The Syrian Observatory for Human Rights said the three adults included a teacher, and that the strike in the town of Anjara also injured at least 20 people, all of them children and teachers.
The monitor said there had been heavy air strikes and clashes between government and rebel forces since Sunday in the northern province, which is controlled by a mixture of moderate and Islamist rebels.
Photos distributed by media activists in Aleppo province showed a classroom full of rubble with the wooden tops of desks blown off their metal frames.
The Britain-based Observatory also reported that three children were killed by rebel rocket fire on a government-held district in Aleppo city.
Control of the city has been divided between government forces in the west and rebel fighters in the east since shortly after fighting began there in mid-2012.
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Government forces regularly carry out air raids on the east, while rebels fire rockets into the west.
The situation is largely reversed in the countryside surrounding the city, with rebels controlling much of the area west of Aleppo, and the government present to the east.
Russia, a staunch ally of President Bashar al-Assad's regime, began air strikes in support of the central government in late September.
It says it is targeting the Islamic State group and other "terrorists," but a third of those killed in its strikes have been civilians, according to the Observatory.
The monitor said in late December that Russian air strikes had killed more than 2,300 people since they began on September 30, among them 792 civilians.
Moscow has slammed as "absurd" allegations that its strikes have killed civilians.
More than 260,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.