Maths Curriculum


“Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers” – Shakuntala Devi

Our Curriculum

Our Intent

By the end of the Year 11 students at Pendle Vale College will: 

  • Develop core functional mathematical capabilities that they can apply to the world around them. 
  • Have the ability to use their knowledge and skills to solve problems and reason mathematically. 
  • Have transferable skills which can be used in wider aspects of life and further study. 

Three Pillars of the Curriculum

We fully believe that Maths contributes to the development of all students at Pendle Vale College through our unrelenting focus on: 

  • Currency: Enabling students to achieve the standards required to access FE, employment and training post 16. 
  • Core Skills: Quality first teaching from our strong team of experienced specialist teachers following well designed schemes of learning that build on prior knowledge and equip students with the skills, and understanding to enable them to apply mathematics to the world around them.  Providing the core maths skills essential to everyday life and extending this to higher level topics. Functional skills, applying mathematical principles in a variety of contexts at appropriate ability levels.  
  • Character:  Developing character through challenging students to think and make connections. Building resilience when applying problem solving and thinking skills, developing logic, organisational skills, and many other employability charateristics that are transferable to many areas.  

Learning and Understanding

We seek to instill a true love of learning in all our students by: 

  • Ensuring students are taught in appropriate abilty groups where they can achieve and progress at the right pace for them. Helping them to feel confident and supported in their learning. 
  • Developing a secure and positive learning environment where students are able to discuss errors and misconceptions using failures as an essential part of the learning process. Students are encouraged to check and reflect on their work at regular intervals and use errors as learning opportunities. 
  • Promoting progress and achievements, providing effort based praise and regular assessments. 
  • Fostering strong teacher pupil and peer relationships and a ‘can do’ attitude to the subject so that student ideas can be discussed and respected and students are able to learn from each other. 
  • Providing students with real stretch and challenge and a sense of achievement. 
  • Ensuring students can see and appreciate their positive steps in learning and are fully aware of their own progress and successes at all ability levels.  

In order to achieve a true understanding of Mathematics, topics have been intelligently sequenced based on the following rationale: 

  • Building on prior knowledge and making connections between areas and concepts previously covered. Developing and moving forward in knowledge and deepening understanding. 
  • Providing a solid foundation of number skills and building confidence in calculations. 
  • Moving to abstract generalisations as often as possible incorporating the use of algebraic techniques into routine problem solving tasks throughout all areas. 
  • Revisiting and developing skills, spiralling the curriculum and working on topics at regular intervals. 
  • Ensuring students can access higher level concepts as early as possible to provide building blocks for sound understanding at KS4. 
  • Making learning relevant to students using real life contexts and applications to add breadth as well as depth to understanding. 
  • Including problem solving and opportunities to apply knowledge and skills throughout the course. 
  • Buliding in regular retrieval practice and consolidation work in order to develop competency, fluency, and allow mastery of skills and confident application. 

Personal Development

Mathematics contributes to the development of students at Pendle Vale through their development in five key areas: 

  • Social development is encouraged through collaborative learning and the discussion process. Working on practical applications of the subject thinking problems through and reasoning. Trialling ideas and solutions to problems, discussing the reasonableness of answers and learning through mistakes. Discovering where problems lie and planning to overcome them through the problem solving process applying knowledge and skills. 
  • Moral development of students is promoted when developing trust as learners. Using solutions effectively as a learning tool. Respecting the ideas of others and sharing own ideas in order to contribute to the development of others. Analysing and commenting on the work of others.   
  • Spiritual development is highlighted when providing space for independent thought and encouraging students to reflect on their own development. Allowing opportunities for students to become self aware and reflective learners judging the reasonableness of their solutions. Helping and supporting others through collaborative learning. 
  • The curriculum contributes to the cultural development of students by providing equal opportunities and removing ceilings on student ambition. Challenging misconceptions and breaking down barriers.  
  • Personal development is taught by encouraging students to observe and track their own progress. Building confidence in students skills and abilities, rewarding successes at all levels and building on students progress and achievements contributing to their increase in value and self worth. Developing students organisational skills and ability to meet deadlines for homework tasks. Strong focus on transferable skills in working on students ability to problem solve applying logic and thinking skills. Building strong teacher pupil relationships based on trust, developing skills and potential.

