KEY STAGE 3  YEAR 7 AND 8
Year 7 and 8 are set by ability and follow an accelerated curriculum in Mathematics which enables them to take their end of Key stage 3 Teacher Assessment in the Summer Term of year 8. The Scheme of Work they follow is based on Kangaroo Maths (http://www.kangaroomaths.com), depending on their level students follow schemes at the following stages;
Stage 6 (support year 7)
Term

Topics and Key Concepts

Autumn 1

Number and the number system
 use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple
 use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions
Counting and comparing
 order positive and negative integers, decimals and fractions
 use the symbols =, ≠, <, >, ≤, ≥

Autumn 2

Calculating
 understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)
 apply the four operations, including formal written methods, to integers and decimals
 use conventional notation for priority of operations, including brackets
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
Visualizing and constructing
 use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries
 use the standard conventions for labelling and referring to the sides and angles of triangles
 draw diagrams from written description
Investigating properties of shapes
 identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
 derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language
Algebraic proficiency: tinkering
 understand and use the concepts and vocabulary of expressions, equations, formulae and terms
 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, a/b in place of a ÷ b, brackets
 simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket
 where appropriate, interpret simple expressions as functions with inputs and outputs
 substitute numerical values into formulae and expressions
 use conventional notation for priority of operations, including brackets

Spring 1

Exploring fractions, decimals and percentages
 express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
 define percentage as ‘number of parts per hundred’
 express one quantity as a percentage of another
Proportional reasoning
 use ratio notation, including reduction to simplest form
 divide a given quantity into two parts in a given part:part or part:whole ratio
Pattern sniffing
 generate terms of a sequence from a termtoterm rule

Measuring space
 use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
 use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
 change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts
 measure line segments and angles in geometric figures

Spring 2

Investigating angles
 apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
Calculating fractions, decimals, percentages
 apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers
 interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
 compare two quantities using percentages
 solve problems involving percentage change, including percentage increase/decrease

Summer 1

Solving equations and inequalities
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
 solve linear equations in one unknown algebraically
Calculating space
 use standard units of measure and related concepts (length, area, volume/capacity)
 calculate perimeters of 2D shapes
 know and apply formulae to calculate area of triangles, parallelograms, trapezia
 calculate surface area of cuboids
 know and apply formulae to calculate volume of cuboids
 understand and use standard mathematical formulae
Checking, approximating and estimating
 round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
 estimate answers; check calculations using approximation and estimation, including answers obtained using technology
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)

Summer 2

Mathematical movement
 work with coordinates in all four quadrants
 understand and use lines parallel to the axes, y = x and y = x
 solve geometrical problems on coordinate axes
 identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation
 describe translations as 2D vectors
Presentation of data
 interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use
Measuring data
 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean and mode) and spread (range)

Stage 7 (year 7)
Term

Topics and Key Concepts

Autumn 1

Numbers and the number system
 use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple
 use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions
Counting and comparing
 order positive and negative integers, decimals and fractions
 use the symbols =, ≠, <, >, ≤, ≥
Calculating
 understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)
 apply the four operations, including formal written methods, to integers and decimals
 use conventional notation for priority of operations, including brackets
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)

Autumn 2

Visualizing and constructing
 use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries
 use the standard conventions for labelling and referring to the sides and angles of triangles
Investigating properties of shapes
 identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
 derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language
Algebraic proficiency: tinkering
 understand and use the concepts and vocabulary of expressions, equations, formulae and terms
 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, a/b in place of a ÷ b, brackets
 simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket
 where appropriate, interpret simple expressions as functions with inputs and outputs
 substitute numerical values into formulae and expressions
 use conventional notation for priority of operations, including brackets
Exploring fractions, decimals and percentages
 express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
 define percentage as ‘number of parts per hundred’
 express one quantity as a percentage of another

Spring 1

Proportional reasoning
 use ratio notation, including reduction to simplest form
 divide a given quantity into two parts in a given part:part or part:whole ratio
Pattern sniffing
 generate terms of a sequence from a termtoterm rule
Measuring space
 use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
 use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
 change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts
 measure line segments and angles in geometric figures

