I don't think you can predict how much to give. It depends on age, body weight, assimilation, time in the sun, etc.
20 is really low. If it were my son and I thought he was experiencing symptoms, I would start with 10k IU for a week and then move to 5k and get him tested in a couple of months.
ETA: I have in the past given my son, who has poor assimilation, 20k IU for a couple of days. I recommend Carlson's Vitamin D Drops. The little bottle is expensive but each drop contains 4k IU and we've noticed good results with absorption.