"We've had more incidents of kids running into each other - it's ridiculous, really," said board of trustees chairman Richard Green.
"It is becoming a health and safety issue for kids."
Government estimates show most student growth - 26 per cent, or around 27,820 students - will occur in the city's central isthmus.
Unlike other areas in Auckland, that increase will mostly be accommodated by existing schools. Ms Kaye said the Government would work with the Auckland Council to use housing development information and census data to plan school upgrades.
Nearly $20 million had been spent on 63 classrooms that were under construction or had been recently completed.
She expected at least another $80 million of spending over the next three years.
"I think there has been a catch-up, when you look at the amount of construction that is under way ... with the Auckland Plan there is an opportunity to make sure we are prepared."
Pt Chevalier School and nearby Pasadena Intermediate are expecting to be told this month how they will be affected by roll growth in the area.
The ministry has proposed turning the intermediate into a full primary school, for years 1-8, or building more classrooms at Pt Chevalier primary.
Mr Green said his board felt the more classrooms option was unrealistic unless the school boundaries were expanded, "and given the prices in Pt Chev, I don't think that's going to happen".
Mt Albert Grammar School is also in a rapidly growing area. Its roll is 2600, up from 2034 in 2003.
"It is a problem. But we are on the ministry's radar and I'm very impressed with how strategic they have been in recent times," said headmaster Dale Burden.
Some central Auckland schools would have to have three or even four-storey buildings, Mr Burden said.
"Under the legislation, kids have an absolute right to attend the school they are in zone for ... I'd rather go up another storey than lose a field.
"At the end of the day, what goes on inside a classroom on the third floor is no different to what goes on in the ground floor."
Ms Kaye said she expected schools with three-storey buildings to be the exception. Several new Auckland schools would be confirmed within the next six months.
Changing school zones - which can affect house prices - was also a tool to deal with growth, in close consultation with the community.
"Since 2008 we have had over 50 zone changes. So that is a process that happens pretty regularly."