Umar Balogun, 16, from Waltham Forest, London, died at Bawsey Pits, near King's Lynn, Norfolk, in July 2013.
Umar, who was in care at Castle Homes centre, Cambridgeshire, was at the lake with another boy and two care workers.
The staff members had not seen a document which said Umar was a "high risk" for swimming, Norfolk Coroner's Court heard.
Despite a sign saying "No swimming", the boys entered the water and started splashing about before Umar suddenly disappeared under the surface, the coroner's court was told.
A diver later recovered his body on the bottom of the lake.
The coroner's court heard from the two care workers  - Vanda Cawley and Kevin Roweth - who took Umar and another boy to Bawsey on 16 July.
Ms Cawley had been brought in for the day from another home.
Mr Roweth, who had started the job a couple of weeks previously, is currently under investigation by the Health and Safety Executive.
Both staff members said they were not familiar with the boys' risk assessment forms.
The jury returned a verdict of accidental death after a four-day inquest.
An inquest jury has returned a verdict of accidental death after a boy drowned while swimming in a former quarry.