive "bucks" for returning the books with parent signature.
Wednesday.... 1 sided worksheet for math is sent home and due on Thursday.
Friday.. spelling test of 8 words and 2 "star" words focused on the week and 2 short sentence dictations.
Any work that is not completed in class is completed during recess time. Some children really need the extra time to complete the work, others are there in work completion because they are too talkative, active, etc in class and choose not to do the work in class.
The "homework" they have is very minimal and it basically helps them with a routine for more homework as they get older. Most children in this elementary are not bombarded with nightly homework unless they are just not productive in class and work completion during the day. More than ample time is provided during the class day to get work completed.
That is typical for our first grade in our district which is one of the highest rated districts in the US.