National Curriculum

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. The expectation is that the majority of pupils will move through the programme 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. 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.

Through the mathematics content, pupils should be taught to: Develop fluency -consolidate their numerical and mathematical capability from key stage 2 and extendtheir understanding of the number system and place value to include decimals,fractions, powers and roots -select and use appropriate calculation strategies to solve increasingly complexproblems -use algebra to generalise the structure of arithmetic, including to formulatemathematical relationships -substitute values in expressions, rearrange and simplify expressions, and solveequations -move freely between different numerical, algebraic, graphical and diagrammaticrepresentations [for example, equivalent fractions, fractions and decimals, andequations and graphs] -develop algebraic and graphical fluency, including understanding linear and simplequadratic functions use language and properties precisely to analyse numbers, algebraic expressions, 2-Dand 3-D shapes, probability and statistics. Reason mathematically -extend their understanding of the number system; make connections between numberrelationships, and their algebraic and graphical representations -extend and formalise their knowledge of ratio and proportion in working with measuresand geometry, and in formulating proportional relations algebraically -identify variables and express relations between variables algebraically and graphically -make and test conjectures about patterns and relationships; look for proofs or counter- examples -begin to reason deductively in geometry, number and algebra, including usinggeometrical constructions -interpret when the structure of a numerical problem requires additive, multiplicative orproportional reasoning -explore what can and cannot be inferred in statistical and probabilistic settings, andbegin to express their arguments formally. Solve problems -develop their mathematical knowledge, in part through solving problems and evaluatingthe outcomes, including multi-step problems -develop their use of formal mathematical knowledge to interpret and solve problems,including in financial mathematics -begin to model situations mathematically and express the results using a range offormal mathematical representations -select appropriate concepts, methods and techniques to apply to unfamiliar and non- routine problems.

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 amodel 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 factorisationproperty use the four 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), recognisepowers of 2, 3, 4, 5 and distinguish between exact representations of roots and theirdecimal approximations -interpret and compare numbers in standard form A x 10n 1≤A10, where n is a positive or negative integer or zero -work interchangeably with terminating decimals and their corresponding fractions (such 7 as 3.5 and 2 3 or 0.375 and 8 ) -define percentage as ‘number of parts per hundred’, interpret percentages andpercentage changes as a fraction or a decimal, interpret these multiplicatively, expressone quantity as a percentage of another, compare two 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 withdecimal quantities -round numbers and measures to an appropriate degree of accuracy [for example, to anumber of decimal places or significant figures] -use approximation through rounding to estimate answers and calculate possibleresulting errors expressed using inequality notation ax≤b -use a calculator and other technologies to calculate results accurately and theninterpret them appropriately -appreciate the infinite nature of the sets of integers, real and rational numbers.

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 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 Mathematics 45 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 two or more binomials understand and use standard mathematical formulae; rearrange formulae to changethe subject model situations or procedures by translating them into algebraic expressions orformulae and by using graphs use algebraic methods to solve linear equations in one variable (including all forms thatrequire rearrangement) work with coordinates in all four quadrants recognise, sketch and produce graphs of linear and quadratic functions of one variablewith 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 two variables to the standard form y = mx + c;calculate and interpret gradients and intercepts of graphs of such linear equationsnumerically, graphically and algebraically use linear and quadratic graphs to estimate values of y for given values of x and viceversa and to find approximate solutions of simultaneous linear equations find approximate solutions to contextual problems from given graphs of a variety offunctions, 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.

Pupils should be taught to: -derive and apply formulae to calculate and solve problems involving: perimeter andarea of triangles, parallelograms, trapezia, volume of cuboids (including cubes) andother 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, includinginterpreting scale drawings -derive and use the standard ruler and compass constructions (perpendicular bisector ofa 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 aline 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 polygonsthat are reflectively and rotationally symmetric -use the standard conventions for labelling the sides and angles of triangle ABC, andknow and use the criteria for congruence of triangles -derive and illustrate properties of triangles, quadrilaterals, circles, and other planefigures [for example, equal lengths and angles] using appropriate language andtechnologies -identify properties of, and describe the results of, translations, rotations and reflectionsapplied to given figures -identify and construct congruent triangles, and construct similar shapes byenlargement, with and without coordinate grids -apply the properties of angles at a point, angles at a point on a straight line, verticallyopposite angles -understand and use the relationship between parallel lines and alternate andcorresponding angles Mathematics 47 -derive and use the sum of angles in a triangle and use it to deduce the angle sum inany polygon, and to derive properties of regular polygons -apply angle facts, triangle congruence, similarity and properties of quadrilaterals toderive results about angles and sides, including Pythagoras’ Theorem, and use knownresults to obtain simple proofs -use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problemsinvolving 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.

