The year 6 pupil at Selwyn Primary School loved his scooter and going to cub scouts, his family said.
He was to start at Kaitao Intermediate School next year.
"He was a good lad, full of energy - just a typical 10-year-old boy really," Selwyn principal Peter Barker said.
"We'd just like to extend our sympathies to the whanau."
The family had several connections to the school. Matthew's younger brother Lee and several members of his extended family are also pupils and his grandmother is a member of staff, said Mr Barker.
"The family are understandably distressed. They're absolutely devastated as any family would be," he said.
Staff will decide how to acknowledge Matthew's life when school restarts.
Ambulance and fire service crews performed CPR on Matthew at the scene.
He was rushed to Rotorua Hospital where doctors spent at least 30 minutes trying to save him but he remained unresponsive and was pronounced dead. His death has been referred to the coroner.
"The family would like to thank everyone who has contacted them over the past few days with their thoughts, best wishes and support," a family spokeswoman said.
Anyone wishing to send flowers or donations should contact Greys Funeral Services.
