There are to be separate mental arithmetic tests for 11 and 14-year-olds; all seven-year-olds will attempt a comprehension text.
The moves are part of a concerted drive to improve the teaching of number and reading in response to concern about standards.
Preliminary results from the International Mathematics and Science Study, undertaken last year, place 13-year-olds from England 19th in a maths league of 27 countries. The result represents a fall in standards since a similar study in 1990, when English pupils scored 3 per cent above the world average.
The recent Office for Standards in Education report on reading in three London boroughs suggested that as many as 80 per cent of seven-year-olds were falling behind in reading.
Teachers are to be provided with tables that will allow schools to produce scores in English and maths at seven and 11 that are adjusted for age. The current recording rules do not take account of research that demonstrates summer-born children are at a disadvantage.
The form of the mental arithmetic test has yet to be decided. The setting of mental arithmetic tests with written answers presents practical problems.
Ministers are also studying ways of introducing greater emphasis on correct English in the tests for 14-year-olds. The School Curriculum and Assessment Authority is considering options for redesigning the tests to take greater account of grammar, spelling and punctuation.
The compulsory Shakespeare paper is to remain, even though it is unpopular with teachers. However, a range of options on ways of assessing results is being evaluated by academics commissioned by SCAA.
The results of this year's tests for 11-year-olds are to be used to produce the first primary school performance tables.
These are expected to appear in February and schools are likely to be measured against the proportion of pupils that score level four and above (the attainment to be expected of a child of that age) in maths, English and science.
Announcing the changes, the minister of state for education, Lord Henley, said: "This package of reforms will bring extra focus to basic literacy and numeracy, increase rigour and provide more help for teachers."