“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” – William Paul Thurston
The study of Mathematics at Westhoughton high school has been designed to empower students to become independent, methodical learners, with the aim of becoming analytical, critical thinkers who can tackle problems logically whilst deepening their enjoyment of mathematics and developing a curiosity for the world around us.
Mathematics at Westhoughton High School will explore connections between the different areas of Maths and other STEM subjects. We believe that to understand the development of mathematics through its history will help students with the contemporary applications and appreciate and respect the role mathematics plays in our lives.
Maths is so much more than numeracy! Mathematics has changed the world that we live in, we look after each other by considering topics such as: how mathematics forms the basis for all of our monetary systems and controls the way in which countries interact and exchange financially; how it helps us to create the latest blockbuster computer games, lifesaving medical magnetic resonance imaging and the impact it will have on future technological and scientific breakthroughs.
We designed the mathematics curriculum with the intent of building upon prior knowledge to deepen understanding and prepare students to apply mathematical concepts to the outside world. The curriculum is ambitious but offers enrichment opportunities such as school trips, UKMT maths challenge, artful maths club and historical maths weeks where we have designed pictures using coding and even painted our own Fibonacci inspired frogs.
We want students to aim high and be inquisitive about maths whilst at the same time appreciating what skills they will need in their futures. We want all our learners to feel confident to use numbers in everyday problems in a world that is evolving, changing and developing exponentially. We want our students to never stop learning and increasing their enthusiasm for mathematics as it can help them with the necessary skills and determination to embrace the challenges and new ideas of the future.
Please see parental overview of the course in KS3 and KS4 below.
Key Stage 3
Year 7  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied 
Number Work Develop understanding and mastery of basic number work, the four operations, place value and priority of operations.  Developing Number Work: Factors, Multiples and Prime Further develop understanding and mastery of more complex number work including indices and real roots, estimations of roots, factors and multiples, HCF and LCM, prime numbers and their applications.  More Complex Number Work To review and build upon fraction knowledge from KS2 in preparation for relating fractions to ratio in summer term 1 and built upon further in Year 9. To start working with algebra by learning to manipulate, leading to further algebra skills in Year 8.  Algebraic Terms To embed and enhance the basic algebra skills needed as foundation blocks. These skills will be integral to Year 8s developed curriculum.  Delving Deeper To develop confidence in sharing in a ratio and the relationship the topic shares with fractions.  Project Work Linked with Technology Department regarding the use of mathematics in designing in 3D, to extend knowledge of 3D shapes and their nets from KS2 to looking at plans and elevations from different viewpoints. Students will learn how to draw 3D shapes accurately using isometric paper through a project looking at building properties and budgeting. 
Skills and Key Knowledge Taught 
Ordering numbers
Four operations Place value Directed number Addition and subtraction of decimals Multiplication and division of decimals Priority of operations Inverse operations Powers and roots 
Factors, multiples and prime numbers
Prime factorisation Finding the HCF and LCM of 2 or 3 numbers Area and perimeter of basic shapes 
Fractions of amounts
Equivalent fractions Fraction operations Algebraic vocabulary Simplifying expressions using addition and subtraction Index laws 
Forming expressions and equations
Expanding brackets Factorising expressions Substitution Solving linear equations 
Find and using the nth term of linear sequences
Special sequences Knowledge of the difference between a linear and geometric sequence Understand ratio notation Simplify ratios Share in a ratio Understand the relationship between ratios and fractions 
Terms and notations of 3D shapes
Plans and elevations of 3D shapes Isometric drawing Averages Advantages and disadvantages of averages Draw chart representations of data 
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Year 8  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied 
Fractions, Decimals and Percentages Furthering our KS3 knowledge of rounding including decimal places and significant figures.  Algebra Extending knowledge from Yr 7 Algebra, to apply skills learnt to inequalities. Students manipulate algebra and solving skills will be extended throughout the curriculum to look at quadratics and why we might use iteration.  Graphs and Angles Students use substitution skills from previous topics to look at how to plot a linear graph. Students gain a firm understanding of gradient and intercept as this will be extended further when looking at parallel and perpendicular lines.  Constructions and Transformations To further stretch the Year 7 shape knowledge, students explore bisections, loci and bisections.  Probability Students explore the concept of probability, looking at ideas of randomness and fairness. Students will have a firm understanding of the probability scale and how to calculate simple probabilities.  Probability, Statistics and Shape Students review and extend knowledge of averages. Students review and build upon knowledge of area and perimeter of basic shapes. 
