The area at this time is busy with many young people around being picked up.
As Tawhiti-Ormsby left the school, Hay asked him to follow the flow of the traffic. The driver refused to do this.
Hay then grabbed his mobile phone and took a photo of their Toyota vehicle.
Occupants then started to verbally abuse Hay for taking the photo.
The summary said Tawhiti-Ormsby then got out of the vehicle and "charged" at Hay, punching him to his face with a closed fist and causing him to stumble and fall on the ground.
Tawhiti-Ormsby then got back in the car and it left.
When police spoke to Tawhiti-Ormsby, he admitted what he did and said he was "angry at the victim because he thought the victim was being cheeky".
Judge Greg Hollister-Jones remanded Tawhiti-Ormsby on continued bail to reappear in court on May 10.
On that date, Tawhiti-Ormsby will also be sentenced on charges of burglary and unlawfully getting into a motor vehicle, charges he had earlier pleaded guilty to.
Judge Hollister-Jones also ordered restorative justice, a process where Hay and Tawhiti-Ormsby could meet if Hay agreed to do so.
Outside the court, Tawhiti-Ormsby told the Rotorua Daily Post he didn't want to comment on his guilty plea.
When asked if he had anything to say to the teacher, he said "I will go and see him in my own time".
Defence lawyer Louise Te Kani appeared for Tawhiti-Ormsby.
After this morning's court hearing, Hay told the Rotorua Daily Post he was glad Tawhiti-Ormsby pleaded guilty.
While he wanted to be back at school, he was still off work due to his concussion which had caused frequent headaches and a struggle with concentration.
He said his ankle, which was badly twisted with a piece of the bone cracked, would be x-rayed again soon.
"I am getting better but it is a slow road. Concussion sucks. I'm glad the guy took ownership of the assault. There was no need for it."
Hay said he had received lots of support from the school and community and was not concerned about going back to school, repeating what he had previously said: "It was a one-off."