Mathematics
Intent
At Leighton Middle School, we believe that Mathematics should be ambitious, accessible and meaningful for every pupil. Our aim is to inspire young people to see the beauty, usefulness and power of Mathematics in the wider world, from science and technology to financial literacy, careers, problem solving and independent living.
We want pupils to become fluent, confident and resilient mathematicians who can recall key knowledge, make connections between topics, reason logically and apply their understanding to unfamiliar problems. Through our Year 5 to Year 8 curriculum journey, pupils revisit and build upon the key strands of number, geometry, data and algebra, developing increasingly secure understanding as they move through the school.
Mathematical language is central to our curriculum. Pupils are supported to use correct terminology, explain methods clearly, justify answers and discuss mathematical ideas with confidence. We explicitly teach vocabulary, model mathematical thinking and encourage verbal fluency so that pupils can communicate their reasoning accurately in both spoken and written form.
We are committed to supporting every pupil to make progress from their individual starting point. We recognise the importance of securing prerequisite knowledge, building confidence, providing regular opportunities for practice and ensuring that adaptation is planned in advance so that all pupils can access ambitious mathematical learning.
Implementation
Curriculum sequencing
Our mathematics curriculum is carefully sequenced from Year 5 to Year 8 to ensure progression, revisiting and readiness for the next stage of education. Pupils move through a coherent journey across number, geometry, data and algebra, with important knowledge revisited regularly so that pupils can strengthen, connect and apply their learning over time.
At Key Stage 2, the curriculum is informed by White Rose Maths, DfE Ready to Progress guidance and NCETM materials. At Key Stage 3, MyMaths textbook references support the curriculum structure, while teachers adapt resources and tasks to meet the needs of their classes.
Retrieval, fluency and interleaving
Key knowledge is deliberately revisited through retrieval practice and interleaving. Pupils regularly return to earlier learning so that knowledge is remembered, strengthened and applied in new contexts.
Fluency is developed through regular arithmetic, carefully chosen practice, questioning and low-stakes recall. Teachers prioritise secure understanding, accurate vocabulary, fluency and reasoning rather than simply moving through content quickly.
Teaching approaches and resources
Teachers use clear modelling, worked examples, representations, diagrams, bar models and structured questioning to help pupils understand the Mathematics behind a method, not just copy a process.
Pupils are encouraged to justify answers, compare strategies, analyse mistakes and explain why a method works. Resources such as White Rose Maths, NCETM materials, MyMaths, Times Tables Rock Stars, Google Classroom and teacher-designed activities are used where they best support learning.
Mathematical Terminology and verbal fluency
Mathematical talk is built into lessons through structured learning-partner work, discussion stems and collaborative reasoning. Pupils are taught how to listen, challenge respectfully, explain their thinking and improve their answers using precise mathematical vocabulary.
The Maths Word Wall, three-read protocol and sentence stems support pupils in accessing reasoning and problem-solving questions. Pupils are encouraged to speak and write like mathematicians, using correct terminology to explain, justify and refine their ideas.
Adaptive teaching and inclusion
Adaptive teaching is planned before the lesson begins. Teachers use assessment evidence, pupil profiles, prior knowledge and likely misconceptions to plan scaffolds, representations, support, challenge and extension.
This allows all pupils, including those with SEND, disadvantaged pupils, EAL pupils and pupils who need additional fluency support, to access the intended Mathematics while maintaining high expectations. Adaptation is not about lowering ambition; it is about removing barriers so that pupils can engage successfully with challenging mathematical ideas.
Assessment and responsive teaching
Assessment is used to inform teaching. Teachers use questioning, mini-whiteboards, classwork, homework, formal assessments and question-level analysis to identify strengths, gaps and misconceptions.
This information is used to plan retrieval, re-teaching, intervention and future adaptation. Pupils are given opportunities to respond to feedback, correct errors and understand the next steps in their learning.
Use of technology and AI
Technology and digital tools are used where they enhance learning, planning and adaptation. This may include MyMaths, Times Tables Rock Stars, Google Classroom and carefully selected teacher tools.
The department also encourages responsible and effective use of AI by teachers to support planning, retrieval design, scaffolding, task variation and adaptation. Professional judgement, mathematical accuracy, safeguarding and pupil confidentiality remain central at all times.
Impact
Pupils at Leighton Middle School develop as confident, fluent and resilient mathematicians. They become increasingly able to recall prior learning, select appropriate methods, explain their reasoning and make connections between mathematical ideas.
