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Purpose of study

A high-quality computing education equips pupils to use computational thinking and creativity to understand and change the world. Computing has deep links with mathematics, science and design and technology, and provides insights into both natural and artificial systems. The core of computing is computer science, in which pupils are taught the principles of information and computation, how digital systems work and how to put this knowledge to use through programming. Building on this knowledge and understanding, pupils are equipped to use information technology to create programs, systems and a range of content. Computing also ensures that pupils become digitally literate - able to use, and express themselves and develop their ideas through, information and communication technology - at a level suitable for the future workplace and as active participants in a digital world.

Aims

The national curriculum for computing aims to ensure that all pupils:

can understand and apply the fundamental principles and concepts of computer science, including abstraction, logic, algorithms and data representation

can analyse problems in computational terms, and have repeated practical experience of writing computer programs in order to solve such problems

can evaluate and apply information technology, including new or unfamiliar technologies, analytically to solve problems

are responsible, competent, confident and creative users of information and communication technology

Attainment targets

By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study.

Schools are not required by law to teach the example content in [square brackets].

Subject content

Key stage 1

Pupils should be taught to:

understand what algorithms are, how they are implemented as programs on digital devices, and that programs execute by following precise and unambiguous instructions

create and debug simple programs

use logical reasoning to predict the behaviour of simple programs

use technology purposefully to create, organise, store, manipulate and retrieve digital content

recognise common uses of information technology beyond school

use technology safely and respectfully, keeping personal information private; identify where to go for help and support when they have concerns about content or contact on the internet or other online technologies

Key stage 2

Pupils should be taught to:

design, write and debug programs that accomplish specific goals, including controlling or simulating physical systems; solve problems by decomposing them into smaller parts

use sequence, selection, and repetition in programs; work with variables and various forms of input and output

use logical reasoning to explain how some simple algorithms work and to detect and correct errors in algorithms and programs

understand computer networks, including the internet; how they can provide multiple services, such as the World Wide Web, and the opportunities they offer for communication and collaboration

use search technologies effectively, appreciate how results are selected and ranked, and be discerning in evaluating digital content

select, use and combine a variety of software (including internet services) on a range of digital devices to design and create a range of programs, systems and content that accomplish given goals, including collecting, analysing, evaluating and presenting data and information

use technology safely, respectfully and responsibly; recognise acceptable/unacceptable behaviour; identify a range of ways to report concerns about content and contact

Key stage 3

Pupils should be taught to:

design, use and evaluate computational abstractions that model the state and behaviour of real-world problems and physical systems

understand several key algorithms that reflect computational thinking [for example, ones for sorting and searching]; use logical reasoning to compare the utility of alternative algorithms for the same problem

use 2 or more programming languages, at least one of which is textual, to solve a variety of computational problems; make appropriate use of data structures [for example, lists, tables or arrays]; design and develop modular programs that use procedures or functions

understand simple Boolean logic [for example, AND, OR and NOT] and some of its uses in circuits and programming; understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers [for example, binary addition, and conversion between binary and decimal]

understand the hardware and software components that make up computer systems, and how they communicate with one another and with other systems

understand how instructions are stored and executed within a computer system; understand how data of various types (including text, sounds and pictures) can be represented and manipulated digitally, in the form of binary digits

undertake creative projects that involve selecting, using, and combining multiple applications, preferably across a range of devices, to achieve challenging goals, including collecting and analysing data and meeting the needs of known users

create, reuse, revise and repurpose digital artefacts for a given audience, with attention to trustworthiness, design and usability

understand a range of ways to use technology safely, respectfully, responsibly and securely, including protecting their online identity and privacy; recognise inappropriate content, contact and conduct, and know how to report concerns

Key stage 4

All pupils must have the opportunity to study aspects of information technology and computer science at sufficient depth to allow them to progress to higher levels of study or to a professional career.

All pupils should be taught to:

develop their capability, creativity and knowledge in computer science, digital media and information technology

develop and apply their analytic, problem-solving, design, and computational thinking skills

understand how changes in technology affect safety, including new ways to protect their online privacy and identity, and how to report a range of concerns

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National curriculum in England: computing programmes of study

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A high-quality computing education equips pupils to use computational thinking and creativity to understand and change the world. Computing has deep links with mathematics, science and design and technology, and provides insights into both natural and artificial systems. The core of computing is computer science, in which pupils are taught the principles of information and computation, how digital systems work and how to put this knowledge to use through programming.

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Purpose of study

English has a pre-eminent place in education and in society. A high-quality education in English will teach pupils to speak and write fluently so that they can communicate their ideas and emotions to others, and through their reading and listening, others can communicate with them. Through reading in particular, pupils have a chance to develop culturally, emotionally, intellectually, socially and spiritually. Literature, especially, plays a key role in such development. Reading also enables pupils both to acquire knowledge and to build on what they already know. All the skills of language are essential to participating fully as a member of society; pupils who do not learn to speak, read and write fluently and confidently are effectively disenfranchised.

Aims

The overarching aim for English in the national curriculum is to promote high standards of language and literacy by equipping pupils with a strong command of the spoken and written language, and to develop their love of literature through widespread reading for enjoyment. The national curriculum for English aims to ensure that all pupils:

read easily, fluently and with good understanding

develop the habit of reading widely and often, for both pleasure and information

acquire a wide vocabulary, an understanding of grammar and knowledge of linguistic conventions for reading, writing and spoken language

appreciate our rich and varied literary heritage

write clearly, accurately and coherently, adapting their language and style in and for a range of contexts, purposes and audiences

use discussion in order to learn; they should be able to elaborate and explain clearly their understanding and ideas

are competent in the arts of speaking and listening, making formal presentations, demonstrating to others and participating in debate

Spoken language

The national curriculum for English reflects the importance of spoken language in pupils' development across the whole curriculum - cognitively, socially and linguistically. Spoken language underpins the development of reading and writing. The quality and variety of language that pupils hear and speak are vital for developing their vocabulary and grammar and their understanding for reading and writing. Teachers should therefore ensure the continual development of pupils' confidence and competence in spoken language and listening skills. Pupils should develop a capacity to explain their understanding of books and other reading, and to prepare their ideas before they write. They must be assisted in making their thinking clear to themselves as well as to others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions. Pupils should also be taught to understand and use the conventions for discussion and debate.

All pupils should be enabled to participate in and gain knowledge, skills and understanding associated with the artistic practice of drama. Pupils should be able to adopt, create and sustain a range of roles, responding appropriately to others in role. They should have opportunities to improvise, devise and script drama for one another and a range of audiences, as well as to rehearse, refine, share and respond thoughtfully to drama and theatre performances.

Statutory requirements which underpin all aspects of spoken language across the 6 years of primary education form part of the national curriculum. These are reflected and contextualised within the reading and writing domains which follow.

Reading

The programmes of study for reading at key stages 1 and 2 consist of 2 dimensions:

word reading

comprehension (both listening and reading)

It is essential that teaching focuses on developing pupils' competence in both dimensions; different kinds of teaching are needed for each.

Skilled word reading involves both the speedy working out of the pronunciation of unfamiliar printed words (decoding) and the speedy recognition of familiar printed words. Underpinning both is the understanding that the letters on the page represent the sounds in spoken words. This is why phonics should be emphasised in the early teaching of reading to beginners (ie unskilled readers) when they start school.

Good comprehension draws from linguistic knowledge (in particular of vocabulary and grammar) and on knowledge of the world. Comprehension skills develop through pupils' experience of high-quality discussion with the teacher, as well as from reading and discussing a range of stories, poems and non-fiction. All pupils must be encouraged to read widely across both fiction and non-fiction to develop their knowledge of themselves and the world they live in, to establish an appreciation and love of reading, and to gain knowledge across the curriculum. Reading widely and often increases pupils' vocabulary because they encounter words they would rarely hear or use in everyday speech. Reading also feeds pupils' imagination and opens up a treasure house of wonder and joy for curious young minds.

It is essential that, by the end of their primary education, all pupils are able to read fluently, and with confidence, in any subject in their forthcoming secondary education.

Writing

The programmes of study for writing at key stages 1 and 2 are constructed similarly to those for reading:

transcription (spelling and handwriting)

composition (articulating ideas and structuring them in speech and writing)

It is essential that teaching develops pupils' competence in these 2 dimensions. In addition, pupils should be taught how to plan, revise and evaluate their writing. These aspects of writing have been incorporated into the programmes of study for composition.

Writing down ideas fluently depends on effective transcription: that is, on spelling quickly and accurately through knowing the relationship between sounds and letters (phonics) and understanding the morphology (word structure) and orthography (spelling structure) of words. Effective composition involves articulating and communicating ideas, and then organising them coherently for a reader. This requires clarity, awareness of the audience, purpose and context, and an increasingly wide knowledge of vocabulary and grammar. Writing also depends on fluent, legible and, eventually, speedy handwriting.