Spring 2

Investigating angles
 Convert between measures
 Solve problems involving measurement
Calculating fractions, decimals and percentages
 apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers
 interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
 compare two quantities using percentages
 solve problems involving percentage change, including percentage increase/decrease

Summer 1

Solving equations and inequalities
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
 solve linear equations in one unknown algebraically
Calculating space
 use standard units of measure and related concepts (length, area, volume/capacity)
 calculate perimeters of 2D shapes
 know and apply formulae to calculate area of triangles, parallelograms, trapezia
 calculate surface area of cuboids
 know and apply formulae to calculate volume of cuboids
 understand and use standard mathematical formulae
Checking, approximating and estimating
 round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
 estimate answers; check calculations using approximation and estimation, including answers obtained using technology
 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
Mathematical movement
 work with coordinates in all four quadrants
 understand and use lines parallel to the axes, y = x and y = x
 solve geometrical problems on coordinate axes
 identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation
 describe translations as 2D vectors

Summer 2

Presentation of data
 interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use

Stage 8 (top year 7 and year 8)
Term

Topics and Key Concepts

Autumn 1

Numbers and the number system
 use the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem
 round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
 interpret standard form A × 10^{n}, where 1 ≤ A < 10 and n is an integer
Calculating
 apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative
 use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
Visualising and constructing
 measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings
 identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement
 interpret plans and elevations of 3D shapes
 use scale factors, scale diagrams and maps

Autumn 2

Understanding risk I
 relate relative expected frequencies to theoretical probability, using appropriate language and the 0  1 probability scale
 record describe and analyse the frequency of outcomes of probability experiments using tables
 construct theoretical possibility spaces for single experiments with equally likely outcomes and use these to calculate theoretical probabilities
 apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
Algebraic proficiency: tinkering
 use and interpret algebraic notation, including: a²b in place of a × a × b, coefficients written as fractions rather than as decimals
 understand and use the concepts and vocabulary of factors
 simplify and manipulate algebraic expressions by taking out common factors and simplifying expressions involving sums, products and powers, including the laws of indices
 substitute numerical values into scientific formulae
 rearrange formulae to change the subject
Exploring fractions, decimals and percentages
 work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8)

Spring 1

Proportional reasoning
 express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
 identify and work with fractions in ratio problems
 understand and use proportion as equality of ratios
 express a multiplicative relationship between two quantities as a ratio or a fraction
 use compound units (such as speed, rates of pay, unit pricing)
 change freely between compound units (e.g. speed, rates of pay, prices) in numerical contexts
 relate ratios to fractions and to linear functions
Pattern sniffing
 generate terms of a sequence from either a termtoterm or a positiontoterm rule
 deduce expressions to calculate the nth term of linear sequences
Investigating angles
 understand and use alternate and corresponding angles on parallel lines
 derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

Spring 2

Calculating fractions, decimals and percentages
 interpret fractions and percentages as operators
 work with percentages greater than 100%
 solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics
 calculate exactly with fractions
Solving equations and inequalities
 solve linear equations with the unknown on both sides of the equation
 find approximate solutions to linear equations using a graph

Summer 1

Calculating space
 compare lengths, areas and volumes using ratio notation
 calculate perimeters of 2D shapes, including circles
 identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
 know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²
 calculate areas of circles and composite shapes
 know and apply formulae to calculate volume of right prisms (including cylinders)
Algebraic proficiency: visualizing
 plot graphs of equations that correspond to straightline graphs in the coordinate plane
 identify and interpret gradients and intercepts of linear functions graphically
 recognise, sketch and interpret graphs of linear functions and simple quadratic functions
 plot and interpret graphs and graphs of nonstandard (piecewise linear) functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance and speed

Summer 2

Understanding Risk II
 apply systematic listing strategies
 record describe and analyse the frequency of outcomes of probability experiments using frequency trees
 enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams
 construct theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
 apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
Presentation of data
 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data
 use and interpret scatter graphs of bivariate data
 recognise correlation
Measuring data
 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers)
 apply statistics to describe a population

