Mathematics
BackMathematics includes the study of number, geometry, algebra and data handling whilst also developing thinking and problem solving skills. In addition to helping you develop good numeracy skills, studying mathematics, even those topics not immediately applicable to real-world situations, will help you develop your ability to think around a problem and find a creative solution.
Learning Journey
Year 7
At Key Stage 3, all pupils follow the same maths curriculum, which is designed to help them build strong foundations in number, algebra, geometry and statistics. They develop confidence with calculations and learn how to use mathematical language clearly and accurately.
Over the three years, pupils move from learning basic methods to using their maths independently in a range of different situations. They are encouraged to solve problems, explain their thinking, and make connections between different topics. There is a focus on reasoning, spotting patterns, and justifying answers.
As pupils progress through Years 7 to 9, the work becomes more challenging, helping them to deepen their understanding and think more like mathematicians. By the end of Key Stage 3, pupils are well prepared to move on to GCSE Maths with confidence.
| Key Knowledge: | |
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| Number and Algebra Autumn Term Developing: Understand and use simple algebraic expressions Solve one-step equations Predict next term in a sequence Convert between fractions, decimals and percentages Use column methods for addition and subtraction Order integers and decimals Meeting: Solve two-step equations Convert fluently between fractions, decimals and percentages Solve multi-step problems using number and algebra Explain term to term rules Order and compare numbers accurately Explain reasoning clearly using appropriate mathematical language Greater depth: Expand expressions involving brackets Solve equations involving negative numbers Generalise patterns using algebra Finding missing numbers within a sequence Add and subtract numbers given in standard form Solve unfamiliar and non-routine problems Justify answers with clear and precise reasoning Multiplicative Reasoning and Number Spring Term Developing: Find fractions, decimals and percentages of amounts in simple cases Understand positive and negative numbers Perform basic calculations using the four operations Meeting: Solve multi-step problems involving fractions, decimals and percentages Use all four operations confidently and accurately Apply mathematical skills in real-life contexts Work fluently with directed (positive and negative) numbers Greater Depth: Solve complex problems involving fractions, decimals and percentages Link different areas of number together Apply reasoning to unfamiliar problems Work efficiently and accurately with increasing independence Geometry, Algebra and Synoptic Reasoning Summer Term Developing: Identify and name angles Use simple fractions in calculations Substitute values into algebraic expressions Recognise types of triangles and quadrilaterals Meeting: Solve problems involving angles Construct triangles and more complex polygons Substitute into expressions and solve equations Interpret and draw pie charts Solve multi-step problems across topics Explain reasoning clearly Greater Depth: Solve complex geometry problems Perform calculations with fractions fluently Demonstrate strong algebraic fluency Apply skills independently in mixed-topic problems Communicate solutions clearly and logically | |
| Year 7 Assessment Points: Students complete a check in at the end of each unit to reflect on what they have learnt, which includes fluency, reasoning and problem solving. These help students to identify their strengths and weaknesses and their level for each topic to help them prepare for formal assessments throughout the year. The formal assessment points enable students to demonstrate whether they are developing, meeting or at greater depth for the topics in the assessment. The formal assessment points in year 7 are: Baseline assessment – review of prior KS2 knowledge Assessment 1 – Sequences, algebraic notation, equality and equivalence, place value, fractions, decimals and percentages Assessment 2 – Four operations, fractions and percentages of amounts, directed number | |
| Key Vocabulary Algebra, expression, equation, substitute, integer, decimal, fraction, percentage, equivalent, simplify, expand, factor, order, compare, reciprocal, product, sum, difference, quotient, negative number, directed number, angle, vertex, parallel, perpendicular, reasoning, justify | Enrichment Maths puzzles and investigations to develop reasoning (e.g. pattern spotting, sequences, logic problems) Practical activities such as measuring, constructing shapes, and using maths in real-life contexts (e.g. budgeting challenges) Online platforms to build confidence with number fluency and algebra basic Junior UKMT challenges or in-school competitions to develop reasoning and justification skills |
Year 8
At Key Stage 3, all pupils follow the same maths curriculum, which is designed to help them build strong foundations in number, algebra, geometry and statistics. They develop confidence with calculations and learn how to use mathematical language clearly and accurately.
Over the three years, pupils move from learning basic methods to using their maths independently in a range of different situations. They are encouraged to solve problems, explain their thinking, and make connections between different topics. There is a focus on reasoning, spotting patterns, and justifying answers.
