Beginner band (when I was in school) was for 11 and 12 year olds (7th graders), and typically the SOUSAPHONE (no 3/4 tubas, then) was assigned to the kids who more resembled junior-sized ogres...
...but the old "butterfly" sousaphone stands (as well as the later-invented "sousaphone chair" allowed small children to play the sousaphone.
a .687" - .734" bore sousaphone doesn't really require much more "air" than a 3/4 tuba, and the subtle air requirement can be adjusted at the mouthpiece throat. (Mary Ann is a small person, but - and she's perfectly free to disagree - I believe she's found that - aside from the toting and holding issues - she can PLAY a very large tuba just as well as she can play a smaller one...and - actually - her smaller tubas are NOT small-bore tubas.)
If you locate a fiberglass sousaphone and a used sousaphone chair, your 4th grader will be able to mess around with a tuba that offers a full-size tuba resonance, and - hey - you can use the fiberglass yourself for stand-up gigs.
suspicion: If you buy a 3/4 tuba, your 4th grader will lose interest and - unlike a fiberglass sousaphone - you'll feel compelled to sell the 3/4 tuba (as you yourself won't be interested in playing it.)
Possibly as early as the 1940's (even earlier?) stands such as this were made in the USA...The player sat to their left of the instrument, put their arm though the "donut", rotated the neck way around to the left, sat in a regular chair, and played the sousaphone. This is a K&M copy of that American design...I don't know if K&M still offers these (??) If available, I like this better than a "sousaphone chair" and (again) these can ALSO be used by ADULTS.
