Saying the Florida Department of Children and Families didn’t do its job, state lawmakers last month approved paying $3.75 million in a 2011 child-abuse case that drew national headlines.

But the planned payment in the death of 10-year-old Nubia Barahona and injuries suffered by her twin brother, Victor, was part of a broader effort this year by lawmakers to compensate people for injuries or deaths caused by actions — or negligence — of government agencies.