Question: Our eleven-year-old daughter came back from school telling us about the three fasts that she is supposed to fast before her bas mitzva. What is this about?
Answer: The Mishna (Yoma 82a) teaches that we start training children to fast for ‘hours’ before they are bar mitzva or bas mitzva. Thus, the Shulchan Aruch (OC 616:2) writes that when a child reaches the age of nine, we begin to educate them about fasting by feeding them a little later than usual on Yom Kippur. When they reach eleven, there is a rabbinic obligation to fast the whole day. The Rema, however, disagrees, writing that there is no such obligation.
Nonetheless, the Bach (OC 616:6) demonstrates from the Gemara that children who study all day are considered to be weak and therefore have the status of a choleh who does not fast. This justifies the practice of children not fasting before they are bar mitzva or bas mitzva (See Kaf Hachaim OC 616:16). Likewise, the Mishna Berura (616:9) writes that children nowadays should not fast before they are bar mitzva or bas mitzva as they are assumed to be weak. Only if one can ascertain that the child is fit to fast, may they do so.
While many children observe the three fasts before their bar mitzva and bas mitzva, R’ Shlomo Zalman (Halichos Shlomo, Yom Kippur 6:n67) maintained that this custom is erroneous and has no source.
The Mishna Berura (550:5) also writes that there is no obligation for children to fast for a few hours on the other fasts, though they should not eat too much.
In conclusion, eleven-year-old girls and twelve-year-old boys should ideally eat breakfast a little later on Yom Kippur. There is no obligation to train children to fast at all before their bar mitzva or bas mitzva for Tisha B’av or the other minor fasts.