Equality

The Mathematics curriculum ensures that any potential equality issues are mitigated by: 

  • Allowing students to progress at the appropriate pace following differentiated SOL in the appropriate ability group. Groupings regularly reviewed and changes made to allow all to progress.  
  • Close monitoring of assessment data and targets identifying and supporting any potential underachievement.  
  • Analysis of KS4 mock results including comparisons with other schools through participation in Pixl wave. Providing targeted support to help all students perform at least at the average line.  
  • Providing in class support and intervention through TA and learning mentors. 
  • Provision of revision resources and workbooks for all to support independent work. 
  • Small targeted form time coaching groups aimed at supporting and  building confidence in KS4 students. Study Saturday sessions, lunch time and after school support sessions.

Homework

Our belief is that homework should be a deliberate practice of what has been modelled and taught in lessons, as well as interleaved revision to ensure students are embedding previously learn knowledge but also developing high level skills alongside powerful knowledge. All Science homework is meaningful and contributes towards students’ progress. KS3 tasks focuses on literacy and key terminology and KS4 focuses on long term memory; repetition and retrieval.

Careers, Opportunities and beyond the Curriculum

Opportunities are built in to make links to the world of work to enhance the careers advice and guidance that students are exposed to including: 

  • Development of transferable skills, ensuring students reach levels needed to open doors to many career options. Links are made to a wide range of subject areas and careers. 
  • Core and Functional applications of maths skills in many real life areas e.g, financial capability. 
  • Further Maths and Statistics GCSE offered to prepare students for further study and ‘A’Levels. 

Whilst ensuring students are well prepared for their GCSE examinations, we teach beyond the exam specification by: 

  • Developing skills in applying logic, problem solving, reasoning and thinking that are transferable. 
  • Providing maths challenges and weekly numeracy puzzles to engage students outside of lessons. 
  • Running UKMT competitions and maths challenges. 
  • Delivering Further Maths and Statistics to provide stretch and challenge and prepare for further study. 
  • KS4 intervention groups working on developing confidence in abilities and the application of skills. 
  • Cross curricular collaborations, including STEM projects, with other subject areas.  
  • Developing numeracy skills through use of Numeracy Ninjas with KS3 groups.  
  • Providing access to and encouraging the use of on line platforms such as Sparx Maths, GCSE Pod, Dr. Frost Maths and Mathspad for homework and enrichment activities. 

Research Led

The Mathematics curriculum at Pendle Vale has been influenced by: 

  • The essential nature of the subject and a desire to equip students with skills for life. 
  • The need to open up opportunities for students in further study.  
  • The need to develop analytical individuals with ability to reason and problem solve. 
  • Experienced specialist staff with a love of mathematics and a desire to share this with students. 
  • Regular input from LCC Maths Consultant and meetings with subject leaders across the county through attending termly Subject Leader Development meetings. 

Mathematics KS3 / Foundation KS4 / Higher KS4 

Overview of critical knowledge students will learn in this subject from Y7-Y11.  The curriculum is planned giving thought to the optimum knowledge sequence required for building secure, effective schema

A powerful knowledge-rich curriculum teaches both substantive knowledge (facts, knowing something is the case, what we think about) & non-declarative or procedural knowledge (skills & processes, knowing how to do something, what we think with).

Bodies of knowledge are essential to underpin skills. In some subjects, further distinction between substantive knowledge (domain specific knowledge gained e.g. knowledge of the past) & disciplinary knowledge (how the knowledge is gained e.g. historical reasoning) 

Curriculum Plans

Year 7

Autumn Term

Theme

  • Negative Numbers 
  • Algebra concepts. 
  • Place value 
  • BIDMAS 
  • Number concepts 
  • Metric units of length 
  • Perimeter

New Learning

  • Enhanced knowledge of number and place value including negatives, decimals, integer powers and roots. 
  • Algebraic terms: term, expression, expand. 
  • Standard metric units. 
  • Shape properties and formula for perimeter. 
  • Compare and order rational numbers. 
  • Simplify and manipulate algebraic expressions. 
  • Use/apply operations including brackets powers and roots. 
  • Convert standard units of length. 
  • Calculate perimeters of 2D shapes. 
  • Interpret when a numerical problem requires additive, multiplicative or proportional reasoning. 
  • Solve complex calculation problems, including multi step problems. 

