Yoma, Chapter 8, Mishnah 4. This mishnah deals with the status of children on Yom Kippur.
The text of the mishnah:
"HaTinokos ein me'anin osan b'Yom HaKippurim" - we do not require young children to observe the afflictions of Yom Kippur. This refers only to eating and drinking, and not to wearing shoes and the like - in those they are obligated, and even young children should not be given leather shoes to wear.
"Aval mechanchin osam lifnei shanah, lifnei shenasayim" - we train them one year or two years before they become bar mitzvah or bas mitzvah.
"Bishvil sheyihyu regilin b'mitzvos" - so that they will be accustomed to the mitzvos.
The Gemara explains that the statement "one year or two years" depends on the child and on his physical condition: with a weak child we begin the training only one year before the bar mitzvah or bas mitzvah, while with a strong child we would begin two years beforehand.
Two types of training for the fast:
The Gemara presents an approach that differs somewhat from the plain reading of the mishnah, according to which there are two types of training for the mitzvah of fasting on Yom Kippur - training in hours, and training regarding the age at which they begin to complete the entire fast:
Training in hours: With a girl of eight or nine, and a boy of nine or ten, we begin to accustom them to fast for a certain period during Yom Kippur - we delay their breakfast, or we wait until midday and skip breakfast altogether.
Training to complete the fast: Once the girl reaches the age of ten or eleven - one or two years before her bas mitzvah - and likewise the boy at eleven or twelve, one or two years before his bar mitzvah, we train them, by rabbinic requirement, to complete the entire fast, if they are able to do so.
The reason for this: once they reach the age of twelve or thirteen, they are obligated by Torah law to fast the entire time.
In summary: In this mishnah we learned that we do not require children to afflict themselves on Yom Kippur through eating and drinking, even though they are obligated in the other afflictions; rather, we train them one or two years before the age of mitzvos - according to the child's physical strength - so that they will be accustomed to the mitzvos. We also examined the two types of training: training in hours from the age of eight or nine for a girl and nine or ten for a boy, and training to complete the entire fast in the one or two years preceding the Torah obligation.