# Key Stage 4

year 10 – year 11

## Key Stage 4 : Year 10 & 11

**Key Stage 4 (KS4)** is part of the National Curriculum taught to children between the ages of 14 and 16 in their last 2 years of secondary school. Most Key Stage 4 pupils work towards their national qualifications, for example their GCSEs in England.

Aside from teaching the relevant subject and to deepen a pupil’s knowledge, our ambition is to install confidence in young students that is an essential part of growing up. The ability of being able to express yourself so they can fully participate in the society that surrounds them.

Our lessons for this age group can vary in length, they are often conducted on a 1-on-1 basis. This way the lessons can be planned on specifc needs, adapting to your requirements. However, small groups of up to 4 students can also be arranged. To express your interest, or enquire about availability, please Contact Us directly.

Any teacher educating Key Stage 4 takes on many roles. During each lesson a teacher could perform roles varying from “Ally” to “Challenger”, “Provocateur” and even “Devil’s advocate”. The attempt is to enhance the learning within the class, or to challenge their thinking in a new way.

Depending on subject taken pupils will be encouraged to communicate verbally their initial individual thoughts on the issue. Certain activity could focus more on developing clarity in communication and observation. Whilst others allow pupils to prioritise ideas and information and discuss justifications for their choices. This could then be easily transferred into different learning areas.

The Compulsory national curriculum subjects are the ‘core’ and ‘foundation’ subjects. Detailed summary of topics for core subjects for Maths and English & Literature for Key Stage 4 is stated below.

Behind the scenes, planning is underway for detailed **revisio****n** **GCSE** **course** for Maths and English. You can register your interest through our Contact Us page.

To find out availability of our teachers and tutors please email our office@teachingathome.co.uk

## Interested to know what is covered in the national curriculum for key stage 4

### English - Writing

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

- adapting their writing for a wide range of purposes and audiences: to describe, narrate, explain, instruct, give and respond to information, and argue

- selecting and organising ideas, facts and key points, and citing evidence, details and quotation effectively and pertinently for support and emphasis

- selecting, and using judiciously, vocabulary, grammar, form, and structural and organisational features, including rhetorical devices, to reflect audience, purpose and context, and using Standard English where appropriate - 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)
- Write formal and academic essays, imaginative writing, notes and personal and formal letters
- Revise, edit and proof-read through:

- reflecting on whether their draft achieves the intended impact

- restructuring their writing, and amending its grammar and vocabulary to improve coherence, consistency, clarity and overall effectiveness

- paying attention to the accuracy and effectiveness of grammar, punctuation and spelling - Plan, draft, edit and proof-read your own writing

### English - Reading

- Read a wide range of high-quality, challenging, classic literature and extended literary non-fictions, such as essays, reviews and journalism
- Re-read literature and other writing as a basis for making comparisons
- Choose and reading books independently for challenge, interest and enjoyment.
- Understand and critically evaluate texts through:

- reading in different ways for different purposes, summarising and synthesising ideas and information, and evaluating their usefulness for particular purposes

- drawing on knowledge of the purpose, the audience for and context of the writing, including its social, historical and cultural context and the literary tradition to which it belongs, to inform an evaluation

- identifying and interpreting themes, ideas and information

- exploring aspects of plot, characterisation, events and settings, the relationships between them and their effects

- seeking evidence in the text to support a point of view, including justifying inferences with evidence

- distinguishing between statements that are supported by evidence and those that are not, and identifying bias and misuse of evidence

- analysing a writer’s choice of vocabulary, form, grammatical and structural features, and evaluating their effectiveness and impact

- making critical comparisons, referring to the contexts, themes, characterisation, style and literary quality of texts, and drawing on knowledge and skills from wider reading - make an informed personal response, recognising that other responses to a text are possible and evaluating these.

### English - Grammar and Vocabulary

- Consolidate and build on the knowledge of grammar and vocabulary through: - study the effectiveness and impact in the texts they read
- Use Standard English confidently
- Discuss reading, writing and spoken language with precise and confident use of linguistic and literary terminology
- Learn to speak confidently and effectively formally and informally
- Participate in formal debates and structured discussions, summarising and/or building on what has been said
- Give short speeches and presentations, expressing their own ideas and keeping to the point
- Improvise, rehearse and perform play scripts and poetry
- Discuss language use and meaning (tone, volume, mood etc.)

- expanding their existing vocabulary and grammatical constructions from their reading and listening and using these consciously in their writing and speech to achieve particular effects

- analyse the differences between spoken and written language, formal and informal register and between Standard English and other varieties of English

### English - Spoken English

- Speak confidently, audibly and effectively, including through: - using Standard English when the context and audience require it

- review and summarise, contribute to meeting goals/deadlines

- listen to and build on the contributions of others, asking questions to clarify and inform, and challenging courteously when necessary

- plan for different purposes and audiences, including selecting and organising information and ideas effectively and persuasively for formal spoken presentations and debates

- listen and respond in a variety of different contexts, both formal and informal, evaluate content, viewpoints, evidence and aspects of presentation

- improvise, rehearse and perform play scripts and poetry in order to generate language and discuss language use and meaning, using role, intonation, tone, volume, mood, silence, stillness and action to add impact.

### Mathematics - Number/Calculation

- Apply systematic listing strategies, including: - use of the product rule for counting
- 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}n
- calculate with numbers in standard form A × 10n, where 1 ≤ A
- 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}

- estimate powers and roots of any given positive number

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

### Mathematics - Algebra

- 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}
- 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 gradienty
- 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

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

### Mathematics - Geometry and Measures

- 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}

### Mathematics - Ratio, Proportion and Rates of change

- 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}

### Mathematics - Probability

- Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1
- use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
- calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
- calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

### Mathematics - Statistics

- 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
- 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.

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

Every pupil and teacher brings with them a diversity of skills, experience, needs and expectations. These factors will play a large part in shaping the dynamics within each classroom, especially in Key Stage 4 age group.

Many pupils in this age group will be at different stages of experience, confidence, and skill development concerning active methodologies. With our teachers’ knowledge, we will aim to factor this into the planning of lessons. Your input in this new remote learning experience is therefore essential, especially at the beginning of this process.

Please feel free to share with us information about topics and subjects that you would like to see more of in our schedules and for our teachers to concentrate on. Please be specific for which year group within Key Stage 4 this should apply to.

We will compile the information, liaise with our team, and when possible, facilitate and add subjects and lessons that are the most in-demand. Please complete this form, and we’ll start collating your requests! Be assured that your information will be kept confidential and will be held in accordance with GDPR guidelines. For more details, please read our Privacy Policy.

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