State television initially gave a toll of 10 killed, but the official SANA news agency subsequently said eight people had been killed, seven children and a woman.
Russia accuses Syria rebels of using chemical weapons in Aleppo
The rocket fire hit a school in the Furqan neighbourhood, and also injured at least 32 people, SANA said, citing a police source.
The news agency reported additional rebel fire on other parts of west Aleppo, which is regularly targeted by the opposition forces that hold the eastern part of the city.
The Syrian Observatory for Human Rights, a Britain-based monitor of the war, also reported the deaths of seven children in rebel fire.
It said the deaths brought the toll in the last two days in west Aleppo to 13, among them nine children.
Syria regime rolls back rebel gains in Aleppo
Government forces are currently waging a ferocious assault against east Aleppo, targeting it with air strikes, barrel bombs and artillery fire.
They renewed their fire on the east on Tuesday, after a period of relative respite, in a bid to recapture the rebel-held side of the city.
The Observatory says at least 103 civilians have been killed in east Aleppo since the latest government assault began.
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