At Moss Side primary, Lancashire, even pupils could spot the marking errors. Children in Year 6 were asked to look at their returned science scripts to learn from their mistakes. Instead, three found that their marks had been added up incorrectly.
Janice Burdin, head, said: "It's a very onerous job to send papers back for re-marking. You have to sit down and re-mark them yourself, then send a copy to the board. It's very time-consuming.
"Some high schools set pupils on their test marks. It's just not fair to send children up to high school with marks that aren't correct."
It was not the only school to complain about marking errors in this year's key stage 2 tests. Some pupils have been reported absent for tests in spite of their completed scripts, and schools have reported errors in maths, writing and science marking.
At Leyland Methodist junior school, in Lancashire, two children were labelled as absent, even though their completed scripts had been submitted and marks were wrongly added up. One child's test paper had been overlooked entirely. Another's had been marked but the grade not entered on the mark sheet.
Edith Snape, assistant head at Leyland, said: "If the Government insists on having these tests, then the results should be fair."
Tony Jones, head of Balfour junior school, in Brighton, has sent back 20 out of 100 English papers for re-marking. Several children produced papers of almost identical standard, but were marked differently. "The anomalies confirm how unjust the system is," he said. "A child is judged for four years' effort on the evidence of 45 minutes."
Last year, more than one in seven primary schools appealed against the English test results for their 11-year-old pupils. Almost 2,850 schools sent back 15,509 individual papers: the highest number ever. As a result, 1,082 pupils were awarded a higher level; 81 were downgraded.
David Fann, chair of the National Association of Headteachers' primary committee, will be sending back 14 out of 50 papers from his school, Sherwood primary, in Preston.
He said: "Sadly, this is par for the course. KS2 markers are unprepared and slapdash. The solution is to get rid of tests and just rely on teacher assessment. Teachers end up marking the tests anyway."
A spokeswoman for the National Assessment Agency said: "We do our best to ensure that all the marks are added up correctly. Sometimes in a system of this size - with more than 8 million scripts - things do fall through the net. There's a system in place to allow teachers to query something that is incorrect."