Parents should prepare for further time at home with their children, with teacher strike action to continue next week.

The Post-Primary Teachers' Association (PPTA) has announced its strike action for secondary teachers is due to kick off from this coming Tuesday.

The "Rostering home action" will see teachers opt not to teach a certain year group on a particular day, over four weeks; including, Year 9 on June 4, Year 10 on June 11, Year 11 on June 25 and Year 12 on July 2.

Secondary teachers will also take part in rolling regional strikes, taking place during the week beginning June 17.

Teachers from Tamaki Makaurau, Northland, Counties Manukau, Hauraki and Coromandel will strike on June 17.

Teachers from Waikato, Taranaki, Central Plateau, Western Bay of Plenty and Bay of Plenty will strike on June 18.

Teachers from Otago, Southland and Aoraki will strike on June 19.

Teachers from Canterbury, the West Coast, Nelson and Marlborough will strike on June 20.

And teachers from Wellington, Hutt Valley, Wairarapa, Manawatu-Whanganui, Hawkes Bay and the East Coast with strike on June 21.

Next week's action comes after tens of thousands of teachers and supporters took to the streets yesterday in the country's first combined strike by primary and secondary teachers, affecting 773,000 children.

NZ Educational Institute (NZEI) president Lynda Stuart told an Auckland crowd, which police estimated at 10,000 to 12,000 people, that the teachers were willing to strike again if necessary to win better pay and conditions.

"We have come too far not to go further," she declared.

Education Minister Chris Hipkins offered little sign of compromise, telling marchers at Parliament: "I acknowledge you want more progress, and you want it to be fast, and I cannot offer you that."

The Ministry of Education has offered pay rises of 3 per cent a year for three years, and an extra step at the top of the salary scales, to both the PPTA and the primary teachers' union, the NZ Educational Institute (NZEI). It says the offer would cost taxpayers $1.2 billion over four years.

But members of both unions have rejected the offer because the ministry hasn't offered anything to relieve teachers' workloads by providing more classroom release time.

The NZEI is also unhappy with the pay offer because primary teachers' pay has fallen about 3 per cent behind secondary teachers' pay because of the timing of the two collective agreements. The union wants to restore "pay parity" for all teachers - a principle won through repeated strikes in the 1990s.