As pupils move through Years 5 to 8, they build secure foundations in number, geometry, data and algebra and are prepared for the mathematical demands of upper school. They learn that Mathematics is not just about finding an answer, but about explaining, proving, questioning and applying ideas.
Pupils become more confident in using correct terminology, speaking mathematically, working with learning partners and tackling unfamiliar problems with independence and perseverance. Teachers know their pupils well and use assessment information to identify next steps, close gaps and provide appropriate challenge.
The impact of our curriculum is seen in pupils’ confidence, progress, outcomes and attitudes towards Mathematics. Pupils leave Leighton Middle School ready for the next stage of their mathematical journey, with the knowledge, skills, vocabulary and confidence needed to continue progressing successfully.
KS2 Arithmetic Methods
Curriculum Overview
Year 5
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Autumn Term: |
Autumn Term: |
Spring Term: |
Spring Term: |
Summer Term: |
Summer Term: |
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Topics: 2. Multiplication and division in context; 3. Addition and subtraction; 7. Shape, position and direction
Knowledge:
Skills: • Read, write, compose, compare and order whole numbers and decimals; round to specified place values and use negative numbers on a number line. • Multiply and divide by powers of ten, scale known facts and identify common factors, common multiples, primes, square numbers and cube numbers. • Continue number sequences and state term-to-term rules. • Use column addition and subtraction with numbers beyond four digits; estimate, use inverse operations and solve multi-step problems. • Plot coordinates in the first quadrant and describe or perform translations and reflections.
Vocabulary:
Career examples: Game designer |
Topics: 4. Multiplication and division - formal methods; 5. Fractions - continued; 6. Area and perimeter
Knowledge:
Skills: • Recognise equivalent fractions; convert between improper fractions and mixed numbers; compare and order fractions on number lines. • Multiply up to four digits by one or two digits using area and column methods. • Use short division and interpret remainders as remainders, fractions or decimals. • Add and subtract fractions and mixed numbers, including different denominators. • Measure and calculate perimeter, and calculate the area of rectangles, compound shapes and irregular shapes.
Vocabulary:
Career examples: Carpenter |
Topics: 8. Statistics; 9. Decimals and percentages
Knowledge:
Skills: • Multiply integers by unit, non-unit and mixed-number fractions; represent fractions of amounts with bar models. • Read, draw and solve problems using line graphs. • Read and interpret tables, two-way tables and timetables, including duration. • Read, write, order and compare decimals to thousandths; round to the nearest whole, tenth and hundredth. • Write decimals as fractions and identify equivalent fractions, decimals and percentages.
Vocabulary:
Career examples: Event planner |
Topics: 11. Decimals - part 2
Knowledge:
Skills: • Recognise, compare, estimate, measure and draw acute, right, obtuse and reflex angles. • Calculate angles on a straight line, around a point and within shapes. • Describe regular and irregular polygons and reason about properties of 3D shapes. • Add and subtract decimals with the same or different numbers of decimal places, including totals greater than one. • Find complements to one, continue decimal sequences, and multiply or divide decimals by 10, 100 and 1,000.
Vocabulary:
Career examples: Architect |
Topics: 13. Volume; 14. Roman numerals
Knowledge:
Skills: • Convert between metric units and use approximate metric-imperial equivalents. • Convert between minutes and hours and read timetables. • Explain, compare and estimate volume and capacity; find volume by counting cubes. • Read and write Roman numerals to 1,000.
Vocabulary:
Career examples: Chef |
Topics:
Knowledge:
Skills: • Consolidate the four operations, fractions, decimals, measures and geometry through mixed problem solving. • Select efficient methods, explain reasoning and use mathematical vocabulary accurately. • Use bar models and diagrams to represent multi-step calculations. • Plan a budget and explore saving, spending, pricing and value for money. • Revisit class and individual priorities identified through assessment.
Vocabulary:
Career examples: Entrepreneur / business founder |
Year 6
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Autumn Term: |
Autumn Term: |
Spring Term: |
Spring Term: |
Summer Term: |
Summer Term: |
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Topics:
Knowledge:
Skills: • Compose, decompose, compare and calculate with whole numbers and decimals to 10 million; multiply and divide by powers of ten. • Use formal addition, subtraction, multiplication and division, including decimals, remainders and multi-step word problems. • Read and write Roman numerals to 3,000. • Find factors, HCF, multiples, LCM, primes and prime factors; use squares, cubes, roots and index notation. • Find, simplify and order equivalent fractions; find fractions of amounts and money; convert fractions to decimals.
