Rehearsals can be strange things for young kids: When they are with the director their time is highly structured and they know exactly what to do because we are there to tell them... Then we send them off on their own until we need them again. Most 3rd-5th graders have no idea how to handle that independent time on their own in the theatre space, so we have to teach them how to do it. Whatever task you give them during their independent time (play theatre games, memorize lines, smaller rehearsal groups, etc.) take the time to norm what that task will look and sound like before you separate into your groups. If you have them play a theatre game, clearly delineate a space, have a demonstrator group start playing, practice the voice level allowed, and go through how to handle a problem-of-play (not following rules, etc.) If you want the kiddos to memorize on their own, give them a strategy or two, show them what they look like, identify what successful work will sound like, and again, identify the space where the activity will take place. Take time and be specific. You will have to do this for a few days until kids internalize the processes, but after awhile, they will have the confidence to do it on their own.
Look at it this way. When elementary kids work comfortably in stations in the classroom (one group at the math manipulatives table, one group working with the teacher, one at the computer station, and one practicing at their desks,) it didn't happen by accident. The teacher taught the kids at the beginning of the year what to do in each area, they practiced it, and they critiqued it before everything fell into place. As directors, we tend to believe that all actors, no matter their age, will be able to transfer this type of process to our rehearsal spaces, but that's not the case with most younger kids. With the elementary set, we have to teach them how to rehearse as well as how to put on a great show.