As pupils progress through Years 7 to 9, the work becomes more challenging, helping them to deepen their understanding and think more like mathematicians. By the end of Key Stage 3, pupils are well prepared to move on to GCSE Maths with confidence.
| Key Knowledge: | |
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Number, Ratio and Proportional Reasoning, Graphs and Data Autumn Term Developing: Develop confidence with number relationships and use ratio notation Understand simple multiplicative change (e.g. percentages of amounts) Multiply and divide fractions with guidance Plot coordinates in the first quadrant Interpret simple data and charts Construct sample spaces Use clear methods to solve problems Meeting: Apply ratio and scale factors fluently Solve problems involving percentage change and proportional reasoning Multiply and divide fractions confidently Understand and use the reciprocal Recognise and use lines of the form y= kx and link to proportion Represent and interpret data using a range of methods Calculate probabilities from tables and diagrams Greater Depth: Solve complex problems involving ratio and proportional reasoning, including the use of gradient as a ratio Explore direct proportion graphs Explore non-linear graphs Find the midpoint of a line segment Solve multi-step problems involving probability and algebra Analyse and interpret complex data representations Generalise relationships and explain patterns Justify answers using clear mathematical reasoning
Algebra and number Spring Term Developing: Substitute values into simple expressions Solve one-step and simple two-step equations Continue linear sequences from a given rule Find fractions and simple percentages of amounts Recognise and use square and cube numbers Investigate positive powers of 10 Develop number sense including place value, rounding and checking answers Use simple algebraic expressions and sequences Meeting: Expand single brackets Solve two-step equations Form and solve simple inequalities Find simple nth terms for linear sequences Work with percentage change Solve percentage problems including increase and decrease Apply index laws for multiplication and division Write and convert numbers in standard form Use number sense to estimate and check answers Greater Depth: Expand double brackets Solve equations and inequalities with unknowns on both sides Form and use nth term rules for sequences Generalise sequences and represent them algebraically Solve multi-step problems involving fractions and percentages Calculate reverse percentages and repeated percentage change Apply full index laws including negative indices Calculate with numbers in standard form Use number sense to justify methods and check solutions in complex problems Apply algebra fluently in unfamiliar contexts
Geometry and Statistical Reasoning (Summer Term) Developing: Identify lines of symmetry and perform simple reflections in a mirror line Interpret simple data from charts and understand stages of the data handling cycle (collect, process, present, interpret) Find the mean (basic), median and mode from small data sets Use angles on a straight line and around a point Recognise corresponding and alternate angles in parallel lines Calculate the area of triangles, rectangles and parallelograms Meeting: Reflect shapes in horizontal, vertical and diagonal mirror lines on a grid Apply the data handling cycle to solve problems and interpret results Calculate mean, median, mode and range from data sets, including interpreting grouped data Use angle facts in parallel lines to solve problems with reasoning Calculate interior and exterior angles of polygons Use and apply the trapezium area formula confidently Calculate area and circumference of circles and solve simple problems involving circles Greater Depth: Perform reflections in any line and describe transformations fully Interpret and evaluate data using the full data handling cycle, including identifying bias or limitations Compare sets of data using averages and range, and interpret grouped data more deeply Solve multi-step angle problems involving parallel lines and polygons with justification Deduce and apply angle rules in complex diagrams Solve problems involving area of trapezium and circles, including multi-step and compound contexts Construct angle bisectors and perpendicular bisectors of a line segment |
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Year 8 Assessment Points: Students complete a check in at the end of each unit to reflect on what they have learnt, which includes fluency, reasoning and problem solving. These help students to identify their strengths and weaknesses and their level for each topic to help them prepare for formal assessments throughout the year. The formal assessment points enable students to demonstrate whether they are developing, meeting or at greater depth for the topics in the assessment. The formal assessment points in year 8 are: Assessment 1 – Ratio and scale, multiplicative change Assessment 2 – Multiplying and dividing fractions, coordinates and graphs, representing data, probability Assessment 3 – Brackets, equations and inequalities, sequences, indices, fractions and percentages, standard form |
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Key Vocabulary Ratio, scale factor, proportion, percentage change, fraction, multiplicative, Cartesian plane, coordinate, probability, expression, equation, inequality, sequence, index, standard form, angle, polygon, transformation, symmetry, data, mean, median |
Enrichment Problem-solving projects involving ratio, proportion and real-life applications (e.g. scale drawings, best buys) Exploration of graphs through digital tools (e.g. Desmos) to deepen understanding of relationships Data investigations where students collect, represent and interpret their own data Junior UKMT challenges or in-school competitions to develop reasoning and justification skills |
Year 9
At Key Stage 3, all pupils follow the same maths curriculum, which is designed to help them build strong foundations in number, algebra, geometry and statistics. They develop confidence with calculations and learn how to use mathematical language clearly and accurately.
