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MB3 110b: Young Children and Playing Ball on Shabbos (308:41-45)
One may assist a child to walk on Shabbos but not if they will drag their feet through dirt. When do we say חי נושא את עצמו? Carrying a child who is too young to walk. Using a piece of a broken container for another purpose.
Playing ball on shabbos vis-a-vis muktzah.