At what age is it appropriate for a child to fast on Yom Kippur?

Question:
Are children obligated to fast on Yom Kippur?
Discussion:
There are two categories of children that we will discuss here, a child under the age of nine and a child above the age of eleven. One is not obligated to train a child under the age of nine to fast on Yom Kippur. The age of chinuch for fasting is nine years old for a strong child and ten years old for a weaker child (S.A. 617:2). However, some people have the custom of training a child to fast part of the day even if he is younger then nine (Shut Chekrei Lev 109). Once a child reaches the age of nine (or ten), his parents are obligated to train him to fast part of the day. For example he should start the fast at night and eat breakfast later then he would normally eat. Every year the child should fast longer until he is 13 (or 12 for a girl).
If a child’s health is endangered by the fast he must eat or drink immediately.

There is a dispute among the poskim whether a child older then eleven should fast the whole day or not. Therefore, if a child is weak one may rely on the lenient opinion. The Mishna Berura (617:9) says that in today's times all children are considered weak (unless we know that the child is strong) and therefore do not have to fast the entire day.

If a child does eat on Yom Kippur and bentsches he should say Ya’ale V’yavo. If Yom Kippur is on Shabbos, like this year, he should also include R’tzei. However, if one left out either addition bentsching is not repeated (M.B. 618:29).

Summary:
A child under the age of nine need not fast at all on Yom Kippur. Some people have the custom to train the child to fast part of the day. Once a child is over the age of nine (or ten if he is weak) he should begin to fast for part of the day. A child over the age of eleven need not fast the entire day according to the Mishna Berura. However, other poskim disagree and say that such a child should fast the entire day