This is a great round that I'm sure you're familiar with.  It's perfect for this time of year because it's fun to sing around Halloween AND (more importantly) it gets the kiddos singing in 4 parts:

Here's a movement activity I do with Ghost of Tom to encourage independent singing in this round and I've found it makes singing the round in 4 parts more successful.

Formation: standing circle

Action: 

Phrase 1: walk counter-clockwise in the circle, stepping the half note.

Phrase 2: walk clockwise in the circle, stepping the half note

Phrase 3:  turn in place 360 degrees, stepping the half note.

Phrase 4:  in place, lowly sink to a crouching position.

Once students have learned the song and these actions and can perform is as a group (lesson #1), we make two concentric circles (lesson #2).  One circle is assigned to start first.  This circle starts singing the song with the movements and the other circle waits until the moving circle is finished with the first phrase to begin singing the song from the beginning.  When the starting circle starts singing the second phrase, the second circle comes in on the first phrase.  As the round completes, we switch parts so that the starting circle is the circle that comes in second and the circle that came in second is the starting circle.  During later lessons we add circles until we have 4 concentric circles.  Visually, it's fun and the kinesthetic movement really helps the students with phrasing, independent singing and being able to successfully sing this round in 4 parts.