Spelling, vocabulary, grammar, punctuation and glossary

The 2 statutory appendices - on spelling and on vocabulary, grammar and punctuation - give an overview of the specific features that should be included in teaching the programmes of study.

Opportunities for teachers to enhance pupils' vocabulary arise naturally from their reading and writing. As vocabulary increases, teachers should show pupils how to understand the relationships between words, how to understand nuances in meaning, and how to develop their understanding of, and ability to use, figurative language. They should also teach pupils how to work out and clarify the meanings of unknown words and words with more than 1 meaning. References to developing pupils' vocabulary are also included in the appendices.

Pupils should be taught to control their speaking and writing consciously and to use Standard English. They should be taught to use the elements of spelling, grammar, punctuation and 'language about language' listed. This is not intended to constrain or restrict teachers' creativity, but simply to provide the structure on which they can construct exciting lessons. A non-statutory glossary is provided for teachers.
Throughout the programmes of study, teachers should teach pupils the vocabulary they need to discuss their reading, writing and spoken language. It is important that pupils learn the correct grammatical terms in English and that these terms are integrated within teaching.

School curriculum

The programmes of study for English are set out year-by-year for key stage 1 and two-yearly for key stage 2. The single year blocks at key stage 1 reflect the rapid pace of development in word reading during these 2 years. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage if appropriate. All schools are also required to set out their school curriculum for English on a year-by-year basis and make this information available online.

Attainment targets

By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study.

Schools are not required by law to teach the example content in [square brackets] or the content indicated as being 'non-statutory'.

Spoken language - years 1 to 6

Spoken language

Pupils should be taught to:

listen and respond appropriately to adults and their peers

ask relevant questions to extend their understanding and knowledge

use relevant strategies to build their vocabulary

articulate and justify answers, arguments and opinions

give well-structured descriptions, explanations and narratives for different purposes, including for expressing feelings

maintain attention and participate actively in collaborative conversations, staying on topic and initiating and responding to comments

use spoken language to develop understanding through speculating, hypothesising, imagining and exploring ideas

speak audibly and fluently with an increasing command of Standard English

participate in discussions, presentations, performances, role play/improvisations and debates

gain, maintain and monitor the interest of the listener(s)

consider and evaluate different viewpoints, attending to and building on the contributions of others

select and use appropriate registers for effective communication

Notes and guidance (non-statutory)

These statements apply to all years. The content should be taught at a level appropriate to the age of the pupils. Pupils should build on the oral language skills that have been taught in preceding years.

Pupils should be taught to develop their competence in spoken language and listening to enhance the effectiveness of their communication across a range of contexts and to a range of audiences. They should therefore have opportunities to work in groups of different sizes - in pairs, small groups, large groups and as a whole class. Pupils should understand how to take turns and when and how to participate constructively in conversations and debates.

Teachers should also pay attention to increasing pupils' vocabulary, ranging from describing their immediate world and feelings to developing a broader, deeper and richer vocabulary to discuss abstract concepts and a wider range of topics, and enhancing their knowledge about language as a whole.

Pupils should receive constructive feedback on their spoken language and listening, not only to improve their knowledge and skills but also to establish secure foundations for effective spoken language in their studies at primary school, helping them to achieve in secondary education and beyond.

Key stage 1 - year 1

During year 1, teachers should build on work from the early years foundation stage, making sure that pupils can sound and blend unfamiliar printed words quickly and accurately using the phonic knowledge and skills that they have already learnt. Teachers should also ensure that pupils continue to learn new grapheme-phoneme correspondences ( GPCs) and revise and consolidate those learnt earlier. The understanding that the letter(s) on the page represent the sounds in spoken words should underpin pupils' reading and spelling of all words. This includes common words containing unusual GPCs. The term 'common exception words' is used throughout the programmes of study for such words.

Alongside this knowledge of GPCs, pupils need to develop the skill of blending the sounds into words for reading and establish the habit of applying this skill whenever they encounter new words. This will be supported by practice in reading books consistent with their developing phonic knowledge and skill and their knowledge of common exception words. At the same time they will need to hear, share and discuss a wide range of high-quality books to develop a love of reading and broaden their vocabulary.

Pupils should be helped to read words without overt sounding and blending after a few encounters. Those who are slow to develop this skill should have extra practice.

Pupils' writing during year 1 will generally develop at a slower pace than their reading. This is because they need to encode the sounds they hear in words (spelling skills), develop the physical skill needed for handwriting, and learn how to organise their ideas in writing.

Pupils entering year 1 who have not yet met the early learning goals for literacy should continue to follow their school's curriculum for the Early Years Foundation Stage to develop their word reading, spelling and language skills. However, these pupils should follow the year 1 programme of study in terms of the books they listen to and discuss, so that they develop their vocabulary and understanding of grammar, as well as their knowledge more generally across the curriculum. If they are still struggling to decode and spell, they need to be taught to do this urgently through a rigorous and systematic phonics programme so that they catch up rapidly.

Teachers should ensure that their teaching develops pupils' oral vocabulary as well as their ability to understand and use a variety of grammatical structures, giving particular support to pupils whose oral language skills are insufficiently developed.

Year 1 programme of study

Reading - word reading

Pupils should be taught to:

apply phonic knowledge and skills as the route to decode words

respond speedily with the correct sound to graphemes (letters or groups of letters) for all 40+ phonemes, including, where applicable, alternative sounds for graphemes

read accurately by blending sounds in unfamiliar words containing GPCs that have been taught

read common exception words, noting unusual correspondences between spelling and sound and where these occur in the word

read words containing taught GPCs and -s, -es, -ing, -ed, -er and -est endings

read other words of more than one syllable that contain taught GPCs

read words with contractions [for example, I'm, I'll, we'll], and understand that the apostrophe represents the omitted letter(s)

read books aloud, accurately, that are consistent with their developing phonic knowledge and that do not require them to use other strategies to work out words

reread these books to build up their fluency and confidence in word reading

Notes and guidance (non-statutory)

Pupils should revise and consolidate the GPCs and the common exception words taught in reception year. As soon as they can read words comprising the year 1 GPCs accurately and speedily, they should move on to the year 2 programme of study for word reading.

The number, order and choice of exception words taught will vary according to the phonics programme being used. Ensuring that pupils are aware of the GPCs they contain, however unusual these are, supports spelling later.

Young readers encounter words that they have not seen before much more frequently than experienced readers do, and they may not know the meaning of some of these. Practice at reading such words by sounding and blending can provide opportunities not only for pupils to develop confidence in their decoding skills, but also for teachers to explain the meaning and thus develop pupils' vocabulary.

Pupils should be taught how to read words with suffixes by being helped to build on the root words that they can read already. Pupils' reading and rereading of books that are closely matched to their developing phonic knowledge and knowledge of common exception words supports their fluency, as well as increasing their confidence in their reading skills. Fluent word reading greatly assists comprehension, especially when pupils come to read longer books.

Reading - comprehension

Pupils should be taught to:

understand both the books they can already read accurately and fluently and those they listen to by:

drawing on what they already know or on background information and vocabulary provided by the teacher

checking that the text makes sense to them as they read, and correcting inaccurate reading

discussing the significance of the title and events

making inferences on the basis of what is being said and done

predicting what might happen on the basis of what has been read so far

participate in discussion about what is read to them, taking turns and listening to what others say

explain clearly their understanding of what is read to them

Writing - transcription

Pupils should be taught to:

Notes and guidance (non-statutory)

Reading should be taught alongside spelling, so that pupils understand that they can read back words they have spelt.

Pupils should be shown how to segment spoken words into individual phonemes and then how to represent the phonemes by the appropriate grapheme(s). It is important to recognise that phoneme-grapheme correspondences (which underpin spelling) are more variable than grapheme-phoneme correspondences (which underpin reading). For this reason, pupils need to do much more word-specific rehearsal for spelling than for reading.

At this stage pupils will be spelling some words in a phonically plausible way, even if sometimes incorrectly. Misspellings of words that pupils have been taught to spell should be corrected; other misspelt words should be used to teach pupils about alternative ways of representing those sounds.

Writing simple dictated sentences that include words taught so far gives pupils opportunities to apply and practise their spelling.

Handwriting

Pupils should be taught to:

sit correctly at a table, holding a pencil comfortably and correctly

begin to form lower-case letters in the correct direction, starting and finishing in the right place

form capital letters

form digits 0-9

understand which letters belong to which handwriting 'families' (ie letters that are formed in similar ways) and to practise these

Notes and guidance (non-statutory)

Handwriting requires frequent and discrete, direct teaching. Pupils should be able to form letters correctly and confidently. The size of the writing implement (pencil, pen) should not be too large for a young pupil's hand. Whatever is being used should allow the pupil to hold it easily and correctly so that bad habits are avoided.

Left-handed pupils should receive specific teaching to meet their needs.

Writing - composition

Pupils should be taught to:

discuss what they have written with the teacher or other pupils

read their writing aloud, clearly enough to be heard by their peers and the teacher

Notes and guidance (non-statutory)

At the beginning of year 1, not all pupils will have the spelling and handwriting skills they need to write down everything that they can compose out loud.