Knowledge Revisited

KS2 Content

Knowledge Developed

KS2 Knowledge

Spring Term

Theme

  • Area 
  • Fractions 
  • Probability 
  • Negative Numbers 
  • Substitution 
  • Solving equations. 
  • Time units and timetables. 

New Learning

  • Shape formula for area of basic 2D shapes.
  • Equivalent and simplified fractions.
  • Equivalent decimals, fractions and percentages.
  • Probability scale, equally likely outcomes, possible outcomes sum to one.
  • Negative number operating rules. 
  • Algebraic terms substitute, equation, solution.
  • Standard units for time. 
  • Calculate area of basic 2D shapes. 
  • Compare and order fractions. 
  • Reduce a fraction to simplest form. 
  • Calculate probabilities of single independent events. 
  • Use/ apply operations with negative numbers. Substitute into algebraic expressions and simple formula. 
  • Solve linear equations in one variable. 
  • Convert standard units of time and use and apply in context of timetables. 
  • Make connections between number relationships and their algebraic representations. 
  • Model situations by translating them into algebraic expressions or formula. 

Knowledge Revisited

KS2 Content

Knowledge Developed

KS2 Knowledge

Summer Term

Theme

  • Distance Time Graphs 
  • Approximation 
  • Percentages 
  • Coordinates 
  • Angles  
  • Data Handling 
  • Metric units
  • 3D shapes

New Learning

  • Standard units for speed and graphical representations. 
  • Rounding rules. 
  • Percentage equivalences. 
  • Coordinate conventions. 
  • Angle geometry facts. 
  • Statistics: discrete, continuous grouped data. 
  • Standard units for length, mass and capacity. 
  • Shape properties. 
  • Construct and interpret travel graphs. 
  • Round and approximate given values. 
  • Calculate percentages of amounts. 
  • Solve increase/ decrease percentage problems. 
  • Plot coordinates in all four quadrants. 
  • Estimate, measure and draw angles. 
  • Construct charts for grouped and ungrouped data. 
  • Convert standard units for length, mass, capacity. 
  • Represent 3D shapes in 2D forms. 
  • Model situations by using graphs. 
  • Solve complex calculation problems, including multi step problems. 

Knowledge Revisited

KS2 Content

Knowledge Developed

KS2 Knowledge

Year 8

Autumn Term

Theme

  • Sequences 
  • Linear Graphs 
  • Algebraic expansion/Factorising 
  • Prime Factors 
  • Pythagoras’ Theorem 
  • Circle measures 
  • Constructions 

New Learning

  • Linear,(quadratic), geometric and Fibonacci sequence properties. 
  • Algebraic terms: Expand, Factor, Factorise. 
  • Factors, multiples, primes, HCF and LCM. 
  • Pythagoras’ Theorem. 
  • Area and circumference formula for circles. 
  • Generate terms of a sequence, find nth term for a linear pattern. 
  • Construct linear graphs. 
  • Simplify and manipulate algebraic expressions. 
  • Prime factor decomposition, find HCF and LCM 
  • Calculate side lengths in right angled triangles. 
  • Calculate area and circumference of a circle. 
  • Use standard ruler and compass constructions. 
  • Solve complex calculation problems, including multi step problems. 
  • Make connections between number relationships and their graphical representations.

Knowledge Revisited

  • Negative Numbers 
  • Algebra concepts 
  • Area and Perimeter

Knowledge Developed

KS2 and Y7 Knowledge.

