In the earliest attack, the first in Jerusalem for nearly two weeks, two teenaged girls stabbed an elderly man before being shot, police said.
A security camera video of the attack appeared to show the girls -- aged 14 and 16 -- in school uniform chasing a man with scissors before being shot by a member of the security forces.
He then appears to shoot one of them again while already collapsed on the ground.
The man they targeted was identified as a 70-year-old Palestinian, possibly confused for an Israeli Jew, who suffered light injuries.
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One of the girls' brothers had died two years ago during clashes with Israeli security forces, Palestinian security sources said.
Later an Israeli was stabbed to death while another was seriously wounded at a petrol station on the edge of the West Bank.
"A Palestinian murdered an Israeli and wounded another in an attack at a gas station on route 443," the Israeli army said, referring to a main road between Jerusalem and Tel Aviv that passes in part though the West Bank.
In the third attack, a Palestinian was shot dead when trying to stab an Israeli soldier near Huwara to the south of Nablus.
The Palestinian health ministry identified the assailant as 16-year-old Khalil Hashash.
An 18-year-old Palestinian woman, identified by medical sources as Samah Abdullah, was shot and severely wounded in the same attack, apparently by accident.
The stabbings were the latest in a wave of violence since October 1 that has left 92 Palestinians dead, including one Arab Israeli, as well as 17 Israelis, an American and an Eritrean.