Why do we learn maths?
At the square root of Mathematics at Bolingbroke Academy is a belief that all pupils can be successful mathematicians if they are given the tools and the confidence to access the material, all the while supported by passionate maths teachers who believe that maths is fun
Head of Department
Ms M Rowan
Our approach
Courageous
Maths consists of a series of related topics, and the relationships that exist within numerical concepts are taught explicitly to enable pupils to unpack those relationships and to apply their mathematical skills across the curriculum. Our teaching aims to build conceptual understanding incrementally. Depth of understanding will then help pupils to become independent learners who use their existing knowledge to problem solve, as well as build their resilience to tackle unfamiliar questions. This journey enables our pupils to feel the triumph upon successful mastery of new topics.
Mathsfocussed discussions are at the heart of our coplanning sessions: teachers do maths at every opportunity. We use our coplanning time as an opportunity to share best practice, develop subject knowledge and evaluate the effectiveness of lessons and the wider curriculum.
Compassionate
We aim to create engaging and thoughtprovoking lessons and to foster classrooms with a positive attitude to learning maths, where pupils are collaborative yet independent and risktaking. For in maths, you often learn most when you get an answer wrong the first time, so we build a strong culture of error within our classrooms and encourage our pupils to try! We form strong relationships with our pupils and parents with regular contact and data sharing of our question level analysis documents. Ultimately, our aim is that pupils of all abilities can enjoy their mathematical learning in a collaborative and supportive environment. This will be achieved through three core concepts:
• Concretepictorialabstract: physical manipulatives used to introduce all new topics, before the introduction of pictures (e.g. bar modelling) and abstract methods.
• Depth for breadth: our curriculum is structured to enable pupils to spend more time on each topic, building towards a foundation of knowledge, before moving on to the next topic.
• Reasoning and Problem Solving: openended and challenging tasks used to enable pupils to explore topics laterally and encourage application of skills.
Community
All learners need to build a strong base of number skills to be successful. We therefore begin our teaching in Year 7 focusing solely on written and mental methods for the four operations. Throughout their firstyear at Bolingbroke pupils take part in Times Table Rockstars every lesson to strengthen numeracy skills and calculators are not introduced until Year 8.
Mathematical language and notation are prioritised through the insistence of right is right in every lesson in pupils verbal and written responses. Opportunities for paired/group discussion are built in every lesson to check for understanding and build justification skills. Modelling and teacher exposition are discussed within coplanning to ensure consistency and clarity for pupils.
Maths Minutes enrichments are embedded in every key stage to give pupils access to a supportive space in which to bring their maths questions, as well as offering a calm, quiet environment in which to study. Targeted regular small group tutoring takes place across all year groups in Key Stage 3 and 4 to provide pupils the opportunity to work closely with a maths specialist.
In addition to our unflinching dedication to maths within our classrooms, we provide opportunities for our pupils to engage even further with maths in various contexts outside the classroom. Every year we take part in the UKMT challenges and Ark Secondary School Maths Challenges as well as looking at opportunities for pupils to visit universities on maths focus days.
Empowering Excellence
Pupils are given dedicated independent practice time in every lesson to embed conceptual understanding. Homework aims to help pupils review topics from the previous week, revise previous learning and improve application skills through problemsolving questions. Hegarty Maths is used in KS3 and 4 as a further development tool for homework and independent revision.
All pupils are taught all topics, with support and stretch, to reach their target grade throughout the year on termly holistic assessments which are in the style of a GCSE or A Level paper. All pupils in KS3 and 4 are expected to make significant progress between pre and postassessments. Pupils in KS5 are expected to show significant gains in understanding on their threeweekly unit assessments. All assessments are analysed by question to enable teachers to accurately intervene where there are gaps and pupils to focus their revision appropriately.
A positive and aspirational attitude to mathematical learning is encouraged and reinforced throughout the year.
Year 7
Autumn 1  Autumn 2 

