Headteachers have been at pains to point out they must consider the health and safety of pupils as they reach their decisions.
The Government has been urged to hold talks with NUT leaders in a bid to avert the planned strike.
NUT members voted by more than 9-1 in favour of industrial action following a ballot in a long-running dispute over pay and conditions.
A Department for Education spokesman said it was "already in regular and constructive talks" with the NUT on pay and conditions and urged the union to call off the strike.
Schools across West Cumbria will also close or face disruption next Tuesday.
Ian Smith has decided that he can open St Benedict’s School , in Whitehaven, to only those pupils in years seven, eight and nine.
A decision by leaders of the West Lakes Academy in Egremont will be made, at the very latest, on Monday, according to its website.
Adrian Thompson, chairman of governors at the academy, told parents: “Every effort will be made to give notice at the latest by the day before; but in case the decision has to be made on the day itself, we are asking parents to nominate a place of safety, which may be your home, to which your child can go if we have to close.”
The impact of the planned action is also set to hit primary schools.
Those that have announced they will close include St James Juniors , Whitehaven and Thwaites primary in Millom; Broughton Primary , Eaglesfield Paddle and All Saints in Cockermouth.
Ewanrigg Junior School in Maryport will also be closed but the school’s residential trip to London is still going ahead.
Broughton Moor Primary School is likely to be closed on Tuesday. A number of classes at other schools will not be on.
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