Spring Term

Theme

  • Fractions
  • Decimals
  • Angle Facts
  • Equations and Formula
  • Transformations and
  • Congruence

New Learning

  • Enhanced knowledge of number and place value including fractions and decimals. 
  • Geometry facts: basic angle properties. 
  • Algebraic terms: equation, solution, formula. 
  • Properties of transformations. 
  • Properties of congruent and similar shapes. 
  • Use and apply operations for fractions and decimals. 
  • Use/apply angle facts to solve geometry problems. 
  • Solve linear equations in one variable. 
  • Change the subject of a formula. 
  • Transform 2D shapes on a grid. 
  • Transform objects in four quadrants. 
  • Solve complex calculation problems, including multi step problems. 
  • Make connections between number relationships and their algebraic representations. 
  • Model situations by translating them into algebraic expressions or formula.

Knowledge Revisited

  • Fraction concepts 
  • Calculations 
  • Basic equations

Knowledge Developed

KS2 and Y7 Knowledge

Summer Term

Theme

  • Averages and Range 
  • Ratio and Proportion 
  • Conversion graphs 
  • Pie charts/ Scatter graphs 
  • Probability 
  • Inequalities
  • Compound measures

New Learning

  • Mean, median, mode, and range. 
  • Ratio notation and simplified ratios. 
  • Direct and indirect proportion. 
  • Standard conversion rates. 
  • Statistical diagrams. 
  • Probability concepts. 
  • Inequality notation including number line representations. 
  • Compound units of speed, density and pressure. 
  • Calculate averages and range. 
  • Reduce a ratio to simplest form. Divide a given quantity into two parts. 
  • Solve proportion problems in contexts. 
  • Use graphs to convert units. 
  • Construct charts for data. 
  • Calculate probabilities for single and combined events. 
  • Solve inequalities.  
  • Calculate compound measures. 
  • Make connections between number relationships and their graphical representations. 

Knowledge Revisited

  • Data handling 
  • Basic Probability concepts 

Knowledge Developed

KS2 and Y7 Knowledge.

Year 9

Autumn Term

Theme

  • Rules of Indices 
  • Standard Form 
  • Estimation  
  • Error Intervals and Bounds 
  • Percentage problems 
  • Quadratic expressions 
  • Fractions 
  • Ratio and Proportion  
  • Angles

New Learning

  • Index laws. 
  • Standard form notation. 
  • Rounding rules, upper and lower limits. Error interval notation. 
  • Algebraic terms: quadratic expression. 
  • Geometry facts: parallel lines, polygons, interior and exterior angles. 
  • Simplifying expressions using laws of indices. 
  • Converting numbers to and from standard form. Calculating with standard form. 
  • Rounding and approximating, calculating error intervals. 
  • Solving percentage problems in variety of contexts. 
  • Expand and factorise quadratic expressions.  
  • Calculate with fractions, ratio, and proportions. 
  • Use and apply geometry facts to solve problems. 
  • Solve complex calculation problems, including multi step problems. 
  • Relate the language of ratios and the associated calculations to fractions and linear functions. 

Knowledge Revisited

Y7 and Y8 Content

Knowledge Developed

Y7 and Y8 Knowledge

Spring Term

Theme

  • Surface area and volume 
  • Probability 
  • Similarity 
  • Transformations 
  • Pythagoras’ Theorem 
  • Trigonometry 
  • Metric unit conversions 

New Learning

  • Shape formula: volume and surface area of cuboids and prisms. 
  • Probability concepts (Higher) 
  • Properties of transformations, congruent and similar shapes. 
  • Trigonometric ratios in right angled triangles. 
  • Standard metric units and their conversion rates. 
  • Calculate volumes and surface area of 3D shapes. 
  • Calculate probabilities and solve probability problems. 
  • Transform objects in four quadrants. 
  • Use similarity concepts to solve problems. 
  • Use Pythagoras and Trigonometry connections to solve problems. 
  • Convert metric units including area and volume. 
  • Solve complex calculation problems, including multi step problems. 
  • Select appropriate methods to apply to unfamiliar and non-routine problems and interpret the solution given the context.

Knowledge Revisited

Y7 and Y8 Content

Knowledge Developed

Y7 and Y8 Knowledge

Summer Term

Theme

  • Substitution 
  • Equations and Inequalities 
  • Simultaneous Equations 
  • Rearranging Formula 
  • Compound measures 
  • Straight line graphs 
  • Other types of graph. 
  • Constructions and Loci.