Stage 9 (top year 8)
Term

Topics and Key Concepts

Autumn 1

Calculating
 calculate with roots, and with integer indices
 calculate with standard form A × 10^{n}, where 1 ≤ A < 10 and n is an integer
 use inequality notation to specify simple error intervals due to truncation or rounding
 apply and interpret limits of accuracy
Visualizing and constructing
 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)
 use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line
 construct plans and elevations of 3D shapes

Autumn 2

Algebraic proficiency: tinkering
 understand and use the concepts and vocabulary of identities
 know the difference between an equation and an identity
 simplify and manipulate algebraic expressions by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c
 argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
 translate simple situations or procedures into algebraic expressions or formulae
Proportional reasoning
 solve problems involving direct and inverse proportion including graphical and algebraic representations
 apply the concepts of congruence and similarity, including the relationships between lengths in similar figures
 change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts
 use compound units such as density and pressure
Pattern sniffing
 recognise and use Fibonacci type sequences, quadratic sequences

Spring 1

Solving equations and inequalities
 understand and use the concepts and vocabulary of inequalities
 solve linear inequalities in one variable
 represent the solution set to an inequality on a number line
Calculating space
 identify and apply circle definitions and properties, including: tangent, arc, sector and segment
 calculate arc lengths, angles and areas of sectors of circles
 calculate surface area of right prisms (including cylinders)
 calculate exactly with multiples of π
 know the formulae for: Pythagoras’ theorem, a² + b² = c², and apply it to find lengths in rightangled triangles in two dimensional figures

Spring 2

Conjecturing
 use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
 apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
Algebraic proficiency: visualising
 identify and interpret gradients and intercepts of linear functions algebraically
 use the form y = mx + c to identify parallel lines
 find the equation of the line through two given points, or through one point with a given gradient
 interpret the gradient of a straight line graph as a rate of change
 recognise, sketch and interpret graphs of quadratic functions
 recognise, sketch and interpret graphs of simple cubic functions and the reciprocal function y = 1/x with x ≠ 0
 plot and interpret graphs (including reciprocal graphs) and graphs of nonstandard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

Summer 1

Solving equations and inequalities II
 solve, in simple cases, two linear simultaneous equations in two variables algebraically
 derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
 find approximate solutions to simultaneous equations using a graph
Understanding risk
 calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
 enumerate sets and combinations of sets systematically, using tree diagrams
 understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

Summer 2

Presentation of data
 interpret and construct tables, charts and diagrams, including tables and line graphs for time series data and know their appropriate use
 draw estimated lines of best fit; make predictions
 Understand that correlation does not indicate causation; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing

KEY STAGE 4 – YEARS 9 TO 11
In Year 9 all students start their GCSE Mathematics course. They will complete the course in Year 11 and take the final examination in June 2019.
Candidates for this qualification are entered for one of two tiers.
Higher Tier: graded 1 – 9
Foundation Tier: grade 1  5
Exam Board: Edexcel
Year 9 Scheme of Work 20182019
Year 9 students will do the following assessments during the year:
 Autumn 1 assessment (one paper)
 January Year 9 examinations (noncalculator and calculator papers)
 Easter assessment (one paper)
 End of Year examinations (noncalculator and calculator papers)
Half Term

Foundation
Unit of Work

Higher
Unit of Work

Accelerated Higher
Unit of Work

Autumn 1

 Integers and Place Value
 Decimals
 Indices, powers and roots

 Calculations, checking and rounding
 Indices and roots
 Factors, multiples and primes
 Indices and standard form

 Calculations, checking and rounding
 Indices and roots
 Factors, multiples and primes
 Indices and standard form
 Algebra basics
 Equations
 Sequences

Autumn 2

 Factors, multiples and primes
 Algebra basics
 Expanding and factorising single brackets
 Substitution and expressions

 Algebra basics
 Equations
 Sequences
 Averages and range

 Algebra basics
 Equations
 Sequences
 Averages and range
 Representing and interpreting data
 Scatter graphs
 Fractions
 Percentages
 Ratio and proportion
 Polygons, angles and parallel lines
 Pythagoras’ theorem and trigonometry