Over the three years, pupils move from learning basic methods to using their maths independently in a range of different situations. They are encouraged to solve problems, explain their thinking, and make connections between different topics. There is a focus on reasoning, spotting patterns, and justifying answers.
As pupils progress through Years 7 to 9, the work becomes more challenging, helping them to deepen their understanding and think more like mathematicians. By the end of Key Stage 3, pupils are well prepared to move on to GCSE Maths with confidence.
| Key Knowledge: | |
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Algebra Graphs and Geometry Autumn Term Developing: Understand and plot straight line graphs Form and solve simple equations Recognise patterns and relationships in algebra Interpret basic graphical representations Identify properties of 2D and 3D shapes Recognise nets of shapes Construct and interpret scale drawings Identify congruent triangles HCF and LCM Meeting: Solve linear equations and represent them graphically Interpret and use straight line graphs in context Substitute into formulae and equations Test conjectures Rearrange formulae Calculate surface area and volume of prisms Explore and construct Loci Link algebraic and graphical representations Numbers in standard form Greater Depth: Rearrange complex formulae including brackets and squares Model real life graphs involving inverse proportion Explore perpendicular lines Expand three binomials Solve complex problems involving algebra and graphs Explore volumes of cones, pyramids and spheres Understand and use Surds Interpret and analyse relationships between variables Justify conclusions using algebraic reasoning
Geometry and Reasoning Spring Term Developing: Convert between fractions, decimals and percentages; find percentages of amounts Increase and decrease amounts by a percentage Solve simple money problems including totals, change and budgeting Calculate angles in parallel lines Use basic angle facts to find missing angles and explain simple reasoning Rotate shapes by 90° and 180° on a grid, identifying centre of rotation Identify the hypotenuse on a right-angled triangle Calculate the hypotenuse using Pythagoras theorem Meeting: Use multipliers for percentage increase/decrease and calculate percentage change Solve reverse percentage problems and link to proportional reasoning Solve multi-step financial problems including profit, loss and interest Construct chains of reasoning using angle facts and algebra Rotate shapes about any point and describe transformations Apply Pythagoras in problem-solving and coordinate geometry Solve multi-step problems involving right-angled triangles Greater Depth: Solve repeated percentage change and exponential growth problems Apply compound interest and compare financial models Construct multi-step geometric proofs using algebraic reasoning Describe and combine transformations Apply Pythagoras in 3D and with surds Solve complex multi-step problems involving geometry Justify conclusions clearly using structured mathematical arguments
Number, Ratio and Proportional Reasoning Summer Term Developing: Enlarge shapes using positive integer scale factors and identify centres Simplify ratios and share amounts in a given ratio Use simple rate calculations such as distance = speed x time Identify outcomes and calculate simple probabilities Recognise parts of a circle and calculate area and circumference Form simple algebraic expressions and substitute values Solve basic problems linking number, ratio and geometry Meeting: Enlarge shapes using fractional scale factors and solve similarity problems Solve multi-step ratio and proportion problems in context Work with compound measures and convert units in rate problems Use sample spaces and tree diagrams to calculate probabilities Draw and interpret quadratic graphs Greater Depth: Use negative and fractional scale factors and prove similarity results Solve complex proportional reasoning including direct and inverse proportion Interpret and solve multi-step rate problems and graphs Use tree diagrams with dependent events and conditional probability Investigate graphs of simultaneous equations |
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Year 9 Assessment Points: Students complete a check in at the end of each unit to reflect on what they have learnt, which includes fluency, reasoning and problem solving. These help students to identify their strengths and weaknesses and their level for each topic to help them prepare for formal assessments throughout the year. The formal assessment points enable students to demonstrate whether they are developing, meeting or at greater depth for the topics in the assessment. The formal assessment points in year 9 are: Assessment 1 – Equations, straight line graphs, conjectures, Assessment 2 – 3D shapes, constructions and congruency Assessment 3 – Numbers, percentages, maths and money, deduction, rotation and translation, Pythagoras’ theorem End of Year Assessment – covers all KS3 knowledge |
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Key Vocabulary Algebra, equation, expression, variable, coefficient, substitute, inequality, gradient, intercept, graph, axis, coordinate, linear, sequence, term, generalise, conjecture, justify, proof, congruence, construction, polygon, angle, parallel, perpendicular, ratio, proportion, percentage, multiplier, scale factor, compound, interpret, analyse, data, distribution, reasoning |
Enrichment Extended problem-solving tasks linking algebra, geometry and graphs (e.g. modelling real-life situations) Financial maths projects (e.g. interest, budgeting, comparing deals) to support proportional reasoning Introduction to GCSE-style reasoning and multi-step exam questions Intermediate UKMT challenges or in-school competitions to develop reasoning and justification skills |
Year 10
In Years 10 and 11, you will begin and complete your GCSE Maths course. You will build on what you learnt in Key Stage 3 and develop your understanding of number, algebra, geometry and statistics.
