One of the charges stemmed from severe burns suffered by the child, which were not attended to by Barriball. She pleaded guilty to the charges.
Malachi Subecz was found with multiple injuries at a Te Puna property on November 1 last year and was immediately flown to Starship Hospital.
He died 11 days later.
During the hearing, a sombre-looking Barriball sat slumped at the back of the audio-visual suite, with the judge struggling to hear her speak at points.
As each of the charges was read, Barriball quietly read her plea to the court.
Barriball's sister, Sharron Barriball, earlier this month pleaded guilty to a charge of attempting to pervert the course of justice, also related to the offending.
Both are set to be sentenced on June 30.