Syrian government artillery fire killed nine people, including five children, in opposition-held Idlib province on Wednesday, first responders say.
Sixteen others were injured when cluster munitions hit a school in Sarmin which was sheltering displaced people, according to the White Helmets.
It came as pro-government forces continued an offensive to the south.
Idlib is the last major region still held by rebel fighters and jihadists opposed to President Bashar al-Assad.
The United Nations says the hostilities are having devastating consequences for the three million people living there, of whom 76% are women and children.
A ceasefire halted a government assault on Idlib in August that had reportedly left more than 1,000 people dead and displaced an estimated 400,000 others.
However, skirmishes and bombardments continued and on 19 December fighting resumed along the frontlines in the south of the province.
The school in Sarmin hit on Wednesday was run by the UK-based humanitarian organisation Syria Relief, which said two of the children who died were six years old. The others were nine, 11 and 13, it added.
Another 12 children were among the injured, as were two teachers, one of whom had to have a leg amputated.
2020 started in Syria, with the same brutalty of 2019. Another @SyriaRelief school was bombed. Five children were killed. Below is the face of Yahya, one of the victims. He was six-years-old. pic.twitter.com/RWUa93Hyw2— Othman Moqbel (@othman_moqbel) January 2, 2020
Syria Relief said six of its schools had been damaged by military action since April, and that Wednesday's attack meant another 913 children were out of education.
"Unfortunately, our hopes for 2020 to be the year when the suffering of the Syrian people stops feels like they have already been dashed," said Charles Lawley, the organisation's head of advocacy.
Some 284,000 people have fled their homes, mostly in southern Idlib, as a result of the hostilities since 1 December, according to the UN.
The major town of Maarat al-Numan and its surrounding countryside, 30km (19 miles) south of Sarmin, are reportedly almost empty, while people from Saraqeb, only 9km from Sarmin, are fleeing in anticipation of the fighting reaching their area.
Most of the displaced are heading north to the city of Idlib, where public buildings like schools are being used to house them, and to camps near the Turkish border.
The UN says many of them are in urgent need of humanitarian support, including heating, winter clothes and blankets to help them cope with the cold weather.
Last week, the International Rescue Committee warned that many families were being forced to camp in the open, while local doctors said their hospitals were full.
More than 370,000 people have been killed since an uprising against President Assad began in March 2011, according to the UK-based Syrian Observatory for Human Rights. The monitoring group documented 11,215 deaths during 2019.