The figures in the TES Scotland survey show the mammoth problem facing councils in implementing the Government's policy of cutting statutory class sizes from 33 to 30 in the first three primary years.
But while the figures show the scale of the problem, they do not show how many schools will be in serious difficulty because there is no room to form extra classes or money to take on additional teachers. Those most directly affected are likely to be popular schools in middle-class areas that are already overcrowded.
John Stodter, Aberdeen's director of education, said: "If we have to reduce the numbers in some large city centre primaries, we would have to create additional classes but we have no space in which to put them. You can't get huts into some schools."
Edinburgh reports that two much sought-after primaries, Davidson's Mains and Sciennes, have nine
P1-P3 classes, each of which has 31 or more pupils. Another seven schools have six classes over the limit.
Margaret Burnell, senior depute director of education in East Ayrshire, said that of the council's 13 primaries with large classes seven would face serious problems since they are at maximum capacity.
East Lothian and East Dunbartonshire, which have large classes just below the Government's proposed limit, also face uncertainty. Population changes and housebuilding plans in East Lothian could hit more than the 10 primaries currently likely to be affected, Alan Blackie, the council's director, warned.
John McKeown, East Dunbartonshire's head of educational provision and planning, said: "In reality, the figures could be substantially higher as a large number of schools in this area operate with primary classes of 28, 29 or 30 pupils and the enrolment of a few additional pupils may well bring the class size to 31 pupils or over."
Angus warns that estimates of the impact on staffing and accommodation cannot be taken at face value. The education department says the assumption that only four primaries would need an extra classroom is ludicrous.
The council says: "The erection of one additional classroom in one particular school assumes that what is being faced is a single-year bulge, whereas the reality is much more likely to be that any school in this position will find itself facing the same problem several times in the space of any given seven-year period, thereby necessitating the erection of more than one additional classroom. "
A single-stream primary that regularly has an intake of 32 pupils would have to be extended to become a 1.5-stream school with composite classes at various stages, Angus states.
Phil Brown, education officer in Midlothian, said most schools could cope by rearranging classes, creating some composites, while others would refuse placing requests. One school might need an extension but another would not be able to expand on its present site.
The extent of compositing could be severe and may provoke parental outrage, Keir Bloomer, education director in Clackmannan, said. St Mungo's primary in Alloa, for example, is currently full and every class is above 30. There are no composites. If a ceiling of 30 was imposed, there would have to be nine classes of which five would be composites, and two huts would have to go up in the playground.
"Most parents would say that was a bad deal," Mr Bloomer said. "We are manufacturing accommodation problems and parental dissatisfaction for no obvious gains."
John Travers, director of education in North Ayrshire, says parents will also be unhappy if councils are forced to rezone school catchment areas. "Rezonings have proved divisive in the past but may be necessary if there is no funding or no suitable space for additional classrooms," Mr Travers said.
North Ayrshire and Renfrewshire, which carried out a detailed survey of class sizes for the Association of Directors of Education in Scotland, conclude that a range of measures will be needed to comply with a 30-pupil limit. These include refusing placing requests, re-compositing classes throughout schools, employing extra teachers and putting in extra classrooms.
Seven of North Ayrshire's primaries would have to be re-composited. Renfrewshire would have to create new composite classes in five primaries and limit placing requests in 15 schools. Two Renfrewshire primaries would each need three teachers at a total cost of #163;150,000.
Even a council like Fife where classes are close to the Government's preferred sizes will incur significant expenditure. The council's policy is already to limit primary 1 and primary 2 classes to 30 pupils, but it would still have to increase the number of composite classes and provide six additional teachers and three classrooms.
Council leaders and opposition critics are coming increasingly to believe that the Government's plans may be a sledgehammer to crack a nut, largely to solve an English problem. While Inverclyde, for example, has 519 pupils in 17 classes of 31 or more pupils, there are only 38 "excess" pupils.
Chris Mason, leader of the Liberal Democrats on Glasgow City Council, said: "It makes little or no sense in Scotland and practically none in Glasgow. The schools which are affected do not suffer from educational disadvantage. "
The grant-aided Jordanhill School, of which he is a governor, would have to reduce classes from 33 to 30. "Is Jordanhill really disadvantaged? The policy would do nothing at all and cause maximum disruption," Dr Mason said. There were other more important objectives than cutting class sizes.