Pupils should understand, through demonstration, the skills and processes essential to writing: that is, thinking aloud as they collect ideas, drafting, and rereading to check their meaning is clear.

Writing - vocabulary, grammar and punctuation

Pupils should be taught to:

develop their understanding of the concepts set out in English appendix 2 by:

leaving spaces between words

joining words and joining clauses using 'and'

beginning to punctuate sentences using a capital letter and a full stop, question mark or exclamation mark

using a capital letter for names of people, places, the days of the week, and the personal pronoun 'I'

learning the grammar for year 1 in English appendix 2

use the grammatical terminology in English English appendix 2 in discussing their writing

Notes and guidance (non-statutory)

Pupils should be taught to recognise sentence boundaries in spoken sentences and to use the vocabulary listed in English appendix 2 ('Terminology for pupils') when their writing is discussed.

Pupils should begin to use some of the distinctive features of Standard English in their writing. 'Standard English' is defined in the glossary.

Key stage 1 - year 2

By the beginning of year 2, pupils should be able to read all common graphemes. They should be able to read unfamiliar words containing these graphemes, accurately and without undue hesitation, by sounding them out in books that are matched closely to each pupil's level of word-reading knowledge. They should also be able to read many common words containing GPCs taught so far [for example, shout, hand, stop, or dream], without needing to blend the sounds out loud first. Pupils' reading of common exception words [for example, you, could, many, or people], should be secure. Pupils will increase their fluency by being able to read these words easily and automatically. Finally, pupils should be able to retell some familiar stories that have been read to and discussed with them or that they have acted out during year 1.

During year 2, teachers should continue to focus on establishing pupils' accurate and speedy word-reading skills. They should also make sure that pupils listen to and discuss a wide range of stories, poems, plays and information books; this should include whole books. The sooner that pupils can read well and do so frequently, the sooner they will be able to increase their vocabulary, comprehension and their knowledge across the wider curriculum.

In writing, pupils at the beginning of year 2 should be able to compose individual sentences orally and then write them down. They should be able to spell many of the words covered in year 1 correctly - see English appendix 1. They should also be able to make phonically plausible attempts to spell words they have not yet learnt. Finally, they should be able to form individual letters correctly, establishing good handwriting habits from the beginning.

It is important to recognise that pupils begin to meet extra challenges in terms of spelling during year 2. Increasingly, they should learn that there is not always an obvious connection between the way a word is said and the way it is spelt. Variations include different ways of spelling the same sound, the use of so-called silent letters and groups of letters in some words and, sometimes, spelling that has become separated from the way that words are now pronounced, such as the 'le' ending in table. Pupils' motor skills also need to be sufficiently advanced for them to write down ideas that they may be able to compose orally. In addition, writing is intrinsically harder than reading: pupils are likely to be able to read and understand more complex writing (in terms of its vocabulary and structure) than they are capable of producing themselves.

For pupils who do not have the phonic knowledge and skills they need for year 2, teachers should use the year 1 programmes of study for word reading and spelling so that pupils' word-reading skills catch up. However, teachers should use the year 2 programme of study for comprehension so that these pupils hear and talk about new books, poems, other writing, and vocabulary with the rest of the class.

Year 2 programme of study

Reading - word reading

Pupils should be taught to:

continue to apply phonic knowledge and skills as the route to decode words until automatic decoding has become embedded and reading is fluent

read accurately by blending the sounds in words that contain the graphemes taught so far, especially recognising alternative sounds for graphemes

read accurately words of two or more syllables that contain the same graphemes as above

read words containing common suffixes

read further common exception words, noting unusual correspondences between spelling and sound and where these occur in the word

read most words quickly and accurately, without overt sounding and blending, when they have been frequently encountered

read aloud books closely matched to their improving phonic knowledge, sounding out unfamiliar words accurately, automatically and without undue hesitation

reread these books to build up their fluency and confidence in word reading

Notes and guidance (non-statutory)

Pupils should revise and consolidate the GPCs and the common exception words taught in year 1. The exception words taught will vary slightly, depending on the phonics programme being used. As soon as pupils can read words comprising the year 2 GPCs accurately and speedily, they should move on to the years 3 and 4 programme of study for word reading.

When pupils are taught how to read longer words, they should be shown syllable boundaries and how to read each syllable separately before they combine them to read the word.

Pupils should be taught how to read suffixes by building on the root words that they have already learnt. The whole suffix should be taught as well as the letters that make it up.

Pupils who are still at the early stages of learning to read should have ample practice in reading books that are closely matched to their developing phonic knowledge and knowledge of common exception words. As soon as the decoding of most regular words and common exception words is embedded fully, the range of books that pupils can read independently will expand rapidly. Pupils should have opportunities to exercise choice in selecting books and be taught how to do so.

Reading - comprehension

Pupils should be taught to:

develop pleasure in reading, motivation to read, vocabulary and understanding by:

understand both the books that they can already read accurately and fluently and those that they listen to by:

drawing on what they already know or on background information and vocabulary provided by the teacher

checking that the text makes sense to them as they read, and correcting inaccurate reading

making inferences on the basis of what is being said and done

answering and asking questions

predicting what might happen on the basis of what has been read so far

participate in discussion about books, poems and other works that are read to them and those that they can read for themselves, taking turns and listening to what others say

explain and discuss their understanding of books, poems and other material, both those that they listen to and those that they read for themselves

Writing - transcription

Pupils should be taught to:

add suffixes to spell longer words including -ment, -ness, -ful, -less, -ly

apply spelling rules and guidance, as listed in English appendix 1

write from memory simple sentences dictated by the teacher that include words using the GPCs, common exception words and punctuation taught so far

Notes and guidance (non-statutory)

In year 2, pupils move towards more word-specific knowledge of spelling, including homophones. The process of spelling should be emphasised: that is, that spelling involves segmenting spoken words into phonemes and then representing all the phonemes by graphemes in the right order. Pupils should do this both for single-syllable and polysyllabic words.

At this stage, children's spelling should be phonically plausible, even if not always correct. Misspellings of words that pupils have been taught to spell should be corrected; other misspelt words can be used as an opportunity to teach pupils about alternative ways of representing those sounds.

Pupils should be encouraged to apply their knowledge of suffixes from their word reading to their spelling. They should also draw from and apply their growing knowledge of word and spelling structure, as well as their knowledge of root words.

Handwriting

Pupils should be taught to:

form lower-case letters of the correct size relative to one another

start using some of the diagonal and horizontal strokes needed to join letters and understand which letters, when adjacent to one another, are best left unjoined

write capital letters and digits of the correct size, orientation and relationship to one another and to lower-case letters

use spacing between words that reflects the size of the letters

Writing - composition

Pupils should be taught to:

read aloud what they have written with appropriate intonation to make the meaning clear

Notes and guidance (non-statutory)

Reading and listening to whole books, not simply extracts, helps pupils to increase their vocabulary and grammatical knowledge, including their knowledge of the vocabulary and grammar of Standard English. These activities also help them to understand how different types of writing, including narratives, are structured. All these can be drawn on for their writing.

Pupils should understand, through being shown these, the skills and processes essential to writing: that is, thinking aloud as they collect ideas, drafting, and rereading to check their meaning is clear.

Drama and role play can contribute to the quality of pupils' writing by providing opportunities for pupils to develop and order their ideas through playing roles and improvising scenes in various settings.

Pupils might draw on and use new vocabulary from their reading, their discussions about it (one-to-one and as a whole class) and from their wider experiences.

Writing - vocabulary, grammar and punctuation

Pupils should be taught to:

develop their understanding of the concepts set out in English appendix 2 by:

learning how to use both familiar and new punctuation correctly - see English appendix 2, including full stops, capital letters, exclamation marks, question marks, commas for lists and apostrophes for contracted forms and the possessive (singular)

learn how to use:

sentences with different forms: statement, question, exclamation, command

expanded noun phrases to describe and specify [for example, the blue butterfly]

the present and past tenses correctly and consistently, including the progressive form

subordination (using when, if, that, or because) and co-ordination (using or, and, or but)

the grammar for year 2 in English appendix 2

some features of written Standard English

use and understand the grammatical terminology in English appendix 2 in discussing their writing

Lower key stage 2 - years 3 and 4

By the beginning of year 3, pupils should be able to read books written at an age-appropriate interest level. They should be able to read them accurately and at a speed that is sufficient for them to focus on understanding what they read rather than on decoding individual words. They should be able to decode most new words outside their spoken vocabulary, making a good approximation to the word's pronunciation. As their decoding skills become increasingly secure, teaching should be directed more towards developing their vocabulary and the breadth and depth of their reading, making sure that they become independent, fluent and enthusiastic readers who read widely and frequently. They should be developing their understanding and enjoyment of stories, poetry, plays and non-fiction, and learning to read silently. They should also be developing their knowledge and skills in reading non-fiction about a wide range of subjects. They should be learning to justify their views about what they have read: with support at the start of year 3 and increasingly independently by the end of year 4.