New Learning

  • Algebraic terms: formula, function, substitute, equation, inequality, simultaneous equation. 
  • Function properties: linear, quadratic, exponential, reciprocal. 
  • Compound units and their connections. 
  • The locus of a point. 
  • Solve equations and inequalities. Represent solutions on a number line. (Solve simultaneous equations) 
  • Rearrange a formula. 
  • Construct graphs for linear and quadratic functions. Use to find approximate solutions to equations. 
  • Solve problems involving compound measures. 
  • Complete standard compass constructions and solve loci problems 
  • Model situations using algebra or graphs. 
  • Find solutions from graphs.

Knowledge Revisited

Y7 and Y8 Content

Knowledge Developed

Y7 and Y8 Knowledge

Year 10

Autumn Term

Theme Foundation Level

  • Algebra concepts 
  • Equations, Linear and Quadratic  
  • Formula 
  • Inequalities 
  • Sequences 
  • Straight Line graphs 
  • Real life graphs 
  • Averages and Range 
  • Frequency Tables

Theme Higher Level

  • Standard Form 
  • Ratio 
  • Linear equations and Inequalities 
  • Simultaneous equations 
  • Linear Graphs 
  • Equations of Graphs 
  • Parallel and Perpendicular Lines 
  • Indices 
  • Quadratic Equations 
  • Quadratic curves 
  • Transformation of Graphs 
  • Rearranging Formula 
  • Quadratic Formula

New Learning

  • Equations of parallel and perpendicular lines. 
  • Values of negative and Fractional powers. 
  • Roots, intercepts and turning points for quadratic curves 
  • Quadratic Formula 
  • Use and apply operations to standard form and powers. 
  • Solve all forms of ratio problem. 
  • Solve linear and quadratic equations and inequalities 
  • Solve two linear equations in two unknowns. 
  • Construct graphs for non standard functions, translate and reflect graphs of functions. 
  • Find the equation of a line including parallel and perpendicular. 
  • Use the quadratic formula to solve a quadratic equation. 
  • Select concepts, methods, and techniques to apply to unfamiliar and non-routine problems.

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

Spring Term

Theme Foundation Level

  • Algebra concepts 
  • Equations, Linear and Quadratic  
  • Formula 
  • Inequalities 
  • Sequences 
  • Straight Line graphs 
  • Real life graphs 
  • Averages and Range 
  • Frequency Tables

Theme Higher Level

  • Standard Form 
  • Ratio 
  • Linear equations and Inequalities 
  • Simultaneous equations 
  • Linear Graphs 
  • Equations of Graphs 
  • Parallel and Perpendicular Lines 
  • Indices 
  • Quadratic Equations 
  • Quadratic curves 
  • Transformation of Graphs 
  • Rearranging Formula 
  • Quadratic Formula

New Learning

  • Equations of parallel and perpendicular lines. 
  • Values of negative and Fractional powers. 
  • Roots, intercepts and turning points for quadratic curves 
  • Quadratic Formula 
  • Use and apply operations to standard form and powers. 
  • Solve all forms of ratio problem. 
  • Solve linear and quadratic equations and inequalities 
  • Solve two linear equations in two unknowns. 
  • Construct graphs for non standard functions, translate and reflect graphs of functions. 
  • Find the equation of a line including parallel and perpendicular. 
  • Use the quadratic formula to solve a quadratic equation. 
  • Select concepts, methods, and techniques to apply to unfamiliar and non-routine problems

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

Summer Term

Theme Foundation Level

  • Probability 
  • Venn Diagrams 
  • Data Handling 
  • Stem and leaf diagrams 
  • Pythagoras’ Theorem 
  • Trigonometry 
  • Perimeter and Area. 

