The bodies of John Paul Bennett, Lacey Bennett and Connie Gent were found at a home in Chandos Crescent in Killamarsh, near Sheffield, on Sunday morning
The mother of John Paul and Lacey, Terri Harris, 35, was also found dead at the scene. A 31-year-old man has been arrested on suspicion of murder and is being questioned by officers.
The children's school, Outwood Academy City, in Sheffield, paid tribute to them in a statement issued on Tuesday (Sep 21).
It said: “We are all devastated at the loss of three of our students; John Paul Bennett, Lacey Bennett and Connie Gent.
“Our hearts are broken after this weekend’s tragic news, and we would like to offer our deepest sympathies and condolences on behalf of everyone at Outwood Academy City to the families of those affected.
“The children had bright futures ahead of them but sadly none of us will get to see this. The school community will remember them fondly.
“Lacey and Connie had just embarked on their secondary school journey with us and already made a positive impression on everyone they came into contact with.
“John Paul was a popular and polite young man, well-liked by staff and with a close-knit group of friends.”
A fundraising page set up on GoFundMe for the families of the victims has now raised more than £14,000.
Officers did not have any prior contact with those involved in the incident, police said.