The Department for Education and Skills has said it wants a third of 11-year-olds to achieve level 5 or above in English and maths by 2004. Teachers of 10-year-olds will be given a half-day training course in how to bring out the best in more able children. Maths is being targeted because results fell last year, compared with a rise in English scores.
Heads and governing bodies must come up with level 5 targets for 2003 by the end of July, a requirement introduced in April.
At St Augustine's RC primary in High Wycombe, Buckinghamshire, a third of 11-year-olds are expected to get level 5 in English next year, and for maths the target is 40 per cent.
Headteacher Eamon Kennedy said: "The only reason I have set targets is because it is a national expectation.
"I think these targets are being set for political expedience - they are not at all educationally useful. I passionately believe in assessment geared to the child and results shared with parents in a local situation. I don't subscribe to league tables."
Hasan Chawdhry, head of Edinburgh Road primary in Walthamstow, north-east London, said: "Level 4 is the level for children in primary school and level 5 is a bonus. For those children who can get level 5 we will try and stretch them, but I am not sure about target-setting. A requirement for level 5 has come through the back door."
A DFES spokeswoman said: "We think it is important for all schools to have high expectations of what their children can achieve by setting targets for those who are capable of achieving more.
"We do not believe the new requirement will impose a significant additional burden. Many schools already set level 5 targets at the same time as they set their level 4 targets."
Since 1998, the number of 11-year-olds achieving level 5 has risen by 12 percentage points in English to 29 per cent and by 9 per cent in mathematics to 25 per cent.