New South Wales is facing a severe secondary teacher shortage, with unreleased federal government modelling suggesting the state will be short-staffed by 1,700 educators within three years.

Documents obtained by the Guardian show more than 4,000 extra high school teachers are needed nationally over the next four years, with the biggest shortfalls predicted in New South Wales and Queensland.

A separate internal NSW Department of Education briefing shows the state-wide shortage is expected to be most severe in science and technology subjects, in rural, regional and remote schools, and in lower socio-economic areas.

The national forecast said the secondary teacher shortage would jump above 9,000 across Australia if schools only relied on domestic – and no international – students.

While most states and territories are expected to have a shortage of secondary teachers, a glut of more than 8,000 primary school teachers is predicted across the country within four years.

The federal government also expects more than 50,000 teachers to permanently leave the profession between 2020 and 2025, including almost 5,000 teachers aged between 25 and 29.

The NSW Teachers Federation head, Angelo Gavrielatos, described the situation as a “perfect storm that cannot be denied any longer”.

“The sooner all governments stop the denial, the better we will be,” he said.

“The cause is uncompetitive salaries and unsustainable workloads. If you know the cause, you know the solution. Fix it.”

The workforce modelling was completed by the federal Department of Education and circulated to state and territory education ministers to be discussed at an upcoming meeting. It was sent in draft form to the NSW state government and obtained by the Guardian.

The federal Department of Education said the acting education minister, Stuart Robert, has been leading the conversations with ministers “to better understand teacher workforce issues” nationally – a task usually left up to the states.

“These discussions have resulted in the department undertaking modelling of teacher demand and supply, which has been tested with jurisdictions and the non-government schools sector,” a spokesperson for the department said.

The NSW education department documents show one in five students in regional parts of the state are now being taught maths by a non-specialist teacher, while 70,000 students could be affected by shortages by 2030.

Briefings provided to the NSW education minister, Sarah Mitchell, in 2021 warned the department needed to find an additional 4,100 teachers this year, with severe shortages in some regions.

While the state could meet teacher shortages “at an aggregate level”, a shortfall of 800 Stem-qualified teachers meant that about 40,000 students were being taught by “out-of-field” teachers in 2022. In total, the department warned, one in eight secondary students across the state would be taught by “out-of-field” teachers in 2022.

The predicted shortfalls come amid rising concern over the longevity of teachers across the sector, with many reporting feeling overworked even before the pandemic.

A study released by a federal government body in December found a quarter of teachers said they intended to leave the profession before they retired and more than half of those planned to leave within the next decade.

The Australian Institute for Teaching and School Leadership (AITSL) research found one in three teachers under 30 – and almost 40% of teachers aged between 30 and 39 – intended to leave the profession in the next decade.

Low pay, heavy workload, stress and an inability to control the student population were among the top reasons given for planning to leave.

The briefings to the education minister warned the shortage was particularly acute in regional parts of the state, where out-of-field teaching is as high as one-in-five.

“Stem-qualified teacher shortages could affect as many as 70,000 students each year by 2030,” the briefings warned.

“The situation is particularly acute in rural and regional areas, where out-of-field maths teaching is currently as high as 22%.”

The shortfall of teachers in NSW has been well documented. In January Guardian Australia revealed 70 public schools across the state had staff vacancy rates of 20% or higher, while there were 3,300 vacant teaching positions across the state in October last year.

Last year the government announced a new Teacher Supply Strategy to provide 3,700 extra teachers over the next decade. The strategy aims to address shortages in the profession by recruiting teachers from interstate, improving perceptions of teaching by funding a marketing campaign and accelerating the careers of high-performing teachers.

In a statement, the state education department said the government was “on track” to meet its 2019 target of an additional 4,600 teachers over four years.

“The department acknowledges the specific challenges facing specific subject areas in certain locations across the state, and is implementing a range of targeted scholarships and incentives to attract Stem teachers where they are needed most,” a spokesperson for the department said.

But the strategy has been criticised by the NSW Teachers Federation for failing to address teacher pay.

Since 2011, the NSW government has capped wage increases for public servants at 2.5%, a measure that has prompted increased hostility from unions who say pay has not kept pace with rising cost-of-living pressures across the state.

In the briefings obtained by the Guardian, the department provided talking points to the minister on a number of questions relating to teacher pay, including: “NSW teachers are among the lowest paid in Australia. Why is this the case?” and “Teachers play such a critical role which isn’t reflected in their pay. The profession is undervalued – why can’t the government just lift the cap?”.

The briefings blame the shortfall on a lack of qualified teachers in particular subject areas (such as Stem), the difficulty of providing staff to schools in regional or remote parts of the state and what it described as an “increasing” difficulty in finding casual staff to plug holes.

On the latter, the department warned shortages of casual teachers had been exacerbated by their use as part of the Covid Intensive Learning Program, a $383m program placing extra teaching staff in classes to help address education shortfalls resulting from the pandemic. It also cites “higher sick leave” among casuals.

But the minister defended teacher paying, saying public school teacher salaries were “competitive with those offered by other state education systems”.

“In 2011 the annual salary for teachers at the top of the salary scale was $84,759,” her spokesperson said.

“In 2022 the band 2.3 annual salary is $109,978. Over the last 11 years the classroom teacher salary at the top of the scale has increased by $25,219 which represents a 29.75% increase from the 2011 salary.”