Education minister Liz Truss has said new primary school tests will help to ensure no-one leaves school without sound maths and literacy skills.
The Department for Education claims sample questions for the assessments reveal the more exacting standards expected of seven and 11 year-olds when compared with the tests currently in use.
Under the new assessment scheme, which will be introduced in 2016, pupils will be required to demonstrate a more rigorous understanding of their subjects.
In maths, they will need to be able to add and subtract fractions with different denominations and mixed numbers; calculate the area of a parallelogram and triangle, and the volume of a cuboid; and carry out calculations involving division, multiplication, subtraction and addition.
Currently, pupils are not expected to have such detailed knowledge - they are only required to learn their ten times table and calculate the areas of squares and rectangles.
Reading is another area in which youngsters will be expected to demonstrate broader knowledge, including commenting on writers' use of words, phrases and language features including figurative language, as well as distinguishing between facts and opinions.
Grammar, punctuation and spelling assessments will test pupils' knowledge of adverbials and subordinate clauses.
Education minister Elizabeth Truss said: "We know that for children to get on in life, a solid grounding in maths and English at primary is vital.
"There is no reason why our children cannot match the best performers around the world in these vital subjects."
The government says achievement at primary school is often essential for youngsters' future success, enabling them to obtain good GCSEs.
Knowledge of English and maths is also highly valued by employers. The results of a survey released this month by the Confederation of British Industry showed that 85 per cent of businesses wanted more focus on literacy and numeracy at primary school.
Maths is a particularly important subject in terms of people's earning potential: children who perform well in the subject at an early age tend to earn £2,100 a year more in their 30s than others who are just average in the subject.
Posted by Harriet McGowan