David Chater, Al Jazeera's correspondent in Gaza described chaotic scenes at the house and pools of blood in the street and the wreckage of the house.
"There is an overwhelming feeling of bitterness and shock among the residents," he said.
The children were aged between seven months and five years old.
Residents said an Israeli shell smashed through the ceiling of the one storey dwelling; the dead included a school boy who was walking past the house.
"A family was sitting and have their breakfast here and now what? We come to pick up their body parts," said Abu Mohamad, a neighbour.
David Chater said he heard "more tank shells and heavy machine gun fire in the area" as they filmed the rescue operation.
Reports say a member of Islamic Jihad was also killed in the attack.
Militants regularly fire rockets from Beit Hanoun into western Israel, and the Israeli military say three rockets were fired early on Monday morning, but no damage was caused.
Hamas claims one of its snipers shot an Israeli soldier in the town, and the Israeli military confirmed one of its men was "slightly wounded" by gunfire.
A spokeswoman for the Israeli military said the operation in Beit Hanoun was launched to "ensure that rocket crews, snipers and tunnel diggers are kept away from the border".
Hamas has offered a six-month truce if Israel lifts its current embargo on the Gaza Strip, but Israel says the move is a ruse to allow them to re-arm and recruit new fighters.