Skills and Key Knowledge Taught 
Rounding
Error Intervals Truncation Estimation Converting between fractions, decimals and percentages Percentages of amounts Rounding numbers to given decimals places/ significant figures Estimating calculations Finding error intervals of a rounded or truncated number Converting between fractions, decimals and percentages confidently and efficiently Writing a quantity as a fraction of another Finding percentages of an amount 
Expanding brackets
Solving linear equations Linear inequalities Rearranging simple formula Substitution Expanding single and double brackets Solving one and two step linear equations Solving equations with the unknown on both sides of the equals sign Using and solving linear inequalities and show their solution on a number line Substituting numbers into formula Rearranging formula to change the subject 
Straight line graphs
Angle properties Drawing and measuring angles Calculating missing angles using angle facts Plotting coordinates in all four quadrants Finding the midpoint of two coordinates Recognising and drawing horizontal and vertical lines Drawing straight line graphs Identifying gradient and intercepts graphically and algebraically for linear graphs Simplifying ratios Sharing in a ratio Naming and measuring angles Drawing angles using a protractor Angle factors on a straight line, around a point and in a triangle Different types of triangles properties 
Standard ruler constructions
Transformations Bisecting a line using a compass Bisecting an angle using a compass Bisecting a line through a given point using a compass Drawing simple loci Constructing different types of triangles using protractors and a pair of compasses Translating shapes using column vectors Rotating shapes Reflecting shapes Enlarging simple shapes by a positive scale factor Describing single transformations 
Frequency tables and polygons
Systematic listing strategies and product rule for counting The probability scale Probability of simple events Relative frequency tables Sample spaces Read and interpret frequency tables Completing frequency tables from given information and twoway tables Constructing a frequency polygon from a grouped frequency table Listing all possible outcomes of an event Understanding ideas of randomness and fairness Calculating the probability of a simple event Predicting number of outcomes using relative probability Listing all possible outcomes in a sample space Calculating probabilities from sample spaces 
Venn diagrams
Twoway tables Averages review Pie charts Area and perimeter of basic shapes review Completing Venn diagrams from given data Finding probabilities from Venn diagrams using ‘and’ /’or’ Completing twoway tables Calculating mean, median, mode and range Drawing an accurate pie chart Interpreting pie charts Calculating area and perimeter of basic shapes 
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Year 9  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied 
Number Building to the prior knowledge and extending to look at compound interest and depreciation throughout Autumn term.  Transformation, Ratio and Transformations Students extend their knowledge from transformations block in Year 8, with a particular focus on enlargements and describing all transformations.  Shape Students build to Year 8 knowledge in applying skills to compound shapes whilst gaining knowledge of how to work with circles. Students extend their knowledge of area to work with surface area and volume of more complex shapes.  Shape and Measures Having looked at metric units and the concept of compound units, students will study speed, density and pressure.  Graphs Students build to their knowledge of straightline graphs to look at the concept of parallel and perpendicular lines. Adding to their Year 8 knowledge of calculating gradient, students explore reallife concept of gradient and how this applies to reallife graphs such as distance time graphs.  Probability and Statistics Students learn new ways to represent data through stem and leaf diagrams and scatter graphs and their uses. 
