UNDATED (AP) -- Most of the nation fell back into the familiar routine of dropping off children at school, as teachers and parents wrestled with how best to quell children's fears after the killings at Sandy Hook Elementary School in Newtown, Conn.

School districts across the U.S. increased patrols and security plans Monday. Around the country, officials reported some school lockdowns in response to threatening incidents.

In Florida, three Tampa-area schools were locked down after officials found a bullet on the floor of a school bus.

Lily Roswell weighed whether to take her 7-year-old daughter to a Miami elementary school on Monday morning, the first day of classes since the Connecticut elementary school massacre that left 20 children around her child's age dead.

But she says she finally determined a shooting could happen in a movie theater, at the mall, anywhere.

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