You will become more confident in solving longer, more challenging problems and explaining your thinking clearly. Throughout the two years, you will revisit important topics, deepen your understanding and make links between different areas of maths.
You will also practise exam-style questions and learn how to approach them with confidence, so that you are fully prepared for your GCSE exams, whether you are studying at Foundation or Higher level.
| Key Knowledge: | |
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Number, Algebra and Geometric reasoning: Autumn Term Foundation: Use non-calculator methods for the four operations, including with decimals and fractions Simplify and use ratios, including sharing quantities and linking to fractions Solve best buy problems Understand and apply congruency in simple geometric contexts Use enlargement with positive scale factors and recognise similarity Establish a pair of triangles are similar Calculate sides in right angles triangles using Pythagoras Apply basic trigonometry (SOHCAHTOA) to find missing sides in right-angled triangles Represent and solve linear equations and inequalities and show solutions on number lines Higher: Understand rational and irrational numbers including recurring decimals Calculate using bounds Solve complex ratio and fraction problems, including multi-step proportional reasoning Use similarity and enlargement with fractional and negative scale factors Prove and apply congruency using formal criteria (SSS, SAS, ASA, RHS) Explore areas and volumes of similar shapes Apply trigonometry to solve problems, including in 3D contexts Apply the sine and cosine rule to find missing lengths and angles Represent and solve linear and quadratic equations and inequalities, including graphical solutions Interpret regions defined by inequalities and connect algebraic and graphical representations
Algebra and Geometric reasoning: Spring term Foundation: Solve pairs of simultaneous equations (linear) using substitution or elimination Use bearings measured clockwise from north and solve problems in context Calculate angles in geometric figures, including polygons and around parallel lines Calculate circumference and area of circles and use in problem-solving Identify and use basic circle properties Calculator arc length and sector area Understand and calculate the volume and surface area of 3D shapes Represent vectors and describe simple vector movements Perform basic vector calculations (addition and subtraction) Higher: Solve simultaneous equations including linear–quadratic systems Solve problems involving bearings and scale diagrams using sine and cosine rules Apply geometric reasoning to complex angle problems including proofs Use circle theorems (e.g. alternate segment, cyclic quadrilaterals) Solve problems involving arcs, sectors and circle geometry Use vectors algebraically and solve geometric problems with vectors Construct and prove results using vector methods
Summer Term: Geometry, Statistics and Number Reasoning Foundation: Calculate percentage increase/decrease and simple and compound interest Solve probability problems using lists, tables and simple tree diagrams Collect, represent and interpret data using charts and averages including frequency polygons, scatter diagrams and pie charts Calculate averages from a table Understand types of numbers including primes, factors and multiples Generate and find the nth term of a linear sequences Use index notation for positive integer powers and apply addition and subtraction rules Calculate and simplify expressions involving roots (including square roots) Higher: Solve problems involving growth and decay Understand iterative processes Conditional probability in two way tables and venn diagrams Interpret and analyse data, including cumulative frequency, box plots and histograms Generate and use algebraic rules for sequences, including quadratic sequences and surds Apply index laws including fractional and negative powers Simplify surds and solve problems involving indices and roots |
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Assessment Points Students complete a check in at the end of each unit to reflect on what they have learnt, which includes fluency, reasoning and problem solving. This will be either foundation or higher depending on their current tier. These help students to identify their strengths and weaknesses and their level for each topic to help them prepare for formal assessments throughout the year. The formal assessment points enable students to demonstrate the GCSE grade they are working at for the topics in the assessment. The formal assessment points in year 10 are: Baseline assessment – review of prior KS3 knowledge Assessment 1 – Non-calculator methods, ratio and fractions Assessment 2 – Congruence, similarity and enlargement, trigonometry, equations and inequalities, simultaneous equations End of Year assessment – GCSE papers covering all year 10 content |
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Key Vocabulary Non-calculator methods, ratio, proportion, fraction, scale factor, congruence, similarity, enlargement, trigonometry, sine, cosine, tangent, equation, inequality, simultaneous equations, angle, bearing, circle, radius, diameter, circumference, vector, percentage, interest, probability, outcome, frequency, data, sequence, term, index, root, reasoning. |
Enrichment Regular exposure to GCSE exam-style problems beyond the classroom, including higher-tier challenge questions Use of past papers and exam workshops focusing on strategy and problem solving STEM-based enrichment such as applying trigonometry, vectors and algebra in real-world contexts (e.g. engineering links) Maths revision clubs, peer tutoring, and independent study Intermediate UKMT challenges to develop reasoning and justification skills. |
Year 11
In Years 10 and 11, you will begin and complete your GCSE Maths course. You will build on what you learnt in Key Stage 3 and develop your understanding of number, algebra, geometry and statistics.