Skills and Key Knowledge Taught 
Using the laws of indices to simplify expressions
Changing between standard form and ordinary numbers Ordering decimals and fractions Converting between fractions, decimals and percentages Finding percentages of amounts and of increases/decreases Using reverse percentages to find an original amount Calculating compound interest and depreciations Understanding the link between growth and decay and compound interest/ depreciation 
Representing, adding and subtracting column vectors
Translating shapes using vectors Reflecting, rotating and enlarging shapes Describing a single transformation Simplifying ratios and writing as unit ratios Sharing amounts into a 2 or 3part ratio Relating ratios to fractions Calculating best buy deals using unitary method Map scales and find real life distances between two points Bisecting an angle and a line Drawing loci of a point and a line Drawing plans and elevations of simple and complex 3D shapes 
Calculating the area and circumference of a circle
Calculating the area of a sector, arc length and perimeter Calculating area of compound shapes made from basic 2D shapes Calculating the volume of basic prisms Calculating the surface area of prisms using nets Calculating the volume and surface of cylinders Calculating volumes and surface areas of cones, spheres and pyramids Calculating volume and surface areas of composite 3D shapes 
Conversion between metric units of length, mass and capacity
Conversion between compound units of speed Properties of similar shapes Finding missing lengths of similar shapes Finding missing areas and volumes of similar shapes Calculating speed, distance and times using a formula and rearranging Calculating simple densities and of combined events Calculating pressure using a formula and rearranging 
Plotting straight line graphs
Parallel and perpendicular lines Exchange rates Conversion graphs Real life graphs Area under a graph Gradient of a graph Calculation of distance travelled by calculating the area under a distance/ time graph using the trapezium rule Calculating speed by calculating the gradient of a distance time graph As KS3 ends, Maths sets may have variation in pace within the sequence in learning to ensure all core knowledge is secure before progressing into KS4 Maths. 
Tree diagrams (independent and dependent)
Venn diagrams to calculate probability Averages from a table Stem and leaf diagrams Scatter graphs Line of best fit Sampling and its limitations Interpreting sampling using capture/ recapture As KS3 ends, Maths sets may have variation in pace within the sequence in learning to ensure all core knowledge is secure before progressing into KS4 Maths. 
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Key Stage 4
Year 10  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied in Edexcel GCSE Maths – Foundation 
Angles and Algebra Students develop their understanding of finding missing angles on parallel lines and in polygons. Students also further develop their manipulation of algebraic expressions.  Algebra, Pythagoras and Trigonometry Students factorise expressions, rearrange formula and find missing sides and angles using Pythagoras’ Theorem and trigonometry.  Geometry and Bearings Students further develop their understanding of angles, loci, bearings, plans and elevation.  Simultaneous Equations and Shape Students further their work with linear graphs and begin to solve simultaneous equations. Students develop their conceptual knowledge of similar shapes.  Limits, Inequalities, Sequences and Statistics Students find the value of error after rounding or estimation. Students also explore representing and solving inequalities and averages.  Probability Students develop their calculation of simple probabilities and of more than one event. Venn diagrams and methods of representing data are also explored. 
