That IS a lot to expect of a third grader. They don't start implementing this in our district until 4th grade.
FWIW, my gifted 6th grade difficult child has the SAME problems. Doesn't remember to write things down, doesn't remember to turn assignments in. Working way below his potential in several areas. Some weeks he does GREAT. Some weeks he does dismally poor.
I've asked that difficult child be put on a planner contract of sorts. Essentially, the teacher must review his planner at the end of the day and initial it to ensure he hasn't missed anything. Afterall, I can't help him do work that I don't know about. My 8th grader is doing something similar at school getting teacher signatures for his core subjects. It's a lot of hand holding, but he still needs this because he doesn't have the organizational skills to do it himself yet.
As for medications, we now use the Daytrana patch for both difficult child's. It seems to be released very steadily throughout the day, and you can control when it stops to a certain degree. I find, though, that once it's applied, it can take an hour or more before we notice it starting to work. So in the mean time, difficult child 1 has to take short-acting Focalin first in the morning, and then about an hour later I give him the patch to put on. By the time the Focalin wears off, the patch is starting to kick in. We usually see about 10 hours or so of coverage.