Number: Place Value N  Number: Properties of numbers 
Place Value • Powers of 10 • Decimals Addition and Subtraction • Integers and Decimals • Unit conversion • Perimeter Negative Numbers • Addition and Subtraction 
Negative Numbers • Multiplication and Division Factors, Multiples, Primes • Powers and Roots • Multiples, Factors, LCM and HCF • Prime Factorisation Multiplication and Division • Integers and decimals Area • Rectangles, parallelograms, triangles, trapeziums and compound shapes 
Skills developed: • Estimating calculations through rounding • Calculating with the four operations 
Skills developed: • Calculating with negative numbers • Comparing numbers on their properties • Calculating to find the area of a shape 
Spring 1  Spring 2 

Algebra: Manipulating Expressions  Geometry and Measure: Angles 
Order of Operations • Indices, powers and brackets Algebraic Manipulation • Simplifying algebraic expressions • Forming algebraic expressions • Expanding a single bracket • Factorising • Substitution • Function Machines • Solving Equations Sequences • Generating sequences • nth term 
2D shapes • Symmetry • Tessellation Angles • Drawing and Measuring angles • Finding unknown angles (straight line, around a point, vertically opposite, triangle, quadrilateral) 
Skills developed: • Calculating with indices and brackets • Manipulating algebraic expressions through simplifying, expanding and factorising 
Skills developed: • Measuring angles • Calculating to find missing angles in triangles and quadrilaterals 
Summer 1  Summer 2 

Number: Fractions  Statistics: Averages and Tables 
Fractions • Equivalence • Simplifying fractions • Mixed Numbers and Improper Fractions • Compare and order fractions and decimals • Adding and Subtracting fractions • Fraction of an amount • Multiplying and Dividing fractions 
Data • Mean, median and mode averages • Range • Averages from a table • Construct and interpret statistical tables, charts and diagrams including pie charts 
Skills developed: • Comparing fractions • Calculating with fractions 
Skills developed: • Comparing averages of data • Interpreting statistical tables and diagrams 
Year 8
Autumn 1  Autumn 2 

Ratio and Proportion  Algebra: Manipulating Expressions 
Percentages • Converting between fractions, decimals and percentages • Percentages of an amount • Increase and decrease • Finding the whole given a part • Increase and decrease with multipliers • Compound interest and depreciation • Percentage change • Reverse percentages Ratio and Proportion • Sharing in a ratio • Scaling in a ratio • Direct and Inverse Proportion 
Algebraic Manipulation • Simplifying expressions • Solving equations Rearranging Formulae • Substitution • Speed, Distance, Time • Density, Mass, Volume • Pressure, Force, Area Circles • Substitution • Circumference and arc length • Area of circles and sectors 
Skills developed: • Using a calculator to find percentages • Comparing quantities following a percentage increase or decrease • Calculating with percentages and ratios 
Skills developed: • Manipulating algebraic expressions through solving, substituting and rearranging • Using a calculator to find the circumference and area of circles using 𝜋 
Spring 1  Spring 2 

Algebra: Linear Graphs  Geometry and Measure: 3D Objects 
Coordinates • Plotting • Midpoints • Scatter Graphs • Frequency Polygons Linear Graphs • Vertical and horizontal lines • Equation of a straight line: y = mx + c • Solving equations graphically 
3D Objects • Plans and elevations • Nets Surface Area • Prisms and cylinders Volume • Prisms, cylinders and composite solids 
Skills developed: • Plotting on a coordinate grid • Deducing information from a statistical diagram • Deducing the gradient and yintercept from an equation or graph 
Skills developed: • Constructing sketches of plans, elevations and nets • Calculating to find surface are and volume • Manipulating with volume formulae 
Summer 1  Summer 2 

Geometry and Measure: Angles  Probability 
Angles • Measuring and drawing • Finding unknown angles • Angles in polygons Similarity and Enlargement • Similar triangles 
Constructions and Loci • Constructing triangles • Perpendicular and angle bisectors Probability • Theoretical probability vs. relative frequency • Expectation • Probability trees • Twoway tables • Venn Diagrams • Set notation 
Skills developed: • Calculating to find missing angles in polygons • Calculating using scale factor 
Skills developed: • Constructing triangles and bisectors • Deducing probabilities from event descriptions • Calculating to find the probability of a given outcome 
Year 9
Autumn 1  Autumn 2 