Pupils should be taught to: -describe, interpret and compare observed distributions of a single variable through:appropriate graphical representation involving discrete, continuous and grouped data;and appropriate measures of central tendency (mean, mode, median) and spread(range, consideration of outliers) -construct and interpret appropriate tables, charts, and diagrams, including frequencytables, bar charts, pie charts, and pictograms for categorical data, and vertical line (orbar) charts for ungrouped and grouped numerical data -describe simple mathematical relationships between two variables (bivariate data) inobservational and experimental contexts and illustrate using scatter graphs.

A high-quality science education provides the foundations for understanding the world through the specific disciplines of biology, chemistry and physics. Science has changed our lives and is vital to the world’s future prosperity, and all pupils should be taught essential aspects of the knowledge, methods, processes and uses of science. Through building up a body of key foundational knowledge and concepts, pupils should be encouraged to recognise the power of rational explanation and develop a sense of excitement and curiosity about natural phenomena. They should be encouraged to understand how science can be used to explain what is occurring, predict how things will behave, and analyse causes.

The programmes of study describe a sequence of knowledge and concepts. While it is important that pupils make progress, it is also vitally important that they develop secure understanding of each key block of knowledge and concepts in order to progress to the next stage. Insecure, superficial understanding will not allow genuine progression: pupils may struggle at key points of transition (such as between primary and secondary school), build up serious misconceptions, and/or have significant difficulties in understanding higher-order content. Pupils should be able to describe associated processes and key characteristics in common language, but they should also be familiar with, and use, technical terminology accurately and precisely. They should build up an extended specialist vocabulary. They should also apply their mathematical knowledge to their understanding of science, including collecting, presenting and analysing data. The social and economic implications of science are important but, generally, they are taught most appropriately within the wider Science 57 Science school curriculum: teachers will wish to use different contexts

Through the content across all three disciplines, pupils should be taught to: Scientific attitudes -pay attention to objectivity and concern for accuracy, precision, repeatability andreproducibility -understand that scientific methods and theories develop as earlier explanations aremodified to take account of new evidence and ideas, together with the importance ofpublishing results and peer review -evaluate risks. Key stage 3 59 Science Experimental skills and investigations -ask questions and develop a line of enquiry based on observations of the real world,alongside prior knowledge and experience -make predictions using scientific knowledge and understanding -select, plan and carry out the most appropriate types of scientific enquiries to testpredictions, including identifying independent, dependent and control variables, whereappropriate -use appropriate techniques, apparatus, and materials during fieldwork and laboratorywork, paying attention to health and safety -make and record observations and measurements using a range of methods fordifferent investigations; and evaluate the reliability of methods and suggest possibleimprovements -apply sampling techniques. Analysis and evaluation -apply mathematical concepts and calculate results -present observations and data using appropriate methods, including tables and graphs -interpret observations and data, including identifying patterns and using observations,measurements and data to draw conclusions -present reasoned explanations, including explaining data in relation to predictions andhypotheses -evaluate data, showing awareness of potential sources of random and systematic error -identify further questions arising from their results. Measurement -understand and use SI units and IUPAC (International Union of Pure and AppliedChemistry) chemical nomenclature -use and derive simple equations and carry out appropriate calculations -undertake basic data analysis including simple statistical techniques.

Photosynthesis -the reactants in, and products of, photosynthesis, and a word summary forphotosynthesis -the dependence of almost all life on Earth on the ability of photosynthetic organisms,such as plants and algae, to use sunlight in photosynthesis to build organic moleculesthat are an essential energy store and to maintain levels of oxygen and carbon dioxidein the atmosphere -the adaptations of leaves for photosynthesis. Cellular respiration -aerobic and anaerobic respiration in living organisms, including the breakdown oforganic molecules to enable all the other chemical processes necessary for life -a word summary for aerobic respiration -the process of anaerobic respiration in humans and micro-organisms, includingfermentation, and a word summary for anaerobic respiration -the differences between aerobic and anaerobic respiration in terms

Inheritance, chromosomes, DNA and genes -heredity as the process by which genetic information is transmitted from onegeneration to the next -a simple model of chromosomes, genes and DNA in heredity, including the part playedby Watson, Crick, Wilkins and Franklin in the development of the DNA model -differences between species -the variation between individuals within a species being continuous or discontinuous,to include measurement and graphical representation of variation -the variation between species and between individuals of the same species meanssome organisms compete more successfully, which can drive natural selection -changes in the environment may leave individuals within a species, and some entirespecies, less well adapted to compete successfully and reproduce, which in turn maylead to extinction -the importance of maintaining biodiversity and the use of gene banks to preservehereditary material.

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.

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 oflinguistic 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 fora range of contexts, purposes and audiences -use discussion in order to learn; they should be able to elaborate and explainclearly their understanding and ideas -are competent in the arts of speaking and listening, making formalpresentations, demonstrating to others and participating in debate.

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 stages 3 and 4 and teachers should therefore ensure pupils’ confidence and competence English 14 English 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 at key stages 3 and 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 earlier key stages. 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.