Skills and Key Knowledge Taught 
Angle facts on a line, around a point and in a triangle
Interior and exterior angles in polygons Identifying angles on parallel lines Expression, identities, equations and formulae Collecting like terms Simplifying expressions Expanding single and double brackets 
Substitution into formulas
Factorising into single brackets Solving 1 & step equations Changing the subject of the formula Finding missing sides of rightangled triangles using Pythagoras’ Theorem Finding missing sides and angles of rightangled triangles using trigonometry 
Drawing and measuring angles
Reviewing bisecting angles and line through a point Loci around a point and around a line Bearings problemsolving questions Measuring and calculating bearings using angles on parallel lines Drawing plans and elevations of 3D shapes Drawing 3D shapes on isometric paper review 
Plotting straight line graphs using a table of values
Solving linear simultaneous equations Setting up linear simultaneous equations from worded problems Finding approximate solution to linear simultaneous equations graphically Recognising congruent triangles Understanding the properties of similar shapes Finding a missing side on similar shapes Finding a missing area or volume of a similar shape 
Estimating answers to calculations
Finding error intervals after rounding or truncating Drawing linear inequalities on a number line Solving one and two step linear inequalities Describing how to find the next term in a linear sequence Finding and using the nth term of a linear equation Finding the prime factorisation of a number Finding the HCF and LCM of two or more numbers Finding the median, mean, mode and range from a grouped frequency table 
Plotting the probability scale
Finding the probability of simple events Sample spaces Finding probabilities using dependent and independent tree diagrams Completing frequency trees, tables and finding probabilities Completing twoway tables and find probabilities Completing Venn diagrams and finding probabilities Understanding and using set notation for Venn diagrams 
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Year 10  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied in Edexcel GCSE Maths – Higher 
Angles, Algebra and Surds Students further develop their understanding of how to find missing angles in polygons and on parallel lines using known facts. Students are introduced to the concept of a surd and how to manipulate them.  Pythagoras’ Theorem, Trigonometry and Congruency Students explore Pythagoras’ Theorem and trigonometric ratios related to right angled triangles. Students are further introduced to trigonometric rules for the nonrightangled triangle alongside developing understanding of the term ‘congruency’ in triangles and proofs.  Bearings and Quadratics Students develop their understanding on calculating missing angles in bearings and reviewing the links to trigonometry. Students further their understanding of what a quadratic is, developing various ways to solve these and then sketch the solution.  Graphs and Simultaneous Equations Students further their knowledge and skills within graphs (other than linear and quadratic) and how to sketch/plot them. Students develop their solving of linear and quadratic simultaneous equations.  Inequalities, Bounds and Sequences Students build to their understanding of solving and sketching inequalities, using bounds to find error intervals for calculations.  Sequences, Proportion and Statistics Students use their knowledge of linear sequences to understand quadratic sequences. Students explore variables that can be proportional to each other and to find future values. Students learn how to plot and interpret graphs drawn from grouped frequency data. 
Skills and Key Knowledge Taught 
Finding Interior and exterior angles in polygons
Identifying alternate, corresponding and cointerior angles on parallel lines Identifying vertically opposite angles Substitution into formula Expanding single, double and triple brackets Identifying and simplifying surds Applying four operations with surds 
Finding missing sides of a rightangled triangle using Pythagoras’ Theorem
Finding missing sides or angles on a rightangled triangle using trigonometric ratios Finding missing sides in 3D shapes using Pythagoras or trigonometry Trigonometry of exact values Finding the area of triangles Finding missing sides or angles of a triangle using the sine or cosine rule Identifying and proving congruency in a triangle 
Drawing bearing using a pair of compasses
Finding missing bearings using angles on parallel lines Finding missing bearings using trigonometry Factorising quadratics Calculating difference of two squares Solving quadratics using formula Completing the square on quadratics Sketching quadratics graphs 
Plotting cubic, reciprocal and exponential graphs
Identifying and sketching different types of graphs Recognising the equation of a circle Finding approximate solutions to linear simultaneous equations graphically Solving linear simultaneous equations algebraically Setting up linear simultaneous equations Solving quadratic simultaneous equations

Showing linear inequalities on a number line
Solving 1 & 2 step linear inequalities Solving quadratic inequalities Identifying graph inequalities and shade regions Finding error intervals after rounding or truncation Finding lower and upper bounds of calculations Finding and using the nth term of a linear sequence 
Finding and using the nth term of quadratic sequences
Finding new values of variables using direct proportion Finding new values of variables using inverse proportion Finding the mean, median, mode and range from a list of data review Finding quartiles from a list of data Comparing sets of data Plotting and interpreting cumulative frequency graphs Plotting a box plot from a list of data or a cumulative frequency graph Comparing box plots and populations 
