The length of time an arm – or any broken bone, for that matter – is casted depends very largely on what type of fracture or break happened.
Some children have what is called a greenstick fracture, for example. This type of fracture leaves part of the bone intact, like if you bend a young, green stick and it snaps. This type of fracture can heal quickly as the bone has not broken all the way through.
A more severe fracture, however, may require a longer period of time to heal properly. As well, some fractures require surgery to help stabilize the bones, this may add to recovery time.
Each fracture is different in terms of how well it can heal and the type of treatment it may require.