Pupils should be able to write down their ideas with a reasonable degree of accuracy and with good sentence punctuation. Teachers should therefore be consolidating pupils' writing skills, their vocabulary, their grasp of sentence structure and their knowledge of linguistic terminology. Teaching them to develop as writers involves teaching them to enhance the effectiveness of what they write as well as increasing their competence. Teachers should make sure that pupils build on what they have learnt, particularly in terms of the range of their writing and the more varied grammar, vocabulary and narrative structures from which they can draw to express their ideas. Pupils should be beginning to understand how writing can be different from speech. Joined handwriting should be the norm; pupils should be able to use it fast enough to keep pace with what they want to say.

Pupils' spelling of common words should be correct, including common exception words and other words that they have learnt - see English appendix 1. Pupils should spell words as accurately as possible using their phonic knowledge and other knowledge of spelling, such as morphology and etymology.

Most pupils will not need further direct teaching of word reading skills: they are able to decode unfamiliar words accurately, and need very few repeated experiences of this before the word is stored in such a way that they can read it without overt sound-blending. They should demonstrate understanding of figurative language, distinguish shades of meaning among related words and use age-appropriate, academic vocabulary.

As in key stage 1, however, pupils who are still struggling to decode need to be taught to do this urgently through a rigorous and systematic phonics programme so that they catch up rapidly with their peers. If they cannot decode independently and fluently, they will find it increasingly difficult to understand what they read and to write down what they want to say. As far as possible, however, these pupils should follow the year 3 and 4 programme of study in terms of listening to new books, hearing and learning new vocabulary and grammatical structures, and discussing these.

Specific requirements for pupils to discuss what they are learning and to develop their wider skills in spoken language form part of this programme of study. In years 3 and 4, pupils should become more familiar with and confident in using language in a greater variety of situations, for a variety of audiences and purposes, including through drama, formal presentations and debate.

Years 3 and 4 programme of study

Reading - word reading

Pupils should be taught to:

apply their growing knowledge of root words, prefixes and suffixes (etymology and morphology) as listed in - see English appendix 1 , both to read aloud and to understand the meaning of new words they meet

read further exception words, noting the unusual correspondences between spelling and sound, and where these occur in the word

Notes and guidance (non-statutory)

At this stage, teaching comprehension should be taking precedence over teaching word reading directly. Any focus on word reading should support the development of vocabulary.

When pupils are taught to read longer words, they should be supported to test out different pronunciations. They will attempt to match what they decode to words they may have already heard but may not have seen in print (for example, in reading technical, the pronunciation /tɛtʃnɪkəl/ ('tetchnical') might not sound familiar, but /tɛknɪkəl/ ('teknical') should).

Reading - comprehension

Pupils should be taught to:

develop positive attitudes to reading, and an understanding of what they read, by:

retrieve and record information from non-fiction

participate in discussion about both books that are read to them and those they can read for themselves, taking turns and listening to what others say

Writing - transcription

Pupils should be taught to:

use further prefixes and suffixes and understand how to add them - see English appendix 1

spell further homophones

spell words that are often misspelt - see English appendix 1

place the possessive apostrophe accurately in words with regular plurals [for example, girls', boys'] and in words with irregular plurals [for example, children's]

use the first 2 or 3 letters of a word to check its spelling in a dictionary

write from memory simple sentences, dictated by the teacher, that include words and punctuation taught so far

Notes and guidance (non-statutory)

Pupils should learn to spell new words correctly and have plenty of practice in spelling them.

As in years 1 and 2, pupils should continue to be supported in understanding and applying the concepts of word structure - see English appendix 2.

Pupils need sufficient knowledge of spelling in order to use dictionaries efficiently.

Handwriting

Pupils should be taught to:

use the diagonal and horizontal strokes that are needed to join letters and understand which letters, when adjacent to one another, are best left unjoined

increase the legibility, consistency and quality of their handwriting, [for example, by ensuring that the downstrokes of letters are parallel and equidistant, and that lines of writing are spaced sufficiently so that the ascenders and descenders of letters do not touch]

Writing - composition

Pupils should be taught to:

plan their writing by:

discussing writing similar to that which they are planning to write in order to understand and learn from its structure, vocabulary and grammar

discussing and recording ideas

draft and write by:

composing and rehearsing sentences orally (including dialogue), progressively building a varied and rich vocabulary and an increasing range of sentence structures English appendix 2

organising paragraphs around a theme

in narratives, creating settings, characters and plot

in non-narrative material, using simple organisational devices [for example, headings and sub-headings]

evaluate and edit by:

assessing the effectiveness of their own and others' writing and suggesting improvements

proposing changes to grammar and vocabulary to improve consistency, including the accurate use of pronouns in sentences

proofread for spelling and punctuation errors

read their own writing aloud to a group or the whole class, using appropriate intonation and controlling the tone and volume so that the meaning is clear

Notes and guidance (non-statutory)

Pupils should continue to have opportunities to write for a range of real purposes and audiences as part of their work across the curriculum. These purposes and audiences should underpin the decisions about the form the writing should take, such as a narrative, an explanation or a description.

Pupils should understand, through being shown these, the skills and processes that are essential for writing: that is, thinking aloud to explore and collect ideas, drafting, and rereading to check their meaning is clear, including doing so as the writing develops. Pupils should be taught to monitor whether their own writing makes sense in the same way that they monitor their reading, checking at different levels.

Writing - vocabulary, grammar and punctuation

Pupils should be taught to:

develop their understanding of the concepts set out in English appendix 2 by:

use and understand the grammatical terminology in English appendix 2 accurately and appropriately when discussing their writing and reading

Notes and guidance (non-statutory)

Grammar should be taught explicitly: pupils should be taught the terminology and concepts set out in English appendix 2, and be able to apply them correctly to examples of real language, such as their own writing or books that they have read.

At this stage, pupils should start to learn about some of the differences between Standard English and non-Standard English and begin to apply what they have learnt, for example, in writing dialogue for characters.

Upper key stage 2 - years 5 and 6

By the beginning of year 5, pupils should be able to read aloud a wider range of poetry and books written at an age-appropriate interest level with accuracy and at a reasonable speaking pace. They should be able to read most words effortlessly and to work out how to pronounce unfamiliar written words with increasing automaticity. If the pronunciation sounds unfamiliar, they should ask for help in determining both the meaning of the word and how to pronounce it correctly.

They should be able to prepare readings, with appropriate intonation to show their understanding, and should be able to summarise and present a familiar story in their own words. They should be reading widely and frequently, outside as well as in school, for pleasure and information. They should be able to read silently, with good understanding, inferring the meanings of unfamiliar words, and then discuss what they have read.

Pupils should be able to write down their ideas quickly. Their grammar and punctuation should be broadly accurate. Pupils' spelling of most words taught so far should be accurate and they should be able to spell words that they have not yet been taught by using what they have learnt about how spelling works in English.

During years 5 and 6, teachers should continue to emphasise pupils' enjoyment and understanding of language, especially vocabulary, to support their reading and writing. Pupils' knowledge of language, gained from stories, plays, poetry, non-fiction and textbooks, will support their increasing fluency as readers, their facility as writers, and their comprehension. As in years 3 and 4, pupils should be taught to enhance the effectiveness of their writing as well as their competence.

It is essential that pupils whose decoding skills are poor are taught through a rigorous and systematic phonics programme so that they catch up rapidly with their peers in terms of their decoding and spelling. However, as far as possible, these pupils should follow the upper key stage 2 programme of study in terms of listening to books and other writing that they have not come across before, hearing and learning new vocabulary and grammatical structures, and having a chance to talk about all of these.

By the end of year 6, pupils' reading and writing should be sufficiently fluent and effortless for them to manage the general demands of the curriculum in year 7, across all subjects and not just in English, but there will continue to be a need for pupils to learn subject-specific vocabulary. They should be able to reflect their understanding of the audience for and purpose of their writing by selecting appropriate vocabulary and grammar. Teachers should prepare pupils for secondary education by ensuring that they can consciously control sentence structure in their writing and understand why sentences are constructed as they are. Pupils should understand nuances in vocabulary choice and age-appropriate, academic vocabulary. This involves consolidation, practice and discussion of language.

Specific requirements for pupils to discuss what they are learning and to develop their wider skills in spoken language form part of this programme of study. In years 5 and 6, pupils' confidence, enjoyment and mastery of language should be extended through public speaking, performance and debate.

Years 5 and 6 programme of study

Reading - word reading

Pupils should be taught to:

apply their growing knowledge of root words, prefixes and suffixes (morphology and etymology), as listed in English appendix 1, both to read aloud and to understand the meaning of new words that they meet

Notes and guidance (non-statutory)

At this stage, there should be no need for further direct teaching of word-reading skills for almost all pupils. If pupils are struggling or failing in this, the reasons for this should be investigated. It is imperative that pupils are taught to read during their last two years at primary school if they enter year 5 not being able to do so.

