It was the most serious violence against Syrian minors since a twin suicide bombing killed at least 25 children near a school in October.
The children of the Haya School in the town of Qaboun were struck by three mortars, said a local activist who uses the name Abu Akram al-Shami.
Another local activist, Amar al-Hassan, based near Damascus, also confirmed the incident, as did Rami Abdurrahman of the Britain-based Syrian Observatory For Human Rights.
Abdurrahman said 11 children were confirmed killed, but the number was likely to rise because of the seriousness of many of the children's wounds.
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Another showed at least five boys bloodied and lying lifeless on the ground of what appeared to a medical faculty.
The videos appeared genuine and corresponded to Associated Press reporting of the incident.
The local activist collective, the Qaboun Media Office, said at least 17 children were killed. Conflicting death tolls are common after such incidents.
It was not immediately clear who fired the rockets. Both pro-government forces loyal to President Bashar Assad and rebels opposed to his rule use the weapons.
The town hosts thousands of Syrians who have been forcibly displaced from other rebel-held areas.
Activists said they believed Assad loyalist forces fired the mortar shells because it was unlikely that rebels would fire at their own people. Government officials had no immediate comment.
Syrian children have often been the victims of the country's war, now in its fourth year, but they are rarely specifically targeted.
But in October, two suicide bombers targeted a school in the central city of Homs, killing 32 people, including 25 children.