Spring 1

 Tables
 Charts and graphs
 Fractions

 Representing and interpreting data
 Scatter graphs
 Fractions

 Graphs and real life graphs
 Linear graphs and coordinate geometry
 Quadratic, cubic and other graphs

Spring 2

 Pie charts
 Scatter Graphs
 Fractions, decimals and percentages
 Percentages

 Fractions
 Percentages
 Ratio and proportion

 Perimeter, area and circles
 3D forms and volume
 Accuracy and bounds

Summer 1


 Polygons, angles and parallel lines
 Pythagoras’ theorem and trigonometry

 Transformations
 Constructions, loci and bearings

Summer 2

 Sequences
 Properties of shape, parallel lines and angle facts
 Interior and exterior angles of polygons

 Graphs and real life graphs
 Linear graphs and coordinate geometry
 Quadratic, cubic and other graphs

 Solving quadratic and simultaneous equations
 Inequalities
 Probability

Year 10 Scheme of Work 20182019
Year 10 students will do the following assessments during the year:
 Autumn 1 assessment (one paper)
 Autumn 2 assessment (one paper)
 Spring 1 assessment (one paper)
 Spring 2 assessment (one paper)
 Year 10 Summer PPE examinations (one noncalculator and two calculator papers)
Half Term

Foundation
Units of Work

Higher
Units of Work

Accelerated Higher
Units of Work

Autumn 1

 Equations
 Inequalities
 Properties of shapes, parallel lines and angles

 Pythagoras’ theorem and trigonometry
 Graphs and real life graphs

 Pythagoras’ theorem and trigonometry
 Graphs of trigonometric functions
 Real life graphs
 Other graphs

Autumn 2

 Interior and exterior angles of polygons
 Perimeter and area
 3D forms and volume
 Real life graphs

 Linear graphs and coordinate geometry
 Quadratic, cubic and other graphs
 Perimeter, area and circles
 3D forms and volumes

 3D forms and volume
 Accuracy and bounds
 Transformations
 Constructions, loci and bearings

Spring 1

 Straight line graphs
 Transformations

 Accuracy and bounds
 Transformations
 Constructions, loci and bearings

 Solving quadratic and simultaneous equations
 Inequalities
 Probability
 Multiplicative reasoning

Spring 2

 Pythagoras’ theorem and trigonometry
 Probability
 Multiplicative reasoning

 Solving quadratic and simultaneous equations
 Inequalities
 Probability

 Similarity and congruence
 Further trigonometry
 Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics

Summer 1

 Plans and elevations
 Constructions, loci and bearings

 Multiplicative reasoning
 Similarity and congruence

 Circle theorems
 Circle geometry
 Changing the subject of the formula

Summer 2

 Quadratic equations: expanding and factorising
 Quadratic graphs

 Graphs of trigonometric functions
 Further trigonometry

 Vectors and geometric proof

Year 11
Students in Year 11 are focused on the completion of their GCSE studies we offer Linear Foundation and Higher (Edexcel).
In Year 11, students will complete the GCSE schemes of work in the Autumn term and then the will work through a programme of revision and prepare for their exams by completing past papers. Students are also expected to design their own independent revision programmes to assist them in achieving their full potential. They will sit their final examination in June.
The following websites are useful to aid students to achieve their potential;
www.edexcel.com
www.bbc.co.uk/bitesize/
www.mymaths.co.uk
www.corbettmaths.com
Foundation
Units of Work

Higher
Units of Work

Accelerated Higher
Units of Work

 Constructions, loci and bearings
 Quadratic equations
 Quadratic graphs
 Circles, cylinders, cones and spheres
 Fractions and reciprocals
 Similarity and congruence
 Vectors
 Rearranging formulae

 Graphs of trigonometric functions
 Further trigonometry
 Quadratics
 Circle theorems
 Circle geometry
 Rearranging more complex formulae
 Vectors and geometric proof
 Reciprocal and exponential graphs

 Circle geometry
 Rearranging more complex formulae
 Vectors and geometric proof
 Reciprocal and exponential graphs