Pupils should be encouraged to work out any unfamiliar word. They should focus on all the letters in a word so that they do not, for example, read 'invitation' for 'imitation' simply because they might be more familiar with the first word. Accurate reading of individual words, which might be key to the meaning of a sentence or paragraph, improves comprehension.

When teachers are reading with or to pupils, attention should be paid to new vocabulary - both a word's meaning(s) and its correct pronunciation.

Reading - comprehension

Pupils should be taught to:

maintain positive attitudes to reading and an understanding of what they read by:

discuss and evaluate how authors use language, including figurative language, considering the impact on the reader

distinguish between statements of fact and opinion

retrieve, record and present information from non-fiction

participate in discussions about books that are read to them and those they can read for themselves, building on their own and others' ideas and challenging views courteously

explain and discuss their understanding of what they have read, including through formal presentations and debates, maintaining a focus on the topic and using notes where necessary

provide reasoned justifications for their views

Writing - transcription

Pupils should be taught to:

use further prefixes and suffixes and understand the guidance for adding them

spell some words with 'silent' letters [for example, knight, psalm, solemn]

continue to distinguish between homophones and other words which are often confused

use knowledge of morphology and etymology in spelling and understand that the spelling of some words needs to be learnt specifically, as listed in English appendix 1

use dictionaries to check the spelling and meaning of words

use the first 3 or 4 letters of a word to check spelling, meaning or both of these in a dictionary

use a thesaurus

Handwriting and presentation

Pupils should be taught to:

write legibly, fluently and with increasing speed by:

choosing which shape of a letter to use when given choices and deciding whether or not to join specific letters

choosing the writing implement that is best suited for a task

Writing - composition

Pupils should be taught to:

draft and write by:

selecting appropriate grammar and vocabulary, understanding how such choices can change and enhance meaning

in narratives, describing settings, characters and atmosphere and integrating dialogue to convey character and advance the action

précising longer passages

using a wide range of devices to build cohesion within and across paragraphs

using further organisational and presentational devices to structure text and to guide the reader [for example, headings, bullet points, underlining]

proofread for spelling and punctuation errors

perform their own compositions, using appropriate intonation, volume, and movement so that meaning is clear

Writing - vocabulary, grammar and punctuation

Pupils should be taught to:

develop their understanding of the concepts set out in English appendix 2 by:

recognising vocabulary and structures that are appropriate for formal speech and writing, including subjunctive forms

using passive verbs to affect the presentation of information in a sentence

using the perfect form of verbs to mark relationships of time and cause

using expanded noun phrases to convey complicated information concisely

using modal verbs or adverbs to indicate degrees of possibility

using relative clauses beginning with who, which, where, when, whose, that or with an implied (ie omitted) relative pronoun

learning the grammar for years 5 and 6 in English appendix 2

use and understand the grammatical terminology in English appendix 2 accurately and appropriately in discussing their writing and reading

Key stage 3

Subject content

Reading

Pupils should be taught to:

Writing

Pupils should be taught to:

plan, draft, edit and proofread through:

considering how their writing reflects the audiences and purposes for which it was intended

amending the vocabulary, grammar and structure of their writing to improve its coherence and overall effectiveness

paying attention to accurate grammar, punctuation and spelling; applying the spelling patterns and rules set out in English appendix 1 to the key stage 1 and 2 programmes of study for English

Grammar and vocabulary

Pupils should be taught to:

consolidate and build on their knowledge of grammar and vocabulary through:

extending and applying the grammatical knowledge set out in English appendix 2 to the key stage 1 and 2 programmes of study to analyse more challenging texts

studying the effectiveness and impact of the grammatical features of the texts they read

drawing on new vocabulary and grammatical constructions from their reading and listening, and using these consciously in their writing and speech to achieve particular effects

knowing and understanding the differences between spoken and written language, including differences associated with formal and informal registers, and between Standard English and other varieties of English

using Standard English confidently in their own writing and speech

discussing reading, writing and spoken language with precise and confident use of linguistic and literary terminology*

*Teachers should refer to the glossary that accompanies the programmes of study for English for their own information on the range of terms used within the programmes of study as a whole.

Spoken English

Pupils should be taught to:

Key stage 4

Subject content

Purpose of study

English has a pre-eminent place in education and in society. A high-quality education in English will teach pupils to speak and write fluently so that they can communicate their ideas and emotions to others and through their reading and listening, others can communicate with them. Through reading in particular, pupils have a chance to develop culturally, emotionally, intellectually, socially and spiritually. Literature, especially, plays a key role in such development. Reading also enables pupils both to acquire knowledge and to build on what they already know. All the skills of language are essential to participating fully as a member of society; pupils, therefore, who do not learn to speak, read and write fluently and confidently are effectively disenfranchised.

Aims

The overarching aim for English in the national curriculum is to promote high standards of language and literacy by equipping pupils with a strong command of the spoken and written word, and to develop their love of literature through widespread reading for enjoyment. The national curriculum for English aims to ensure that all pupils:

read easily, fluently and with good understanding

develop the habit of reading widely and often, for both pleasure and information

acquire a wide vocabulary, an understanding of grammar and knowledge of linguistic conventions for reading, writing and spoken language

appreciate our rich and varied literary heritage

write clearly, accurately and coherently, adapting their language and style in and for a range of contexts, purposes and audiences

use discussion in order to learn; they should be able to elaborate and explain clearly their understanding and ideas

are competent in the arts of speaking and listening, making formal presentations, demonstrating to others and participating in debate

Spoken language

The national curriculum for English reflects the importance of spoken language in pupils' development across the whole curriculum - cognitively, socially and linguistically. Spoken language continues to underpin the development of pupils' reading and writing during key stage 4 and teachers should therefore ensure pupils' confidence and competence in this area continue to develop. Pupils should be taught to understand and use the conventions for discussion and debate, as well as continuing to develop their skills in working collaboratively with their peers to discuss reading, writing and speech across the curriculum.

Reading and writing

Reading at key stage 4 should be wide, varied and challenging. Pupils should be expected to read whole books, to read in depth and to read for pleasure and information.

Pupils should continue to develop their knowledge of and skills in writing, refining their drafting skills and developing resilience to write at length. They should be taught to write formal and academic essays as well as writing imaginatively. They should be taught to write for a variety of purposes and audiences across a range of contexts. This requires an increasingly wide knowledge of vocabulary and grammar.

Opportunities for teachers to enhance pupils' vocabulary will arise naturally from their reading and writing. Teachers should show pupils how to understand the relationships between words, how to understand nuances in meaning, and how to develop their understanding of, and ability to use, figurative language.

Pupils should be taught to control their speaking and writing consciously, understand why sentences are constructed as they are and to use Standard English. They should understand and use age-appropriate vocabulary, including linguistic and literary terminology, for discussing their reading, writing and spoken language. This involves consolidation, practice and discussion of language. It is important that pupils learn the correct grammatical terms in English and that these terms are integrated within teaching.

Teachers should build on the knowledge and skills that pupils have been taught at key stage 3. Decisions about progression should be based on the security of pupils' linguistic knowledge, skills and understanding and their readiness to progress to the next stage. Pupils whose linguistic development is more advanced should be challenged through being offered opportunities for increased breadth and depth in reading and writing. Those who are less fluent should consolidate their knowledge, understanding and skills, including through additional practice.

Glossary

A non-statutory glossary is provided for teachers.

Reading

Pupils should be taught to:

read and appreciate the depth and power of the English literary heritage through:

reading a wide range of high-quality, challenging, classic literature and extended literary non-fiction, such as essays, reviews and journalism. This writing should include whole texts. The range will include:

at least one play by Shakespeare

works from the 19th, 20th and 21st centuries

poetry since 1789, including representative Romantic poetry

re-reading literature and other writing as a basis for making comparisons

choosing and reading books independently for challenge, interest and enjoyment

understand and critically evaluate texts through:

make an informed personal response, recognising that other responses to a text are possible and evaluating these

Writing

Pupils should be taught to:

write accurately, fluently, effectively and at length for pleasure and information through:

make notes, draft and write, including using information provided by others [e.g. writing a letter from key points provided; drawing on and using information from a presentation]

revise, edit and proof-read through:

Grammar and vocabulary

Pupils should be taught to:

Spoken English

Pupils should be taught to:

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National curriculum in England: English programmes of study

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English has a pre-eminent place in education and in society. A high-quality education in English will teach pupils to speak and write fluently so that they can communicate their ideas and emotions to others, and through their reading and listening, others can communicate with them.

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Purpose of study

Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history's most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

Aims

The national curriculum for mathematics aims to ensure that all pupils:

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils' understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Information and communication technology (ICT)

Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced near the end of key stage 2 to support pupils' conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure. In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.

Spoken language

The national curriculum for mathematics reflects the importance of spoken language in pupils' development across the whole curriculum - cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

School curriculum

The programmes of study for mathematics are set out year-by-year for key stages 1 and 2. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate. All schools are also required to set out their school curriculum for mathematics on a year-by-year basis and make this information available online.