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Year 11  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied in Edexcel GCSE Maths Foundation (sets 11H3 and below) 
Fractions, Indices and Standard Form Students deal with fractions and mixed numbers using the four operations, applying the laws of indices to simplify calculations involving powers. Students learn the concept of a standard form number and apply the laws of indices to these when performing calculations involving standard form. Students multiply/divide fractions and mixed numbers. Students use the laws of indices to simplify numerate and algebraic expressions and use standard form numbers in calculations  Congruence, Similarity and Vectors Students use the rules governing similarity to determine similar shapes, determine the linear scale factor involved in similar shapes to find missing sides. This requires students to understand congruency and use this to determine missing sides and angles in congruent shapes. Students develop their understanding of vectors as well as similarity, enlargement, scale factors and apply this to solve problems involving similar shapes  More Algebra Students focus on plotting and sketching the graphs of cubic, reciprocal graphs and interpret them. Students understand the concept of simultaneous equations and solve them using an algebraic approach or via their graphs. Students develop their ability to rearrange ever increasingly complex equations, understand the differences of expressions, equations & formulae, using the skills acquired in the algebra content to prove results and conditions.  Classspecific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning.  Classspecific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning.  Exams undertaken 
Skills and Key Knowledge Taught 
Topic areas:
Multiplying and dividing mixed numbers and fractions Using the laws of indices Writing large numbers in standard form Converting large numbers from standard form into ordinary numbers Writing small numbers in standard form Converting numbers from standard form with negative powers of ordinary numbers Multiply/divide/add and subtract numbers in standard form 
Topic areas:
Using similarity to solve angle problems Finding the scale factor of an enlargement Using similarity to solve problems Understanding the similarity of regular polygons Calculating perimeters of similar shapes Recognising congruent shapes Congruence to work out unknown angles Congruence to work out unknown sides Adding and subtracting vectors Finding the resultant of two vectors Finding multiples of a vector 
Topic areas:
Drawing and interpreting graphs of cubic functions Drawing and interpreting graphs of y = 1/x Drawing and interpreting nonlinear graphs to solve problems Solving simultaneous equations by drawing a graph Solving simultaneous equations Solving simultaneous equations algebraically Changing the subject of a formula Identifying expressions, equations, formulae and identities Proving results using algebra. 

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Year 11  Autumn Term 1  Autumn Term 2  Spring 1  Spring 2  Summer 1  Summer 2 
Topics Studied in Edexcel GCSE Maths – Higher (set 11W1 11W4 and 11H12) 
Vectors and Geometric Proof Students develop their ability to solve problems involving vectors in a range of contexts, understanding vector notation and the difference between a vector and scalar quantity. Students understand how to determine the magnitude of a vector and find the resultant of two or more vectors. Students learn the determination of parallel and collinear vectors and apply vectors to simple geometric proofs. By the end of the unit, students know how to prove whether vectors are parallel.  Proportion and Graphs Students learn to solve problems involving direct/indirect proportionality (including square, square roots, cubes and cube root) in a range of contexts. Students sketch and interpret exponential graphs and understand how to determine the gradient at a stationary point on a curve. Students use suitable mathematical methods to estimate the area under a curve and develop their understanding of the various transformations of graphs and their associated function notations. Students solve problems involving direct and indirect proportion, including squared, cubed, square root and cube root relationships to functions and their graphs.  Classspecific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning.  Classspecific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning.  Classspecific revision and interventions Revision foci will differ between groups and students to ensure their assessment data is used to direct teaching and independent learning.  Exams undertaken 
Skills and Key Knowledge Taught 
Topic areas:
Vector notation Calculating the magnitude of a vector Calculating using vectors and represent the solutions graphically Calculating the resultant of two vectors Solving problems using vectors Using the resultant of two vectors to solve vector problems Expressing points as position vectors Proving lines are parallel Proving points are collinear Solving geometric problems in two dimensions using vector methods Applying vector methods for simple geometric proofs 
Topic areas:
Using equations to solve problems involving direct proportion Solving problems involving square and cubic proportionality Using equations to solve problems involving inverse proportion Using and recognising graphs showing inverse proportion and exponential functions Calculating the gradient of a tangent at a point Estimating the area under a nonlinear graph Understanding the relationship between translating a graph and the change in its function notation Understanding the effect stretching a curve parallel to one of the axes has on its function form Understanding the effect reflecting a curve in one of the axes has on its function form 

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