Number: Representation  Geometry and Measure: Pythagoras’ and Trigonometry 
Standard Form • Four operations with standard form Proportion • Direct and inverse proportion • Exchange rates Inequalities • Representing on a number line • Solving inequalities 
Pythagoras’ Theorem • Finding missing sides Trigonometry in rightangled triangles • Finding missing sides • Finding missing angles Bearings • Measuring and drawing bearings 
Skills developed: • Calculating with standard form • Interpreting proportion graphs • Manipulating inequalities and • Interpreting inequalities 
Skills developed: • Calculating to find missing missing sides and angles in right angled triangles • Manipulating Pythagoras Theorem’ and trigonometric ratios • Drawing bearings 
Spring 1  Spring 2 

Algebra: Quadratics  Algebra: Graphs 
Quadratics • Factorising quadratic expressions • Solving quadratic equations • Drawing Quadratic Graphs Unit 8: Simultaneous Equations • Solving with elimination • Solving with substitution 
Sequences and Proof • Generating sequences • nth term Linear Graphs • Vertical and horizontal lines • Equation of a straight line: y = mx + c Graphs • Cubic and Reciprocal Graphs • Real Life Graphs • Speed, distance time graphs 
Skills developed: • Manipulating quadratic expressions and equations • Drawing quadratic graphs • Interpreting solutions to solving equations 
Skills developed: • Proving algebraic equivalence • Interpreting graphs • Drawing graphs 
Summer 1  Summer 2 

Geometry and Measure: Transformations  Probability 
Congruence • Congruent triangles Vectors • Adding and subtracting with vectors • Vectors in 2D shapes Transformations • Translation • Rotation • Reflection • Enlargement 
Probability • Probability Trees 
Skills developed: • Proving congruence • Calculating with vectors • Drawing transformations • Reasoning with transformations 
Skills developed: • Calculating to find the probability of a given outcome 
Year 10
Foundation
Autumn 1  Autumn 2 

Number: Fractions, Decimals and Percentages  Geometry and Measure: Angles and 2D shapes 
Basic Number • Rounding • Estimating • Multiples, Factors, LCM and HCF • Prime Factorisation Standard Form • Four operations with standard form Fractions • Fractions, Decimals, Percentages • Four operations with fractions Percentages and Ratio • Percentage of an amount, increase/decrease and reverse • Compound Interest and Depreciation • Simplifying, sharing and scaling with ratios 
Angles • Measuring and drawing • Finding unknown angles • Angles in polygons Surds • Simplifying surds • Four operations with surds Rightangled Triangles • Pythagoras’ Theorem • Trigonometry Bearings • Measuring and drawing bearings 
Skills developed: • Calculating with the four operations, fractions, percentages, ratio and standard form 
Skills developed: • Calculating with surds • Calculating to find missing missing sides and angles in right angled triangles • Manipulating Pythagoras Theorem’ and trigonometric ratios • Drawing bearings 
Spring 1  Spring 2 

Algebra: Expressions and Equations  Algebra: Substitution and Solving 
Algebraic Expressions • Simplifying expressions • Expanding and Factorising expressions Solving Equations • Rearranging Formulae Simultaneous Equations • Solving with elimination • Solving with substitution Quadratics • Drawing Quadratic Graphs • Factorising quadratic expressions • Solving quadratic equations 
Compound Measures • Substitution • Speed, Distance, Time • Density, Mass, Volume • Pressure, Force, Area Linear Graphs • Vertical and horizontal lines • Equation of a straight line: y = mx + c • Cubic and Reciprocal Graphs Real Life Graphs • Speed, distance time graphs • Exchange graphs 
Skills developed: • Manipulating algebraic expressions through substituting, solving, expanding and factorising • Drawing quadratic graphs • Interpreting solutions to solving equations 
Skills developed: • Manipulating formulae • Interpreting graphs • Drawing graphs 
Summer 1  Summer 2 

