Requests for tests are flooding in to the School Curriculum and Assessment Authority.
Nine-year-olds are the target group for the new national test, currently being piloted in 500 schools, and SCAA is astonished by the number of requests it has received for the material.
The reason for the popularity of the new test is that it is not compulsory and gives schools a clear notion of whether pupils are on target to do well in the statutory tests two years later. The idea for tests at nine was sparked by the authority's assessment and testing review 18 months ago.
It seems unlikely that the new test will become statutory, as national tests at seven, 11 and 14 already are.
Tim Coulson, professional officer for assessment and reporting at SCAA, said: "There are no plans to make the Year 4 tests statutory. Teachers have enthusiasm for standardised tests but tremendous scepticism for statutory tests."
He said the authority would not be producing new tests for nine-year-olds every year. This year's tests would be given to next year's nine-year-olds as well, he said.
A total of 10,000 nine-year-old pupils in 500 schools are taking part in a test pilot this summer so the authority can form a standardised picture.
The exams, which are being sent to every school, were developed last autumn. They consist of papers in reading, writing, spelling, mathematics and mental arithmetic.
Mr Coulson said: "We are staggered by the number of people who want the tests. Some schools have ordered additional copies before seeing them. Many want to use them this summer term."
The non-statutory tests will be welcomed by inspectors who have criticised the low achievement of some primary schools in Year 4.
But Arthur De Caux, a senior assistant secretary at the National Association of Head Teachers, said: "We regret more and more testing. It is just a further example of testing driving the curriculum.
"We have to accept that while we have got what we have got, teachers will clamour for them. The tests could be more helpful if we did not have the external pressure of publishing results."
Meanwhile, the mental arithmetic tests have upset mathematicians Ruth Merttens and Sue Price (TES 2, page 16).
They argue that unreasonable time limits induce panic rather than logical thinking.