Attainment targets

By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study.

Schools are not required by law to teach the example content in [square brackets] or the content indicated as being 'non-statutory'.

Key stage 1 - years 1 and 2

The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the 4 operations, including with practical resources [for example, concrete objects and measuring tools].

At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.

Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.

Year 1 programme of study

Number - number and place value

Pupils should be taught to:

Number - addition and subtraction

Pupils should be taught to:

Number - multiplication and division

Pupils should be taught to:

solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Number - fractions

Pupils should be taught to:

recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity

recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity

Notes and guidance (non-statutory)

Pupils are taught half and quarter as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole.

Measurement

Pupils should be taught to:

compare, describe and solve practical problems for:

lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]

mass/weight [for example, heavy/light, heavier than, lighter than]

capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]

time [for example, quicker, slower, earlier, later]

measure and begin to record the following:

lengths and heights

mass/weight

capacity and volume

time (hours, minutes, seconds)

recognise and know the value of different denominations of coins and notes

sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]

recognise and use language relating to dates, including days of the week, weeks, months and years

tell the time to the hour and half past the hour and draw the hands on a clock face to show these times

Geometry - properties of shapes

Pupils should be taught to:

recognise and name common 2-D and 3-D shapes, including:

2-D shapes [for example, rectangles (including squares), circles and triangles]

3-D shapes [for example, cuboids (including cubes), pyramids and spheres]

Geometry - position and direction

Pupils should be taught to:

describe position, direction and movement, including whole, half, quarter and three-quarter turns

Year 2 programme of study

Number - number and place value

Pupils should be taught to:

Number - addition and subtraction

Pupils should be taught to:

solve problems with addition and subtraction:

using concrete objects and pictorial representations, including those involving numbers, quantities and measures

applying their increasing knowledge of mental and written methods

recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

a two-digit number and 1s

a two-digit number and 10s

2 two-digit numbers

adding 3 one-digit numbers

show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot

recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

Number - multiplication and division

Pupils should be taught to:

Number - fractions

Pupils should be taught to:

recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity

write simple fractions, for example of 6 = 3 and recognise the equivalence of and

Notes and guidance (non-statutory)

Pupils use fractions as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a non-unit fraction.

Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line (for example, 1 , 1 (or 1 ), 1 , 2). This reinforces the concept of fractions as numbers and that they can add up to more than 1.

Measurement

Pupils should be taught to:

choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

compare and order lengths, mass, volume/capacity and record the results using >, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

find different combinations of coins that equal the same amounts of money

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

compare and sequence intervals of time

tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times

know the number of minutes in an hour and the number of hours in a day

Geometry - properties of shapes

Pupils should be taught to:

Geometry - position and direction

Pupils should be taught to:

order and arrange combinations of mathematical objects in patterns and sequences

use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

Statistics

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils record, interpret, collate, organise and compare information (for example, using many-to-one correspondence in pictograms with simple ratios 2, 5,10).

Lower key stage 2 - years 3 and 4

The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number.

By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.

Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word-reading knowledge and their knowledge of spelling.

Year 3 programme of study

Number - number and place value

Pupils should be taught to:

Number - addition and subtraction

Pupils should be taught to:

add and subtract numbers mentally, including:

a three-digit number and 1s

a three-digit number and 10s

a three-digit number and 100s

add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction

estimate the answer to a calculation and use inverse operations to check answers

solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

Notes and guidance (non-statutory)

Pupils practise solving varied addition and subtraction questions. For mental calculations with two-digit numbers, the answers could exceed 100.

Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to 3 digits to become fluent (see Mathematics appendix 1 (PDF, 248KB)).

Number - multiplication and division

Pupils should be taught to:

Number - fractions

Pupils should be taught to:

count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

recognise and show, using diagrams, equivalent fractions with small denominators

add and subtract fractions with the same denominator within one whole [for example, + = ]

compare and order unit fractions, and fractions with the same denominators

solve problems that involve all of the above

Notes and guidance (non-statutory)

Pupils connect tenths to place value, decimal measures and to division by 10.

They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to measure.

Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.

They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity.

Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.

Measurement

Pupils should be taught to:

Geometry - properties of shapes

Pupils should be taught to:

Statistics

Pupils should be taught to:

interpret and present data using bar charts, pictograms and tables

solve one-step and two-step questions [for example 'How many more?' and 'How many fewer?'] using information presented in scaled bar charts and pictograms and tables

Year 4 programme of study

Number - number and place value

Pupils should be taught to:

count in multiples of 6, 7, 9, 25 and 1,000

find 1,000 more or less than a given number

count backwards through 0 to include negative numbers

recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)

order and compare numbers beyond 1,000

identify, represent and estimate numbers using different representations

round any number to the nearest 10, 100 or 1,000

solve number and practical problems that involve all of the above and with increasingly large positive numbers

read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value

Number - addition and subtraction

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics appendix 1 (PDF, 248KB)).

Number - multiplication and division

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.

Pupils practise mental methods and extend this to 3-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6).

Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers (see Mathematics appendix 1 (PDF, 248KB)).

Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.

Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or 3 cakes shared equally between 10 children.

Number - fractions (including decimals)

Pupils should be taught to:

Measurement

Pupils should be taught to:

Geometry - properties of shapes

Pupils should be taught to:

Geometry - position and direction

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of co-ordinates, for example (2, 5), including using co-ordinate-plotting ICT tools.

Statistics

Pupils should be taught to:

interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

Upper key stage 2 - years 5 and 6

The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.

By the end of year 6, pupils should be fluent in written methods for all 4 operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Pupils should read, spell and pronounce mathematical vocabulary correctly.

Year 5 programme of study

Number - number and place value

Pupils should be taught to:

Number - addition and subtraction

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics appendix 1 (PDF, 248KB)).

They practise mental calculations with increasingly large numbers to aid fluency (for example, 12,462 - 2,300 = 10,162).

Number - multiplication and division

Pupils should be taught to:

identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers

know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

establish whether a number up to 100 is prime and recall prime numbers up to 19

multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

multiply and divide numbers mentally, drawing upon known facts

divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000

recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes

solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Notes and guidance (non-statutory)

Pupils practise and extend their use of the formal written methods of short multiplication and short division (see Mathematics appendix 1 (PDF, 248KB)). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.

They use and understand the terms factor, multiple and prime, square and cube numbers.

Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 ÷ 4 = = 24 r 2 = 24 = 24.5 ≈ 25).

Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1,000 in converting between units such as kilometres and metres.

Distributivity can be expressed as a(b + c) = ab + ac.

They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10).

Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example 13 + 24 = 12 + 25; 33 = 5 x ?).

Number - fractions (including decimals and percentages)

Pupils should be taught to:

compare and order fractions whose denominators are all multiples of the same number

identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, + = = 1 ]

add and subtract fractions with the same denominator, and denominators that are multiples of the same number

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

read and write decimal numbers as fractions [for example, 0.71 = ]

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

round decimals with 2 decimal places to the nearest whole number and to 1 decimal place

read, write, order and compare numbers with up to 3 decimal places

solve problems involving number up to 3 decimal places

recognise the per cent symbol (%) and understand that per cent relates to 'number of parts per 100', and write percentages as a fraction with denominator 100, and as a decimal fraction

solve problems which require knowing percentage and decimal equivalents of , , , , and those fractions with a denominator of a multiple of 10 or 25

Notes and guidance (non-statutory)

Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.

They extend their knowledge of fractions to thousandths and connect to decimals and measures.

Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.

Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.

Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.

Pupils continue to practise counting forwards and backwards in simple fractions.

Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities. Pupils extend counting from year 4, using decimals and fractions including bridging 0, for example on a number line.

Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.

They mentally add and subtract tenths, and one-digit whole numbers and tenths.

They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1).

Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.

Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is , 50% is , 25% is ) and relate this to finding 'fractions of'.

Measurement

Pupils should be taught to:

Geometry - properties of shapes

Pupils should be taught to:

identify 3-D shapes, including cubes and other cuboids, from 2-D representations

know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

draw given angles, and measure them in degrees (°)

identify:

angles at a point and 1 whole turn (total 360°)

angles at a point on a straight line and half a turn (total 180°)

other multiples of 90°

use the properties of rectangles to deduce related facts and find missing lengths and angles

distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Geometry - position and direction

Pupils should be taught to:

identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

Notes and guidance (non-statutory)

Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.

Statistics

Pupils should be taught to:

solve comparison, sum and difference problems using information presented in a line graph

complete, read and interpret information in tables, including timetables

Year 6 programme of study

Number - number and place value

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils use the whole number system, including saying, reading and writing numbers accurately.

Number - addition, subtraction, multiplication and division

Pupils should be taught to:

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

perform mental calculations, including with mixed operations and large numbers

identify common factors, common multiples and prime numbers

use their knowledge of the order of operations to carry out calculations involving the 4 operations

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

solve problems involving addition, subtraction, multiplication and division

use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Notes and guidance (non-statutory)

Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division (see Mathematics appendix 1 (PDF, 248KB)).

