At least 142 Northland schools are expected to receive more funding next year under a model which provides schools with $92 per at-risk student.
But Te Tai Tokerau Principals' Association president says with schools being asked to take more accountability for things out of their control, schools need more than "half a sandwich per week".
Provisional figures based on Ministy of Education information show at least 142 of 147 Northland schools will be receiving more money through targeted operations grant funding to support at-risk students.
The funding means schools receive an additional $92 for each at-risk student, which is on top of the $1.35 billion in initial operations grants funding for schools.
While some schools nationally will see an increase in funding, others will see a decrease.
Education Minister Hekia Parata said this funding, $12.3 million in targeted operations, represents a 1 per cent increase to the $1.35b in operations grants funding for 2017.
"I am targeting this group because we know, as well as having a higher risk of educational non-achievement, they have a higher chance of coming into contact with the justice system and to suffer from poorer physical health and mental wellbeing," said Ms Parata.
At-risk students are those aged 5 to 18, whose parents have been on benefits for 75 per cent of the first five years of the student's life, or 75 per cent of the most recent five years.
Te Tai Tokerau Principals' Association president and Hora Hora Primary School principal, Pat Newman, said Ms Parata had required schools to be held accountable for their spending, but $92 per at-risk student was not enough.
"If we're made publicly accountable for things out of our control we need more than half a sandwich per week," Mr Newman said.
Hora Hora Primary School will receive $16,712 more in funding.
Mr Newman said while he was happy the funding had at least been spread out across schools with at-risk students, and did not think the previous model was better, more tools were needed.
"Where are the psychologists; where are the counsellors; where are the speech language therapists?"
Ms Parata said it was disingenuous to describe it as "half a sandwich per week" and given Mr Newman's school was one of those benefiting from the targeted funding, she was disappointed by his comments.
"Schools have plenty of tools and support available to them to help them spend their budgets to lift the achievement of all their students, and it's up to them to make the most of what is available. I'm surprised at the idea that being accountable is new or recent to any principal. "