Children who fall behind in maths or English could be offered one-to-one tuition to help get them back on track.
Ministers want all pupils to have what the better off pay for
Struggling pupils in the later years of primary and early years of secondary school will get extra help outside school hours from qualified teachers.
If the short bursts of tuition succeed in helping pupils in pilot areas, it could be rolled out across England.
The NUT welcomed the plans, saying one-to-one tuition should not just be restricted to those who can afford it.
The General Secretary of the National Union of Teachers, Steve Sinnott, told the BBC: "If a youngster is struggling at school and their parents have the money to be able to assist that youngster, what they do is they go and they get them a private tutor.
"We believe that access to that one-to-one tuition shouldn't be restricted simply to the children of those whose parents can afford it."
Many schools already give struggling pupils extra help in key subjects.
On Monday Education Secretary Alan Johnson launches a consultation on the plans to ensure all children succeed.
Under the pilot scheme, children who were behind in these key subjects when they entered Key Stage 2 (at about age 7) or Key Stage 3 (starting secondary school) - and were still lagging behind about two years later - could qualify for the extra help.
Those who did would be given up to 20 hours of tuition in either subject or both, if necessary, outside normal lesson time.
This could be in the school, out of hours, at a drop-in centre or even at home, but would be organised by the school.
Ministers want to make sure that the extra help that some parents buy in, when they see their child is falling behind, is available to all who need it regardless of income.
They realise that poorer parents are not able to fund this extra support, so the pilot scheme would offer it when they and the school felt it was necessary.
However, the extra help would be on the basis of educational need rather than family circumstances.
Numbers and the 10 local authority areas in which the pilot will take place are yet to be confirmed, but it is thought the bottom 5% in each subject of each key stage would get the help.
This could potentially amount to one in 10 pupils - although there is likely to be some overlap between those struggling in maths and those falling behind in English.
Education officials are keen to stress this is not a new parental entitlement, but a tool to help children who might need it most.
Laura Warren of the National Association of Parent Teacher Associations expressed some reservations over the plans.
"As parents... what we will look for is a better understanding of how it's going to work, how it's going to fit in with all the other policies and strategies that are in place to actually see that it's a true benefit to our children," she told the BBC.
The pilot scheme will run for two years from April 2007.