Geometry and Measure: Perimeter, Area and Volume  Geometry and Measure: Circles, construction and transformation 
Perimeter and Area • Perimeter of rectangles, triangles and compound shapes • Area of rectangles, triangles, parallelograms, trapeziums and compound shapes • Unit Conversion Volume and Surface Area • Volume of prisms, cylinders and composite solids • Surface area of prisms and cylinders 
Circles • Circumference of a circle and arc length • Area of a circle and sector Similar Shapes • Similar triangles Loci and construction • Constructing triangles • Perpendicular and angle bisectors Vectors • Adding and subtracting with vectors • Vectors in 2D shapes Transformations • Translation • Rotation • Reflection • Enlargement 
Skills developed: • Calculating to find perimeter, area, surface area and volume • Manipulating with volume formulae 
Skills developed: • Manipulating circle formulae • Calculating with vectors • Drawing transformations • Deducing what transformation has been applied 
Higher
Autumn 1  Autumn 2 

Number: Surds, Standard Form and Bounds  Geometry and Measure: Angles, Pythagoras and Trigonometry 
Basic Number • Multiples, Factors, LCM and HCF • Prime Factorisation • Index Laws Surds • Simplifying surds • Four operations with surds • Rationalising surds Standard Form • Four operations with standard form Recurring Decimals • Recurring Decimals Bounds • Four operations in bounds Ratio, Proportion and Percentages • Ratio and Proportion • Percentages 
Angles • Angles in polygons and on parallel lines Pythagoras Theorem • Finding missing sides Trigonometry • Finding missing sides • Finding missing angles • Sine rule • Cosine rule • Area of a triangle Bearings • Measuring and drawing bearings Trigonometry Graphs • Sine, cosine and tangent graph 
Skills developed: • Calculating indices, surds, percentages, ratio and standard form • Manipulating algebraic expressions involving indices • Representing bounds through inequalities • Calculating with bounds 
Skills developed: • Calculating to find missing missing sides and angles in triangles • Manipulating Pythagoras Theorem’, and sine and cosine rules • Drawing bearings • Drawing trigonometry graphs 
Spring 1  Spring 2 

Algebra: Quadratics  Algebra: Equations of Lines and Circles 
Quadratics • Factorising quadratic expressions • Solving Equations • Solving quadratic equations by factorising, completing the square and applying the quadratic formula • Drawing Quadratic Graphs Simultaneous Equations • Solving Inequalities • Simultaneous Equations • Substitution Iteration • Iteration 
Equations of a Straight Line • Linear Graphs Equation of a Circle • Equation of a Circle Real Life Graphs • Speed, Distance, Time • Density, Mass, Volume • Pressure, Force, Area 
Skills developed: • Manipulating quadratic expressions and equations • Drawing quadratic graphs • Interpreting solutions to solving equations 
Skills developed: • Manipulating linear equations and equations of a circle • Interpreting graphs • Drawing graphs 
Summer 1  Summer 2 

Geometry and Measure: Circles and Similarity  Geometry and Measure: Vectors, Loci and Transformations 
Circle Geometry • Circumference of a circle and arc length • Area of a circle and sector • Circle Theorems Congruence and Similarity • Congruence and Similarity • Area • Volume of prisms, cylinders, composite solids and frustums • Surface area of prisms and cylinders 
Vectors • Magnitude of Vectors • Vector calculations Loci and Construction • Loci and construction Transformations • Translation • Reflection • Rotation • Enlargement 
Skills developed: • Calculating to find the area and perimeter of part circles • Manipulating circle formulae • Calculating to find surface area and volume 
Skills developed: • Calculating with vectors • Drawing accurate triangles and bisectors • Drawing transformations • Deducing what transformation has been applied 
Year 11
Foundation
Autumn 1  Autumn 2 

