How often does the teacher send this stuff home?  If a whole week's worth of work comes home in the folder on Friday, that's different than if work gets sent home every day, such that mom has 4 days' worth and dad has 1 day's worth.  I can understand both parents wanting to see/keep some of the work, and think scanning/photographing things you want to keep makes a lot of sense (while keeping a select few).  Frankly, you'll be happy your house isn't cluttered with all the stuff there will be by the end of the year!

Kindergarten work isn't a big deal, but once you get into the higher grades, I do think it's important that the work goes to the house that has primary custody during the school week (if there is one), as it might be ongoing work that needs to be referred to, so it should be where the child will be during the school week.  

How often do graded papers go home? Daily? A couple of times a week? Only on Friday?

If they only go home on Friday, and you keep them, then BM doesn't get to see graded papers. Both BM and DH should see all the graded papers.

What are you going to do with the papers? Most people look at them and keep some that they want to preserve so that the kid can throw them away when they are an adult. The rest usuallty get tossed.

BM wants to see the papers; just as you and BD want to see the papers. If it's important to you to keep them, maybe BD can work out something with BM so that every other month or week one parent keeps the papers after the other parent sees them.

Enjoy them over the weekend then send everything home to BM. BM should extend the same courtesy to you. She sends everything from the week to your house on a Friday. Mark what you want and so does BM and keep what you want in the folder to be returned to your house and vice verse. If there’s a battle on what one or the other wants because you see her name on it then just freakin scan it.

You can't save everything, and SD seeing you turning her work in to a shrine will give her the impression that everything she does needs to be save.  You will drown in paper before high school if you do that!  LOL   If BM needs to keep every paper , let her clutter up her house.  Be selective about what you keep and send the rest to BM.  

It depends.... is she making a scrap book for her? Is it your DH wanting them or you wanting them? If it’s only you who cares about it I would send them home to Mom. If SD mom wanted them I would def send them back.... and same with my ex H, he didn’t care to keep stuff like that.   Who does most of the school work with her? Does most of her “good” stuff come home on Fridays?

i usually wanted everything back because I didn’t want papers going missing (for field trips and things like that). You guys might be different but I know my ex H would lose things the second he dug through the backpack. Lol. I was constantly having to ask for new forms.

Wow I can't imagine my ex even asking about school, much less wanting any papers! He won't come to any school things, the only way we could get him involved was to remind him many times before an event. I finally quit that bc I'm not his wife anymore and he's capable of reading the school's website same as me. I've kept all her K papers in a box and her older siblings have looked at them occasionally but her father has never once asked how either kid is or anything about school. SO(my dd6's stepdad) gets excited about the breakfasts with dad and other family school events.