They undertake mental calculations with increasingly large numbers and more complex calculations.

Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency.

Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50, etc, but not to a specified number of significant figures.

Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9.

Common factors can be related to finding equivalent fractions.

Number - Fractions (including decimals and percentages)

Pupils should be taught to:

use common factors to simplify fractions; use common multiples to express fractions in the same denomination

compare and order fractions, including fractions >1

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, × = ]

divide proper fractions by whole numbers [for example, ÷ 2 = ]

associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ]

identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places

multiply one-digit numbers with up to 2 decimal places by whole numbers

use written division methods in cases where the answer has up to 2 decimal places

solve problems which require answers to be rounded to specified degrees of accuracy

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Notes and guidance (non-statutory)

Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (for example, + = ] and progress to varied and increasingly complex problems.

Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle.

Pupils use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for example, if quarter of a length is 36cm, then the whole length is 36 × 4 = 144cm).

They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators.

Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to 2 decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.

Pupils are introduced to the division of decimal numbers by one-digit whole numbers, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication.

Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.

Ratio and proportion

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (for example, similar shapes and recipes).

Pupils link percentages or 360° to calculating angles of pie charts.

Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work.

Pupils solve problems involving unequal quantities, for example, 'for every egg you need 3 spoonfuls of flour', ' of the class are boys'. These problems are the foundation for later formal approaches to ratio and proportion.

Algebra

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

missing numbers, lengths, coordinates and angles

formulae in mathematics and science

equivalent expressions (for example, a + b = b + a)

generalisations of number patterns

number puzzles (for example, what 2 numbers can add up to)

Measurement

Pupils should be taught to:

Notes and guidance (non-statutory)

Pupils connect conversion (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs.

They know approximate conversions and are able to tell if an answer is sensible.

Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature.

They relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this.

Pupils could be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.

Geometry - properties of shapes

Pupils should be taught to:

Geometry - position and direction

Pupils should be taught to:

describe positions on the full coordinate grid (all 4 quadrants)

draw and translate simple shapes on the coordinate plane, and reflect them in the axes

Statistics

Pupils should be taught to:

interpret and construct pie charts and line graphs and use these to solve problems

calculate and interpret the mean as an average

Key stage 3

Introduction

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects.

Decisions about progression should be based on the security of pupils' understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on.

Working mathematically

Through the mathematics content, pupils should be taught to:

Develop fluency

Reason mathematically

Solve problems

Subject content

Number

Pupils should be taught to:

understand and use place value for decimals, measures and integers of any size

order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

recognise and use relationships between operations including inverse operations

use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or 0

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and or 0.375 and )

define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%

interpret fractions and percentages as operators

use standard units of mass, length, time, money and other measures, including with decimal quantities

round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

use a calculator and other technologies to calculate results accurately and then interpret them appropriately

appreciate the infinite nature of the sets of integers, real and rational numbers

Algebra

Pupils should be taught to:

use and interpret algebraic notation, including:

ab in place of a × b

3y in place of y + y + y and 3 × y

a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b

in place of a ÷ b

coefficients written as fractions rather than as decimals

brackets

substitute numerical values into formulae and expressions, including scientific formulae

understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

simplify and manipulate algebraic expressions to maintain equivalence by:

collecting like terms

multiplying a single term over a bracket

taking out common factors

expanding products of 2 or more binomials

understand and use standard mathematical formulae; rearrange formulae to change the subject

model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)

work with coordinates in all 4 quadrants

recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane

interpret mathematical relationships both algebraically and graphically

reduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

generate terms of a sequence from either a term-to-term or a position-to-term rule

recognise arithmetic sequences and find the nth term

recognise geometric sequences and appreciate other sequences that arise

Ratio, proportion and rates of change

Pupils should be taught to:

change freely between related standard units [for example time, length, area, volume/capacity, mass]

use scale factors, scale diagrams and maps

express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1

use ratio notation, including reduction to simplest form

divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio

understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction

relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

solve problems involving direct and inverse proportion, including graphical and algebraic representations

use compound units such as speed, unit pricing and density to solve problems

Geometry and measures

Pupils should be taught to:

derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

draw and measure line segments and angles in geometric figures, including interpreting scale drawings

derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

understand and use the relationship between parallel lines and alternate and corresponding angles

derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs

use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

interpret mathematical relationships both algebraically and geometrically

Probability

Pupils should be taught to:

Statistics

Pupils should be taught to:

Key stage 4

This programme of study specifies:

the mathematical content that should be taught to all pupils, in standard type

additional mathematical content to be taught to more highly attaining pupils, in braces { }

Together, the mathematical content set out in the key stage 3 and key stage 4 programmes of study covers the full range of material contained in the GCSE Mathematics qualification. Wherever it is appropriate, given pupils' security of understanding and readiness to progress, pupils should be taught the full content set out in this programme of study.

Working mathematically

Through the mathematics content pupils should be taught to:

Develop fluency

Reason mathematically

Solve problems

Subject content

Number

In addition to consolidating subject content from key stage 3, pupils should be taught to:

apply systematic listing strategies, {including use of the product rule for counting}

{estimate powers and roots of any given positive number}

calculate with roots, and with integer {and fractional} indices

calculate exactly with fractions, {surds} and multiples of π {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}

calculate with numbers in standard form A × 10n, where 1 ≤ A < 10 and n is an integer

{change recurring decimals into their corresponding fractions and vice versa}

identify and work with fractions in ratio problems

apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}

Algebra

In addition to consolidating subject content from key stage 3, pupils should be taught to:

simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by:

factorising quadratic expressions of the form x² + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax² + bx + c}

simplifying expressions involving sums, products and powers, including the laws of indices

know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}

where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the 'inverse function'; interpret the succession of 2 functions as a 'composite function'}

use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient

identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}

recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = with x ≠ 0, {the exponential function y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}

{sketch translations and reflections of the graph of a given function}

plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

{calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}

{recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point}

solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph

solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph

{find approximate solutions to equations numerically using iteration}

translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution

solve linear inequalities in 1 {or 2} variable {s}, {and quadratic inequalities in 1 variable}; represent the solution set on a number line, {using set notation and on a graph}

recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}

deduce expressions to calculate the nth term of linear {and quadratic} sequences.

Ratio, proportion and rates of change

In addition to consolidating subject content from key stage 3, pupils should be taught to:

compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios)

convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

understand that X is inversely proportional to Y is equivalent to X is proportional to ; {construct and} interpret equations that describe direct and inverse proportion

interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

{interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts}

set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}

Geometry and measures

In addition to consolidating subject content from key stage 3, pupils should be taught to:

interpret and use fractional {and negative} scale factors for enlargements

{describe the changes and invariance achieved by combinations of rotations, reflections and translations}

identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

{apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results}

construct and interpret plans and elevations of 3D shapes

interpret and use bearings

calculate arc lengths, angles and areas of sectors of circles

calculate surface areas and volumes of spheres, pyramids, cones and composite solids

apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures

apply Pythagoras' Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures

know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45°, 60°

{know and apply the sine rule, = = , and cosine rule, a² = b² + c² - 2bc cos A, to find unknown lengths and angles}

{know and apply Area = ab sin C to calculate the area, sides or angles of any triangle}

describe translations as 2D vectors

apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}

Probability

In addition to consolidating subject content from key stage 3, pupils should be taught to:

Statistics

In addition to consolidating subject content from key stage 3, pupils should be taught to:

infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

interpret and construct tables and line graphs for time series data

{construct and interpret diagrams for grouped discrete data and continuous data, ie, histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use}

interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:

appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}

appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}

apply statistics to describe a population

use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

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National curriculum in England: mathematics programmes of study

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Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history's most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment.

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Raising levels of achievement in maths, and increasing appreciation of the power and wonder of maths

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Teachers | Primary Science Education Consultancy

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Links to useful primary science websites and documents organised by topic

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Minecraft Education: M.A.T.H. Mummy Mayhem

Cambridge Mathematics has partnered with Minecraft Education to develop an exciting new Minecraft world designed to support mathematics learning for students everywhere.

M.A.T.H. Mummy Mayhem transports you to Egypt, where a Mummy is said to roam the ancient sites. Gamers will put their mathematics skills to the test to unlock the secrets of the past.

Minecraft offers an engaging way to teach and learn mathematics, as the game's fundamental structure requires exploration and a problem-solving approach. Geometry concepts like shape, symmetry and spatial reasoning, are woven into the world more tightly than the wrapping of the Mummy's bandages.

A game-based approach can increase students' interest and engagement in mathematics. Engaged students are more likely to actively participate in their learning, which can lead to improved mathematical outcomes.

M.A.T.H. Mummy Mayhem, which is accessible to learners of primary ages onwards, is available in 29 languages for both Minecraft Education and Bedrock in the Minecraft Marketplace.