Algebra: Sequences and Inequalities  Probability and Statistics 
Sequences • Generating sequences • nth term Expressions and Equations • Simplifying expressions • Expanding and Factorising expressions • Solving Equations • Rearranging Formulae Inequalities • Representing • Solving inequalities Proof • Representing odd and even numbers algebraically 
Probability • Theoretical probability vs. relative frequency • Expectation • Probability trees • Twoway tables • Venn Diagrams • Set notation Statistics • Mean, median and mode averages • Range • Averages from a table • Construct and interpret statistical tables, charts and diagrams including pie charts • Scatter Graphs • Frequency Polygons 
Skills developed: • Manipulating algebraic expressions through substituting, solving, expanding and factorising • Representing inequalities • Proving algebraic equivalence 
Skills developed: • Deducing probabilities from event descriptions • Calculating to find the probability of a given outcome • Representing data on statistical tables and diagrams 
Higher
Autumn 1  Autumn 2 

Algebra: Functions, Proof and Algebraic Fractions  Statistics and Probability 
Functions • Composite and Inverse Functions Transformation of Graphs • Translation, reflection, ‘stretch’ of graphs Algebraic Proof • Algebraic Proof Algebraic Fractions • Four operations with algebraic fractions Quadratic Sequences • Quadratic Sequences 
Data • Mean, median and mode averages • Comparing sets of data • Averages from a table • Box Plots • Construct and interpret statistical diagrams including pie charts • Histograms Probability • Probability Sampling • Stratified Sampling • Capture/Recapture 
Skills developed: • Manipulating with functions • Drawing a graph following a transformation • Deducing what transformation has been applied • Manipulating with algebraic fractions 
Skills developed: • Deducing probabilities from event descriptions • Calculating to find the probability of a given outcome • Representing data on statistical tables and diagrams 
Year 12
Pure Maths
Autumn 1  Autumn 2 

Expressions and Equations

Coordinate and Circle Geometry

Spring 1  Spring 2 

Calculus

Trigonometry

Summer 1  Summer 2 

Exponentials and Logarithms 
Trigonometry
*A Level Content 
Applied Maths
Autumn 1  Autumn 2 

Statistics: Interpreting Data and Probability

Statistics: Probability Distributions and Data Representations

Spring 1  Spring 2 

Statistics: Hypothesis Testing Mechanics: Constant Acceleration

Mechanics: Forces and Motion

Summer 1  Summer 2 

Mechanics: Variable Acceleration

Statistics: The Normal Distribution

Further Maths
Autumn 1  Autumn 2 

Core – Complex Numbers, Series, Roots of Polynomials

Core – Matrices, Linear Transformations, Proof by Induction

Spring 1  Spring 2 

Decision – Algorithms, Graphs and Networks, Algorithms on Graphs

Core –Vectors, Volumes of Revolutions Decision – Linear Programming

Summer 1  Summer 2 

Decision – Critical Path Analysis, Travelling Salesman, Linear Programming

Core – Complex Numbers Problem Solving

Year 13
Pure Maths
Autumn 1  Autumn 2 

Trigonometry

Differentiation 
Spring 1  Spring 2 

Integration, Functions and Graphs 
Sequences and Series

Summer  

Parametrics, Vectors and Numerical Methods

Applied Maths
Autumn 1  Autumn 2 

Statistics: Conditional Probability

Mechanices: Forces and Projectiles

Spring 1  Spring 2 

Mechanics: Moments, Further Kinematics

Mechanics: Application of Forces 
Further Maths
Autumn 1  Autumn 2 

Core – Complex Numbers, Hyperbolic Functions, Series Further Pure  Vectors

Core – Series Further Pure – Conic Sections

Spring 1  Spring 2 

Core – Methods in Calculus, Polar Coordinates, Hyperbolic Functions Further Pure – Inequalities, tformulae, Numerical Methods

Core & Further Pure – Differential Equations Core – Volumes of Revolutions
