Justin Michael Martin has received a sentence of 20 to 26 years in prison for the attack last August in Aberdeen.
The 22-year-old Martin pleaded guilty to three counts of assault with a deadly weapon. He could have faced more than 38 years in prison on three counts of attempted murder without the plea agreement.
Martin and his father had gone to the home in Aberdeen the night before the attack to visit the children's father. Martin's defense lawyer said his client has no recollection of the crime.
A prosecutor said the slashings may have followed a bout of drinking and smoking marijuana and an argument about the television.
The children have recovered, and some have had plastic surgery to mend the scars.