1. It's your turn to unlock the secrets!
Read more

2. View a range of resources designed to support teachers of mathematics
View resources

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Minecraft Education: M.A.T.H. Mummy Mayhem

# data[].attributes.attachment_link.description
Cambridge Mathematics has partnered with Minecraft Education to develop an exciting new Minecraft world designed to support mathematics learning for students everywhere. M.A.T.H. Mummy Mayhem transports you to Egypt, where a Mummy is said to roam the ancient sites. Gamers will put their mathematics skills to the test to unlock the secrets of the past.

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Explorify

Explorify makes science accessible for all - discussion-based and open-ended activities are great for enabling ALL pupils, including those with SEND, to participate in science lessons without a fear of failure and increasing their independence.

With proven impact for teachers and pupils, Explorify increases teacher confidence and teaching time, which improves pupils' science knowledge, use of scientific vocabulary and reasoning skills.

Using Inspiring ideas to develop scientific enquiry skills, add a twist to your science lessons with activities that inspire questioning, deepen thinking and extend reasoning skills. Try challenges that develop scientific enquiry skills and tackle confidence-building group tasks.

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Resources - Primary Science Teaching Trust

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Explorify Explorify makes science accessible for all - discussion-based and open-ended activities are great for enabling ALL pupils, including those with SEND, to participate in science lessons without a fear of failure and increasing their independence. With proven impact for teachers and pupils, Explorify increases teacher confidence and teaching time, which improves pupils' science knowledge, use of scientific vocabulary and reasoning skills.

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The developer, Polished Play, LLC, indicated that the app's privacy practices may include handling of data as described below. For more information, see the developer's privacy policy.

Privacy practices may vary based on, for example, the features you use or your age. Learn More

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‎Create your own unique shows with animation and audio in real time! Simply pick out your actors and backdrops, drag them on to the stage, and tap record. Your movements and audio will be recorded in real time for playback later. This app is as fun as your own creativity.

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design discussions
no-schedule meetings
professional development
collaborate with clients
sales and marketing

replace text-only discussions
interactive lectures
support UDL principles
no-schedule office hours
professional development

student presentations
conversational practice
professional development
rich assessment
safe and accountable

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design discussions no-schedule meetings professional development collaborate with clients sales and marketing replace text-only discussions interactive lectures support UDL principles no-schedule office hours professional development student presentations conversational practice professional development rich assessment safe and accountable

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multimodality story telling - sound effect website

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Sound Effects Library - Royalty Free Sound Effects | Soundstripe

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Browse our entire production music library comprised of thousands of high quality sound effect selections. Easily search and filter our expansive catalog to find the perfect sound effect for your video project.

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Skip to main content

Try it free for 30 days,
or join an existing school account.

Explore creative sound making in the classroom

Soundtrap for Education empowers students and teachers to explore creative sound recording in all subjects, for all ages and ability levels. Whether students are exploring the ways music can take presentations to the next level, collaborating with classmates to create a song, or recording podcasts to share knowledge on subjects, Soundtrap for Education amplifies learning.

Create, communicate and collaborate...

Enjoy endless collaboration; between students, teachers, different classes wherever you are, in real-time.

...from anywhere on any device

Soundtrap works seamlessly across all wifi connected devices. And since the Studio is completely cloud-powered, students can continue working on their music or podcasts from home. You will have access to an extensive collection of quality loops, effects, and software instruments. Soundtrap is easy and intuitive to use by both teachers and students-of all ability levels-who want to create professional and polished projects.

How teachers are using Soundtrap today

Sound creation for your digital classroom

Take music class online with integrations to Noteflight Learn and Flat for Education, and also with LMS platforms like Google Classroom, Canvas, Schoology and MusicFirst Classroom. Creation, assessment, and evaluation of assignments is smooth and seamless. Soundtrap is committed to being responsive to the future-ready classroom.

Safe and secure environment

Soundtrap for Education provides students with a safe and secure online environment to learn and play in. We work hard to meet or exceed legal compliance requirements and to stay abreast of the fast-changing privacy law landscape. We are committed to being a trusted partner for our schools and to help schools meet their own compliance obligations under the privacy laws. For more information, please visit our Trust Center.

Soundtrap for Education is trusted by more than 10,000 teachers worldwide

"Young people who struggle with academic writing and have brilliant ideas... these young people are frightened by the paper and pen. They want to sing, dance, shout, use slang, challenge conventions. This is where Soundtrap comes in."

Tamar Brown
New York City DOE Teacher

"My goal is for my students to be people who can think on a deeper level. Project based learning, which Soundtrap greatly supports, takes them out of the 'give me the answers' mentality and forces them to think and create on their own."

Kelly Martin
New York City Teacher

"Soundtrap is a game changer for my students. It has helped them learn that music is a tool that can spark the imagination and bring people together. Once those doors are open the possibilities are endless."

Melissa Salguero
Music Teacher at PS 48

"Soundtrap allows my students to express themselves to me emotionally, socially and academically when it is often so hard for them to do so verbally."

Allessandra Moore
Middle School Speech Language Pathologist

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Soundtrap for Education - Make music and podcasts online

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Create a podcast or use the beat maker for music or math. Soundtrap is a safe online tool for teachers and schools. Start your free trial now!

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Practical Action Schools produce FREE resources for primary and secondary teachers that help pupils understand and engage with global issues, focus

How to stay safe in the prep room and classroom. This resource offers detailed look at topics including working with DNA and the use of chemicals.

Primary upd8 is a series of high-quality, engaging science activities for 5-11 year olds. These activities are free as part of ASE Membership.

The UK's chilled food production sector offers a wealth of ways to turn your students' passion for science into rewarding, opportunity-filled caree

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Practical Action Schools produce FREE resources for primary and secondary teachers that help pupils understand and engage with global issues, focus How to stay safe in the prep room and classroom. This resource offers detailed look at topics including working with DNA and the use of chemicals.

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All devices with the same username and password will synchronise lists. Your list is encrypted on your devices using your username and password. It can not be seen or decrypted by admins or anyone who doesn't have your credentials. Synchronization is not instant, it can take a few seconds for your changes to come through on other devices.

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We target our work in the communities that need help most, working with local partners to deliver place-based solutions. National Literacy Trust Hubs create long-term change in communities where low levels of literacy are entrenched, intergenerational and seriously impacting on people's lives.

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We target our work in the communities that need help most, working with local partners to deliver place-based solutions. National Literacy Trust Hubs create long-term change in communities where low levels of literacy are entrenched, intergenerational and seriously impacting on people's lives.

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Home : iSpot Nature - Your place to share nature. iSpot is a website aimed at helping anyone identify anything in nature. Once you've registered, you can add an observation to the website and suggest an identification yourself or see if anyone else can identify it for you.

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This activity introduces Darwin's ideas on evolution by looking at variation, adaptation and distribution of banded snails. Children learn about Charles Darwin, then work as science explorers looking at different habitats and the snails found in them. Using correct vocabulary, they describe habitats and the snails...

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This activity introduces Darwin's ideas on evolution by looking at variation, adaptation and distribution of banded snails. Children learn about Charles Darwin, then work as science explorers looking at different habitats and the snails found in them. Using correct vocabulary, they describe habitats and the snails...

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Classrooms and educational tools built for students, teachers, and explorers of all kinds. Powered by the Zooniverse.

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SciStarter connects people to citizen science projects, citizen scientists, and resources. Real science we can do together.

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Arts & Culture Expeditions - Google Arts & Culture

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Go on a virtual field trip with Google Arts & Culture

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PSTT advises teachers to refer to either the CLEAPSS website or SSERC website for up to date health and safety information when planning practical activities for children.

PSTT is not liable for the actions or activities of any reader or anyone else who uses the information in these resource pages or the associated classroom materials. PSTT assumes no liability with regard to injuries or damage to property that may occur as a result of using the information contained in these resources. PSTT recommends that a full risk assessment is carried out before undertaking in the classroom any of the practical investigations contained in the resources.

All materials are ©Primary Science Teaching Trust (PSTT) and are freely available to download and share for educational purposes. Whilst educators are free to adapt the resources to suit their own needs, acknowledgement of copyright on all original materials must be included. Rights to images included in the resource have been purchased for PSTT use only - as such, these images may only be used as part of this resource and may not copied into or used in other materials.

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Materials Science - Primary Science Teaching Trust

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Discover the Materials Science resource from PSTT! Create a Materials Trail for young students to explore the materials that make up their environment using QR codes and tablets.

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Step 1: Submit - Input a series of questions and answers

Step 2. Create - Get a QR code for each question

Step 3. Display - Put the QR codes around your school

Step 4. Begin - Students find and answer the questions

(Just cut and paste from a word processor or type directly)

(Automatically generated as text files to read via phones)

(Be creative - different sizes, different places!)

(The team with the most correct answers in the time available wins)

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QR Code Treasure Hunt Generator | ClassTools

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Produce a QR Code scavenger 'Treasure Hunt' - free and easy!