You will become more confident in solving longer, more challenging problems and explaining your thinking clearly. Throughout the two years, you will revisit important topics, deepen your understanding and make links between different areas of maths.
You will also practise exam-style questions and learn how to approach them with confidence, so that you are fully prepared for your GCSE exams, whether you are studying at Foundation or Higher level.
| Key Knowledge: | |
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Autumn Term: Algebra and Graphical Reasoning Foundation: Find gradients from graphs and between two coordinates Identify and sketch basic non-linear graphs (quadratic, cubic) Rearrange simple linear expressions Recognise key features of graphs (intercepts, turning points) Use graphs to find approximate solutions Expand single and double brackets Factorise expressions into brackets including quadratics Change the subject of simple formulae Solve equations involving brackets Higher: Calculate gradients including parallel and perpendicular lines Sketch and interpret quadratic, cubic, reciprocal graphs Expand and simplify expressions with multiple terms Recognise transformations of graphs Use algebraic manipulation to prepare for solving equations Factorise quadratics (including where a ≠ 1) Use graphs to solve equations (including quadratics) Interpret gradient and area under graphs Rearrange complex formulae (subject in denominator, brackets) Link algebraic solutions to graphical representations
Spring Term: Functions, Multiplicative and Algebraic Reasoning Foundation: Understand and use function notation (e.g. f(x)) Substitute values into functions Use ratio in real-life contexts Use basic Pythagoras’ Theorem Solve linear equations (including with brackets) Form expressions and equations from word problems Recognise and describe transformations (reflection, rotation, translation) Plot and describe transformations on grids Construct triangles using given measurements Identify symmetry in shapes Higher: Use composite functions and inverse functions Solve problems involving direct and inverse proportion Apply ratio and proportion in multi-step problems Solve angle problems including algebraic reasoning Solve simultaneous equations (algebraically and graphically) Solve quadratic equations (factorising and formula where needed) Use algebra in complex problem-solving contexts Describe and perform combined transformations Construct loci and interpret regions Solve geometric problems using reasoning and proof |
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Assessment Points Students complete a check in at the end of each unit to reflect on what they have learnt, which includes fluency, reasoning and problem solving. This will be either foundation or higher depending on their current tier. These help students to identify their strengths and weaknesses and their level for each topic to help them prepare for formal assessments throughout the year. The formal assessment points enable students to demonstrate the GCSE grade they are currently working at. The formal assessment points in year 11 are: Baseline assessment – review of year 10 content Mock set 1 – GCSE papers covering all content Mock set 2 – GCSE papers covering all content |
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Key Vocabulary Gradient, line, graph, expression, factorise, expand, non-linear, function, formula, subject, multiplicative, proportion, geometric reasoning, algebraic reasoning, transform, construct, proof, justify, describe, sequence, revision, exam technique. |
Enrichment Structured revision programmes including walking-talking mocks and targeted intervention sessions Completion and analysis of past GCSE papers to refine exam technique and timing High-level problem-solving practice (especially for Higher tier students) focusing on reasoning and proof Independent revision resources, including checklists, topic-based practice and self-quizzing strategies. Intermediate UKMT challenges to develop reasoning and justification skills |
| Subject Documents |
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| Maths GCSE Foundation Revision Tasks |
| Maths GCSE Higher Revision Tasks |