Five-year-olds will learn fractions and computer coding, while those in early secondary school will have to study at least two Shakespeare plays.
The curriculum is being implemented for most year groups simultaneously.
Teachers' leaders say the timetable is unrealistic, but the Department for Education said its aim was to prepare children for "life in modern Britain".
A spokesman said the government wanted "all children to learn the core knowledge in key subjects - the ones universities and employers value the most".Continue reading the main story “Start Quote
Teachers are saying they haven't had enough information”End Quote Jill Stokoe Association of Teachers and Lecturers 'Keep pace'
All state primary and secondary schools have to start teaching the new national curriculum from the start of term.
The rewritten national curriculum, described by the prime minister as "rigorous, engaging and tough", sets out the framework for what children 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.
Former education secretary Michael Gove has said changes were necessary for England to keep pace with the most successful education systems in the world.
The new-look curriculum puts a stronger emphasis on skills such as "essay writing, problem-solving, mathematical modelling and computer programming".The Department for Education said it was "right that changes are made as soon as possible"
In primary schools where the most significant changes are in maths, English and computing, pupils going into Years 2 and 6 this year will continue with the old curriculum in English, maths and science, so they can sit national tests at the end of the year.
Russell Hobby, general secretary of the National Association of Head Teachers, said teachers had worked hard to prepare for the new curriculum over the past year.
He said he was confident they would cope with its implementation but he warned there could be some difficulties with maths, where more advanced topics are to be taught at a younger age.'A lot of cramming' Continue reading the main story “Start Quote
We are confident that all the reforms can be implemented within our planned timeframe.”End Quote Department for Education
"One of the mistakes in the implementation of the curriculum is that it's all being implemented at once," he said.
"In maths you need to learn the early concepts before you learn the later concepts, so there is a problem that there will be children who have not learned the earlier concepts before being expected to learn the more demanding ones."
Mr Hobby warned that there would have to be "a lot of cramming in maths this year" as whole classes are made to catch up with the new demands.
He added: "The worst thing you can do with maths is rush ahead."
The Association of Teachers and Lecturers has warned that many of its members feel their schools are not yet prepared to teach the new curriculum.
The association's education policy adviser, Jill Stokoe, said: "Teachers are saying they haven't had enough information and some people really haven't got to grips with the new curriculum. What we are saying to them is to use their judgement."
She added that there were particular problems with maths introducing some quite complex ideas for very young children.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" to be studied include Elizabeth I, 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 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. By the end of Year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value 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 eight- and nine-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 the 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"
The Department for Education said the reforms reflected the government's desire to "ensure every child leaves school prepared for life in modern Britain".
"We believe it is right that changes are made as soon as possible to benefit the most young people," a spokesperson said.
"We are confident that all the reforms can be implemented within our planned timeframe which is a testament to the dedication of our high-quality teaching profession."
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