Theme Higher Level

  • Averages and Range 
  • All basic charts for displaying data. 
  • Data comparisons 
  • Cumulative Frequency 
  • Box plots 
  • Histograms 
  • Probability 
  • Functions 
  • Iterative processes 
  • Rates of change 
  • Gradient of a tangent 
  • Area under a curve 

New Learning

  • Statistics: Modal class, quartiles and interquartile range, cumulative frequency and box plots. 
  • Probability: dependent and combined events, tree diagrams. 
  • Function properties: inverse and composite functions 
  • Iteration formula 
  • Trapezium rule. 
  • Construct graphs for time series, box plots, histograms, cumulative frequency graphs. 
  • Calculate quartiles and interquartile range. 
  • Compare data using statistics. 
  • Calculate probability of combined events. 
  • Approximate solutions to equations using iterations. 
  • Find equation of a tangent to a curve and circle.  
  • Find area under a curve using trapezium rule. 
  • Reflect on how solutions have been affected by modelling assumptions.

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

Year 11

Autumn Term

Theme Foundation Level

  • Linear and Simultaneous equations 
  • Transformations 
  • Congruence and Similarity 
  • Angles and Bearings 
  • Measures and conversions 
  • Compound Measures 
  • Constructions and Loci 
  • Pythagoras and Trigonometry 

Theme Higher Level

  • Pythagoras’ Theorem 
  • Trigonometry 
  • Surds 
  • Area and Perimeter 
  • Arc length and Sector area 
  • Volume and Surface Area 
  • Similarity 
  • Transformations 
  • Angles and Bearings 
  • Sine and Cosine rule 
  • Sine rule for Area 
  • Circle Theorems

New Learning

  • Enhanced knowledge of number including surds. 
  • Shape formula: surface areas and volumes of spheres, pyramids and cones. Arc length and sector area formula. Invariant points. Trigonometric facts: sine rule, cosine rule, A=1/2abSinC. Geometric facts: Angles, bearings & circle theorems. 
  • Use/Apply operations to surds. 
  • Simplify, manipulate and factorise algebraic expressions involving surds. 
  • Calculate arc lengths, angles, and areas of sectors. Calculate volumes and surface areas of spheres, pyramids and cones. Construct enlargements of shapes with negative and fractional scale factors. Locate invariant points. 
  • Use and apply circle theorems when solving geometry problems 
  • Select concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

Spring Term

Theme Foundation Level

  • Types of Graph 
  • Real life Graphs 
  • Graphical solutions 
  • Area and Circumference  
  • 3D Shapes 
  • Volume and Surface Area 
  • Density and Rates of Change 
  • Trigonometry 
  • Similar Triangles

Theme Higher Level

  • Direct and Indirect Proportion 
  • Quadratic Equations and curves 
  • Non Linear Simultaneous equations 
  • Compound Measures 
  • Populations (capture/ recapture) 
  • Product rule for combinations 
  • Similarity (Area and Volume) 
  • Inequalities and regions 
  • Gradient and Equation of a Tangent  
  • Circle equations 
  • Area under a curve 
  • Vector Geometry 
  • Algebraic and Geometric proof 
  • Graphs of Trig functions 
  • Trig exact values (non calc methods) 
  • Congruence conditions 
  • Constructions and Loci

New Learning

  • Product rule for counting. 
  • Area and volume scale factors. 
  • Function properties of circles. 
  • Algebraic terms Identity, proof. Trigonometric facts: exact values of sin, cos, tan Properties of Trig functions. 
  • Geometric facts: vector notation. 
  • Conditions of congruence & similarity. 
  • The locus of a point. 
  • Construct and use equations to solve direct and indirect proportion problems. 
  • Solve linear and quadratic equations together using a substitution method. 
  • Convert compound units of density, pressure, and speed. Identify and use properties of congruent and similar shapes.  Add and subtract vectors, multiply a vector by a scalar.  
  • Construct the locus of a point. 
  • Identify variables & express relationships between variables algebraically & graphically. Use algebra to support and construct arguments and proof. Assess validity of an argument.

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

Summer Term

Theme Foundation Level

  • Transformations 
  • Vector Geometry 
  • Exam Practice  
  • Tailored revision topics.

Theme Higher Level

  • Exam Practice
  • Tailored revision topics

New Learning

Knowledge Revisited

Ks3 Content

Knowledge Developed

Ks3 Knowledge

For further information regarding our curriculum please contact the admin team at reception@pendlevale.lancs.sch.uk