The KS4 curriculum provides students with opportunities to build on their learning experiences gained during Key Stage 3.
The aims and objectives of the KS4 curriculum are to enable students to develop fluent knowledge, skills and understanding of mathematical methods and concepts; acquire, select and apply mathematical techniques to solve problems; reason mathematically, make deductions and inferences, and draw conclusions; and comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.
Transferable skills enable young people to face the demands of further and higher education, as well as the demands of the workplace, and are important in the teaching and learning of our curriculum. Our curriculum aims to develop students’ cognitive skills (non-routine problem solving, expert thinking, metacognition, creativity), systems thinking (decision making and reasoning) and their critical thinking (cognitive skills such as analysing, synthesising and reasoning skills). At same time we seek to improve students’ interpersonal skills (active listening, oral communication, written communication, assertive communication and non-verbal communication) and their capacity for collaborative problem solving (teamwork, establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation).
As a school we follow the Edexcel GCSE 9-1 specification which is aligned with the DfE KS4 Mathematics Programme of Study. Themes covered are:
In this unit, students will develop a secure understanding of estimation, approximation and bounds. They will apply and interpret limits of accuracy when rounding or truncating, including upper and lower bounds.
- Students will know that numbers can be estimated, rounded and truncated, and that where numbers have been rounded there are limits of accuracy which can be represented using error interval notation.
- Students will know how to round numbers to decimal places and significant figures and when it is appropriate to do so; how to estimate and check calculations using approximation and estimation; and how to apply and interpret limits of accuracy, including performing calculations using upper and lower bounds.
In this unit, students will consolidate their knowledge and skills relating to simplifying and manipulating expressions involving sums, products and powers. Students will argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs.
- Students will know the definitions of expression, equation, identity, variables and unknowns. They will know that the laws of arithmetic can be extended to algebraic expressions.
- Students will know how to use the laws of arithmetic to manipulate algebraic expressions, including forming algebraic proofs, and will know the processes for solving different types of equations.
In this unit, students will work with fractions, decimals and surds, extending to algebraic expressions. Students will calculate with indices and standard form.
- Students will know the conventional notation for indices, standard form, surds and priority of operations. They will know the laws of indices, including negative and fractional powers, and they will know common fraction, decimal and percentage equivalences.
- Students will know how to convert between fractions, decimals and percentages, including recurring decimals, and how to calculate with indices, surds, and numbers written in standard form.
Geometry and Measures 1.
In this unit, students will consolidate their knowledge of area and perimeter, and extend to calculating surface area and volumes of shapes including spheres, pyramids, cones and composite solids, including finding arc lengths, angles and areas of sectors of circles. Students will apply Pythagoras’ Theorem, trigonometric ratios and the sine and cosine rules, to find angles, lengths and areas of triangles, and extend to 3D shapes.
- Students will know formulae relating to area, volume, surface area, Pythagoras’ theorem and trigonometry. They will know exact trigonometric values.
- Students will know how to use the formulae to solve problems involving angles, lengths, areas and volumes of 2D and 3D shapes, including compound shapes.
Ratio, Proportion and Rates of Change 1.
In this unit, students will develop their understanding of ratio and proportion, and extend to properties of similar shapes. Students will recognise and interpret graphs and equations describing direct and inverse proportion. Students will set up, solve and interpret answers in growth and decay problems, including compound interest and general iterative processes.
- Students will know the notation and vocabulary relating to ratio of amounts and equations of proportionality. They will know that any two quantities can be connected via a multiplicative relationship, expressed as both a ratio and as a fraction, and will extend this to quantities represented as expressions.
- Students will know how to solve problems involving ratio and proportion, and how to construct and interpret equations of proportionality, including those represented algebraically and graphically.
In this unit, students will deduce expressions to calculate the nth term of linear and quadratic sequences, translate simple stations or procedures into algebraic expressions or formulae, and where appropriate interpret simple expressions as functions with inputs and outputs, extending to inverse and composite functions.
- Students will know notation and vocabulary relating to sequences and functions, including linear, non-linear and iterative sequences, and composite and inverse functions.
- Students will know how to find nth terms of a range of sequences, solve problems involving formulae and functions, and approximate solutions to equations using iteration.
Geometry and Measures 2.
In this unit, students will consolidate their knowledge of the four transformations, extending to fractions and negative scale factors for enlargements. Students will describe the changes and invariance achieved by combinations of transformations. Students will apply the angle rules, including parallel lines and polygons, and apply and prove the standard circle theorems.
- Students will know angle rules including those relating to parallel lines, polygons and circles. They will know the nature of rotations, enlargements, translations and reflections, and appreciate what changes and what is invariant
- Students will know how to solve problems involving missing angles in a range of 2D shapes, including circles, and how to describe transformations, including single and combined transformations.
In this unit, students will infer properties of populations or distributions from a sample, and will apply statistics to describe a population.
- Students will interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency and spread.
- Students will know how to use a variety of sampling methods and understand the limitations of each. Students will know how to calculate a range of measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers).
In this unit, students will consolidate their understanding of probability using a range of representations, extending to conditional probability.
- Students will know notation and vocabulary relating to probability, and will know that probabilities can be described using words or values represented as fractions, decimals or percentages.
- Students will know how to calculate probabilities of single and combined events, of independent and dependent events, and calculate probabilities using expected frequencies, and expressions represented algebraically.
Geometry and Measures 3 In this unit, students will convert between related compound units in numerical and algebraic contexts.
- Students will know formulae relating to compound measures including speed, density and pressure, and common conversions relating to measures.
- Students will know how to solve problems involving compound measures, including those involving time, and those which involve conversion between standard units in numerical and algebraic contexts.
In this unit, students will consolidate their understanding of solving equations, and extend to solving simultaneous and quadratic equations, using a variety of methods.
- Students will know notation relating to equations and inequalities and formulae relating to quadratic equations.
- Students will know how to form, solve and interpret different types of equations and inequalities, including simultaneous and quadratic equations and inequalities, and how to represent these on a number line, using set notation, and on a graph.
In this unit, students will recognise, sketch and interpret graphs of a variety of functions. Students will find the equations of straight lines and circles, including tangents. Students will sketch translations and reflections of given functions. Students will calculate or estimate gradients of graphs, and points on a curve, and areas under graphs, and interpret results.
- Students will know the shapes and properties of different types of graphs, and their general equations.
- Students will know how to calculate or estimate, and interpret gradients, intercepts and areas under graphs, how to find equations of straight line graphs including tangents, and how to sketch translations and reflections of a given function.
In this unit, students will interpret and construct tables and graphs for data including grouped, discrete and continuous data.
- Students will interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data.
- Students will know how to construct and interpret a range of graphs and charts, and will be able to use these to make comparisons and predictions.
Geometry and Measures 4.
In this unit, students will apply addition and subtraction of vectors, multiplication of vectors by a scalar and diagrammatic and column representation of vectors. Students will use vectors to construct geometric arguments and proofs.
- Students will know vocabulary and notation relating to vectors, including the representation of vectors and combinations of vectors diagrammatically.
- Students will know how to calculate using column vectors, and how to solve problems involving diagrammatic vectors, including using vectors to construct geometric arguments and proofs.