Two of the victims were killed shortly after dawn in separate raids around the southern city of Khan Yunis, which also left two injured.
And shortly afterwards, a 15-year-old boy was killed and six other school children injured in what medics said was another airstrike near the northern town of Beit Lahiya.
Adham Abu Selmiya, spokesman for the Gaza emergency services, said 73 people had been injured since the bloodshed began on Friday, and that Israel had carried out 36 airstrikes on the territory.
He named the latest victim as Nayef Qarmut saying he was on his way to school when he was killed in a drone strike in Beit Lahiya.
"A drone strike hit a group of students who were walking by empty land on their way to school," he told AFP, saying six others had been injured, two of whom were in critical condition.
The latest killings came after another schoolboy, 12-year-old Ayoub Assaleya, was killed in an Israeli airstrike on a predominantly civilian neighborhood on Sunday in the Jabalya refugee camp, according to medics.
His seven-year-old cousin was injured in the attack and taken to Kamal Adwan hospital in Jabalya, north Gaza.
Israeli warplanes also fired on the Zeitoun neighborhood of Gaza City, killing one militant, Abu Selmiya said.
Gazan farm keeper Adel al-Issi, 52, was also killed midday on Sunday when a missile hit a field in Gaza City, Abu Selmiya said, bringing the death toll since Friday evening to 18.
Israel's army said it had targeted a terrorist "moments before firing a Grad rocket at the city of Ashdod."
Earlier, the Israeli army said that it had targeted a "terrorist squad" preparing to fire rockets from northern Gaza.
It also confirmed a direct hit on "two rocket launching sites, in the northern Gaza Strip, used by terror organizations."
Gaza militants have responded to Israeli airstrikes with more than 100 rockets since Friday, injuring six Israelis, one of them seriously.
Islamic Jihad and the Popular Resistance Committees said it had fired rockets and mortars into Israel on Friday and Saturday.
A Palestinian official speaking on condition of anonymity said Egypt had begun mediating a ceasefire on Sunday. The Egyptian Foreign Ministry had no comment.
"Israel said it was willing to end this round of violence if rockets from Gaza stopped," the Palestinian official said on Sunday.
"Palestinian factions also told Egypt they were not interested in escalation and that they did not start the round, but Israel cannot decide to end it whenever it wants to do so."
Israel routinely carries out airstrikes on the Gaza Strip, and has intensified its campaign in recent months, while Hamas insists on maintaining restraint.
Suspicions of a new war were raised after Israeli army chief Benny Gantz said in December that Israel should launch a "swift and painful" war against Gaza.
Israel's previous war against Gaza in late 2008 killed at least 1,400 Palestinians and three Israeli non-combatants.