Five year olds will start tackling fractions and computer algorithms, as a more stretching national curriculum is announced for state schools in England.
The government says the curriculum changes are designed to catch up with the world's best education systems.
Prime Minister David Cameron says this "revolution in education" is vital for the country's economic prosperity.
Labour said the curriculum should be written by experts and not depend on ministers' "personal prejudices".
Teachers' unions have warned that the timetable for implementing the changes in autumn 2014 is "completely unrealistic".
Head teachers have also asked whether politicians should be so directly involved in deciding what is taught in the classroom.
'Engaging and tough'
The re-written national curriculum sets out the framework for what children in England's state schools should be taught between the ages of five and 14.
However, academies - which are now a majority of secondary schools - will not be required to follow the curriculum.
"This is a curriculum that is rigorous, engaging and tough," said the prime minister.
Education Secretary Michael Gove said the changes to the curriculum were necessary to keep pace with the achievement of pupils in other countries.
"No national curriculum can be modernised without paying close attention to what's been happening in education internationally," said Mr Gove.
He cited Hong Kong, Massachusetts, Singapore and Finland as "the world's most successful school systems".
The new-look curriculum puts a stronger emphasis on skills such as "essay writing, problem-solving, mathematical modelling and computer programming".
- The history curriculum takes primary pupils through British history from the stone age to the Normans. They can also study a later era, such as the Victorians. "Significant individuals" studied include Elizabeth 1st, Neil Armstrong, Rosa Parks and suffragette Emily Davison. Secondary schools will teach British history from 1066 to 1901, followed by Britain, Europe and world events from 1901, including the Holocaust and Winston Churchill. This is a less detailed curriculum than an earlier draft, no longer including Clive of India, Wolfe or a reference to economic changes up to the election of Margaret Thatcher.
- Maths will expect more at an earlier age. There will be a requirement for pupils to learn their 12 times table by the age of nine. Basic fractions, such as half or a quarter, will be taught to five year olds.
- English will strengthen the importance of Shakespeare, with pupils between the ages of 11 and 14 expected to have studied two of his plays. Word lists for 8 and 9 year olds include "medicine" and "knowledge", by 10 and 11 they should be spelling "accommodate" and "rhythm".
- Science will shift towards a stronger sense of hard facts and "scientific knowledge". In primary school, there will be new content on the solar system, speed and evolution. In secondary school, there will be a clearer sense of separate subjects of physics, biology and chemistry. Climate change will also be included.
- Design and technology is linked to innovation and digital industries. Pupils will learn about 3D printing and robotics.
- Computing will teach pupils how to write code. Pupils aged five to seven will be expected to "understand what algorithms are" and to "create and debug simple programs". By the age of 11, pupils will have to "design, use and evaluate computational abstractions that model the state and behaviour of real-world problems and physical systems".
Anthony Seldon, head master of Wellington College, welcomed the idea of a more demanding curriculum, saying that "young people shouldn't be patronised by work that is too easy".
"Factual knowledge is essential," he said, providing the "building blocks" for more advanced ideas in subjects in the sciences, arts and humanities.
He says it is important for all youngsters to learn a common core of knowledge.
"It can get too fluffy to say 'It's all on the internet,'" said Dr Seldon.
Brian Lightman, leader of the ASCL head teachers' union, said that heads shared the aspiration for high standards, but warned of the practical problems of implementation.
"One year to implement such ambitious proposals effectively alongside the vast number of concurrent reforms is a tall order."
He also questioned the level of political involvement in the process.
"Drafting a curriculum is a highly specialised and professional task. Unlike previous versions of the national curriculum, which were drafted with a heavy involvement of teachers and school leaders, these proposals have been driven and closely directed by politicians without that professional input."
He said the government needed to take "urgent steps" to include head teachers in implementing the changes.
The CBI's Neil Carberry welcomed the changes to the design and technology curriculum, saying that it seemed "much sharper and focused on the technical skills industry and employers need".
But he called for more improvements in maths. "The big challenge is equip all young people with the basic numeracy they need before the GCSE syllabus starts," he said.
Mary Bousted, leader of the ATL teachers' union, accused the education secretary of wanting to "steamroller ahead" with rushed changes.
"The timescales to which he is operating are completely unrealistic. He shows a fundamental lack of understanding of how much planning is needed to bring in a totally new curriculum and new exams for children in all age groups at the same time."
Chris Keates, leader of the Nasuwt teachers' union, accused the education secretary of "trotting out tired old and false assertions about England's alleged slide down the international leagues tables as a justification for tearing up the qualifications and curriculum framework and pursuing his personal ideological crusade".
The National Union of Teachers' deputy leader, Kevin Courtney, said: "This is a curriculum written by government advisers and officials, not teachers."
She warned that it failed to recognise the need to serve children of different ability levels and that the time for introducing this was "ridiculously short".
Shadow education secretary Stephen Twigg said: "David Cameron and Michael Gove have spent the last three years trying to personally rewrite the national curriculum - they should have listened to the experts in the first place.
"They have had to go back and change the programmes of study for design and technology, geography and history after experts warned there were serious omissions and they were not suited to prepare young people for the challenges of the modern world. It's right that changes have been made to ICT and computing following concerns raised by Labour and the ICT sector, but we await further details.
"Labour wants to ensure the national curriculum sets clear expectations for the knowledge and skills children and young people should reach by a certain age. This curriculum looks like more of the same though."