um, a back tuck is pretty much a necessary in gymnastics.
there really isn't a level that involves back tucks.
i mean, if you're just starting gymnastics, then a back flip won't come till later.
but if you're Shawn Johnson or nastia liukin or some olympian, back tucks are pretty much the easiest thing.
or if you're just an AMAZINGGG gymnast, back tucks should be very easy.
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Level 7 I think, because in level 6 you do back tucks. It is level 7 when you do back layouts on floor.
A backhandspring is in the current level 4 floor routine, but with the routine/requirement change of next year, it will be part of the level 3 routine.