The 14-year-old, who cannot be named for legal reasons, attacked Dawn McKenzie, 34, at a flat in Hamilton, Lanarkshire in June last year after he had been grounded for bad behaviour.
Sentencing him at the High Court in Edinburgh, Lord Pentland paid tribute to the victim.
"No order I impose can possibly put right the appalling consequences of her tragic death," he said.
Ms McKenzie was "an admirable person" who dedicated her life to the welfare of children, the court heard.
The boy admitted culpable homicide on the grounds of diminished responsibility for the attack on June 24 last year. He lashed out days after his mobile phone, laptop computer and X-box video game console were confiscated.
On the day of the killing he was told to go to bed early as punishment for going swimming when he was supposed to be grounded.
Lord Pentland told him: "You subjected Ms McKenzie to a vicious attack in which you used a high degree of violence. It is no surprise you were originally indicted with the crime of murder."
Ms McKenzie was stabbed in the body and head. The force of a blow to the scalp broke the end of the knife off and left it embedded in her skull.
Her attacker was described as a frightened boy by Donald Findlay QC who represented the teenager. "Biologically and legally he should be out there being one of that generation who is being inspired by events most of us are watching in London," he said.
"The reality is that (he) faces the formative years of his life in custody." The judge imposed a seven-year sentence, reduced from a possible eight years because he pleaded guilty. The boy will be supervised for a further five years.