DD skipped from 1st to 2nd mid year. It was the district's first ever skip.

DD's skip was so smooth I can't imagine a better one. DD just went in and said hi to everyone and that was about it. She's talkative and friendly so it's quite easy. The kids don't have anything against someone grade skipping. Maybe they think it's cool. I do think we should have prepped her for one question. On the first day at recessed a queen bee type asked her why she skipped. Since she wasn't really prepared she said "I'm smart."
LOL. I told her next time say something like "Oh the teacher suggested I skip." Which was also part true. BTW queen bee and her became very good friends.

A month later I had a big party and she invited everyone. We got to know parents and girls very quickly. Some of them were so cool and the girls all got along well. I still am good friends with the parents in that grade even though now she's skipped again. They thought it was great she skipped and really supported her and invited her over etc.

I'm a pretty open person who likes to have people over and make friends. I like people who are genuine and reciprocate. I found plenty of them once I made the first move. DD's the same way. She makes the first move and kids tend to really open up.

In this last skip into 6th there was no prep. She did announce it on FB. So everyone would know. It worked out great.