Mathematics Programme of Study
Key Stage 3

Year 7 
Year 8 
Autumn Term 1 


Autumn Term 2 


Spring Term 1 


Spring Term 2 


Summer Term 1 


Summer Term 2 


Extracurricular provision 
MathsWatch for consolidation of curriculum, independent learning, homework & revision 
MathsWatch for consolidation of curriculum, independent learning, homework & revision 
Mathematics Programme of Study: Key Stage 3
Department for Education  Purpose of Study
Working mathematically through the mathematics content, students should be taught to:
Develop fluency
 consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots
 select and use appropriate calculation strategies to solve increasingly complex problems
 use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
 substitute values in expressions, rearrange and simplify expressions, and solve equations
 move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
 develop algebraic and graphical fluency, including understanding linear and simple quadratic functions
 use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
Reason mathematically
 extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
 extend and formalise their knowledge of ratio and proportion in working with measures and 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 using geometrical constructions
 interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
 explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.
Solve problems
 develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep 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 of formal mathematical representations
 select appropriate concepts, methods and techniques to apply to unfamiliar and non routine problems.
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 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), 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 zero
 work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
 define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one 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 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
 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
 a/b n 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 two 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 one variable (including all forms that require rearrangement)
 work with coordinates in all four quadrants
 recognise, sketch and produce graphs of linear and quadratic functions of one 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 two 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 piecewise linear, exponential and reciprocal graphs
 generate terms of a sequence from either a termtoterm or a positiontoterm 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 one 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 two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
 understand that a multiplicative relationship between two 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 2D 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 rightangled triangles
 use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D
 interpret mathematical relationships both algebraically and geometrically.
Probability
 Pupils should be taught to:
 record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 01 probability scale
 understand that the probabilities of all possible outcomes sum to 1
 enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
 generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.
Statistics
 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 frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
 describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.
Mathematics Programme of Study: Key Stage 4

Year 9 
Year 10 
Autumn Term 1 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Autumn Term 2 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Spring Term 1 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Spring Term 2 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Summer Term 1 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Summer Term 2 
Higher Tier
Foundation Tier

Higher Tier
Foundation Tier

Extracurricular provision 
MathsWatch for consolidation of curriculum, independent learning, homework & revision 
MathsWatch for consolidation of curriculum, independent learning, homework & revision 
Mathematics Programme of Study: Key Stage 4
Department for Education  Purpose of Study
Working mathematically through the mathematics content, students should be taught to:
Develop fluency
 consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots
 select and use appropriate calculation strategies to solve increasingly complex problems
 use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
 substitute values in expressions, rearrange and simplify expressions, and solve equations
 move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
 develop algebraic and graphical fluency, including understanding linear and simple quadratic functions
 use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
Reason mathematically
 extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
 extend and formalise their knowledge of ratio and proportion in working with measures and 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 using geometrical constructions
 interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
 explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.
Solve problems
 develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep 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 of formal mathematical representations
 select appropriate concepts, methods and techniques to apply to unfamiliar and non routine problems.
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 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), 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 zero
 work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
 define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one 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 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
 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
 a/b n 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 two 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 one variable (including all forms that require rearrangement)
 work with coordinates in all four quadrants
 recognise, sketch and produce graphs of linear and quadratic functions of one 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 two 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 piecewise linear, exponential and reciprocal graphs
 generate terms of a sequence from either a termtoterm or a positiontoterm 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 one 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 two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
 understand that a multiplicative relationship between two 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 2D 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 rightangled triangles
 use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D
 interpret mathematical relationships both algebraically and geometrically.
Probability
 Pupils should be taught to:
 record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 01 probability scale
 understand that the probabilities of all possible outcomes sum to 1
 enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
 generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.
Statistics
 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 frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
 describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.