According to final versions, pupils will also be expected to study computer programming in their first year of school

The education secretary Michael Gove's efforts to revolutionise learning in England's schools will see five-year-olds studying fractions and writing computer programs in their first year of school, according to final versions of the new national curriculum published on Monday.

Among the changes are a requirement for 3-D printers to be used in design and technology lessons, after major revisions to the subject's curriculum.

According to a Whitehall source: "Three-dimensional printers will become standard in our schools – a technology that is transforming manufacturing and the economy. Combined with the introduction of programming, it is a big step forward from Labour's dumbed-down curriculum."

The latest versions of the national curriculum include revisions to drafts that were fiercely criticised when they were published in February. Subjects such as history and geography have had massive rewrites from their initial drafts.

Key skills in many subjects have been brought forward in a child's school career, so primary-age pupils will be given more demanding tasks. For example, tThe teaching of word processing will be dropped in favour of allowing five-year-olds to create and test programs they write themselves. The maths curriculum will see nine-year-olds taught multiplication up to 12 times tables, which is more advanced than the current curriculum allows for 11-year-olds; while the design and technology curriculum will see seven-year-olds introduced to computer-aided design techniques.

David Cameron hailed the new curriculum as "rigorous, engaging and tough". "As a parent this is exactly the kind of thing I want my children to be learning. And as prime minister I know this revolution in education is critical for Britain's prosperity in the decades to come."

Gove said: "This curriculum is a foundation for learning the vital advanced skills that universities and businesses desperately need – skills such as essay-writing, problem-solving, mathematical modelling and computer programming."

Under the new computing curriculum, pupils will be taught internet safety at a much younger age, including how to keep personal details private. Pupils from the age of five will be taught how to create digital information and content, as well as learning how to write and test simple programs and to organise and store data.

Despite its name, the national curriculum applies only to schools in England. Academies and free schools can choose to ignore it.

Stephen Twigg, Labour's shadow education secretary, has pledged to allow all schools to opt out of the national curriculum, while Gove himself has hinted this version may be the last of its kind.

The first consultation papers for history caused controversy, with critics including historian Simon Schama attacking the focus on British events. The Guardian reported last month that plans had been dramatically rewritten to allow more world history, although Winston Churchill has since been restored.

There was considerable criticism of the geography curriculum's failure to mention climate change, and it appears the Department for Education has bowed to critics and brought it back.

The initial design and technology draft curriculum was quickly withdrawn after a battering from industry leaders. The latest version has drawn praise from Sir James Dyson, inventor of the eponymous vacuum cleaner. "Michael Gove has listened to industry and teachers, and created a curriculum that will develop the skills required for the inventive jobs of the future," Dyson said.

The new national curriculum is to be used from September 2014. But teachers' unions say that is unrealistic, given the need to rewrite teaching plans and textbooks.

Kevin Courtney, deputy general secretary of the National Union of Teachers, said Gove was expecting "an unprecedented amount of change" in schools, with the new curriculum on top of reforms to GCSEs, A-levels and vocational qualifications. "The timescale for implementation is far too compressed, with no indication that will be properly resourced," Courtney said.

Adopting a new curriculum while allowing academies to opt out of it suggested an ulterior motive by the government, Courtney said. "In particular it is encouraging schools it sees as weak to convert to academies where the new curriculum will not apply."Education secretary Michael Gove is to publish the final versions of the national curriculum revisions. Here is a summary of the major changes in each subject so far:

• English: secondary school pupils between the ages of 11 and 14 will have to study two Shakespeare plays. Primary-age pupils should be able to recite poetry by heart in the first two years at school and have mastered around 200 complex spellings by the end of primary school.

• Design and technology: primary pupils to be taught to plan, design and build a product and evaluate its final result. Pupils will use mechanisms such as levers, sliders, wheels and axles in their products. From the age of seven, pupils will use mechanical and electrical systems, such as series circuits incorporating switches, bulbs and motors.

At secondary school, pupils will use advanced design techniques such as mathematical modelling and biomimicry. They will learn to use specialist tools, such as 3-D printers, laser cutters and robotics. Pupils will be taught to incorporate and program microprocessor chips into products they have designed and made.

• History: primary pupils expected to study history up to 1066, including compulsory study of ancient Greece, and comparison of significant figures including Rosa Parks and Tim Berners-Lee. Secondary school pupils to study post-Norman conquest. Key historical figures to study include Henry VIII, Queen Victoria and Winston Churchill.

• Computing: primary school children to design, test and write computer programs, and to organise, store and retrieve data. All pupils to be taught internet safety from the age of five, including how to keep their personal details private, how to spot danger, and how to communicate safely through the internet.

• Computing: at secondary school, pupils will be taught to use a range of programming languages. They will study networked computer systems, and how hardware and software interact. Pupils interested in pursuing a professional career in computing will be given the opportunity to study in greater depth.

• Geography: the new version will include specific references to changes in weather and the climate from the ice age to the present. Pupils to be taught about the role of humans in climate change, and how human and physical processes interact to influence and change landscapes, environments and the climate, and how humans depend on the effective functioning of natural systems.

• Mathematics: five-year-olds to be taught fractions for the first time, for a solid grounding at an early age in preparation for algebra and more complex arithmetic. The new curriculum states that nine-year-olds must be taught times tables to 12, with more emphasis on the skills of mathematical modelling and problem-solving.

• Science: evolution will be taught to primary school pupils for the first time, with the new curriculum having a greater focus on scientific knowledge, practical work and mathematical requirements. In secondary school, pupils will study biology, chemistry and physics in greater depth, with greater emphasis on mathematical modelling and problem-solving.