Vocabulary:
Career examples: Software engineer; cybersecurity analyst; pharmacist |
Topics:
Knowledge:
Skills: • Plan surveys and represent or interpret data in pictograms, bar graphs and line graphs; calculate mean, median, mode and range. • Multiply and divide decimals by 10, 100 and 1,000; measure accurately and convert metric units. • Calculate perimeter and read or convert 12-hour and 24-hour timetables. • Measure and draw angles, including reflex angles; use facts for straight lines, opposite angles and angles around a point. • Recall FDP equivalents, find percentages of amounts and solve percentage-change problems.
Vocabulary:
Career examples: Sport statistician; civil engineer; air traffic controller; marketing analyst |
Topics:
Knowledge:
Skills: • Order positive and negative integers and decimals; find differences, double and halve, use money, round and estimate. • Classify 2D shapes; compare quadrilaterals and triangles; identify line and rotational symmetry and label circle parts. • Calculate perimeter and area of squares, rectangles, triangles, parallelograms, compound shapes and, where appropriate, trapeziums. • Represent perimeter and area with algebraic expressions. • Solve one- and two-unknown problems; express, simplify and use ratios, scale factors and direct proportion. • Construct and interpret line graphs, bar graphs and simple pie charts.
Vocabulary:
Career examples: Meteorologist; graphic designer; architect; chef; data journalist |
Topics:
Knowledge:
Skills: • Add, subtract, multiply and divide fractions and mixed numbers; simplify, compare and convert between fractions, decimals and percentages. • Calculate with positive and negative numbers and use BIDMAS. • Continue negative and decimal sequences; state term-to-term rules and use nth-term rules. • Round whole numbers and decimals, then calculate missing angles in triangles, quadrilaterals and combined diagrams. • Plot coordinates and translate or reflect shapes in four quadrants.
Vocabulary:
Career examples: Medical researcher; robotics programmer; surveyor; game designer |
Topics:
Knowledge:
Skills: • Compare data represented in different ways, including missing data; interpret pie charts and time-distance graphs. • Read time accurately, convert durations and calculate time differences. • Read varied scales and convert mass, length and distance units. • Calculate the volume of cubes and cuboids and solve volume problems. • Collect like terms, use indices in expressions and find values satisfying equations with two unknowns. • Revisit division by fractions and complex fraction-decimal equivalents in money contexts.
Vocabulary:
Career examples: Transport planner; aerospace engineer; economist |
Topics:
Knowledge:
Skills: • Complete SATs and GL assessments and respond to identified areas for consolidation. • Use reasoning and problem solving in investigations such as tessellations and orienteering. • Prepare for KS3 sequences, expressions, substitution and equations. • Apply number, fraction and reasoning skills in unfamiliar contexts. • Explore saving, spending, budgeting and managing money.
Vocabulary:
Career examples: Entrepreneur / business founder |
Year 7
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Autumn Term: |
Autumn Term: |
Spring Term: |
Spring Term: |
Summer Term: |
Summer Term: |
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Topics:
Knowledge:
Skills: • Convert units, calculate with time, read scales and find perimeter and area; extend to surface area and volume where secure. • Compare, order and convert fractions, decimals and percentages; add and subtract fractions and find fractions or percentages of amounts. • Use algebraic notation, collect like terms, substitute, write formulae and expand simple brackets. • Plot coordinates, draw and interpret line graphs and connect tables, rules and graphs. • Use BIDMAS, calculators, rounding and estimation accurately.
Vocabulary:
Career examples: Quantity surveyor; sports performance analyst; software developer; transport planner |
Topics:
Knowledge:
Skills: • Plan data collection and represent information in tables, bar charts, pictograms, pie charts and frequency tables. • Calculate and compare mean, median, mode and range; discuss bias and reliability. • Use efficient mental and formal methods for all four operations, round appropriately and solve multi-step problems. • Apply BIDMAS, estimation, inverse operations and calculator checks. • Measure and draw angles; use angle facts at a point, on a line, in triangles, quadrilaterals and parallel lines.
Vocabulary:
Career examples: Data analyst; accountant; architect |
Topics:
Knowledge:
Skills: • Find factors and multiples; identify primes, squares and roots; use divisibility tests and prime factor decomposition. • Use HCF and LCM to solve problems where secure. • Solve one- and two-step equations, construct equations from contexts and check by substitution. • Reflect, translate and rotate shapes and identify line or rotational symmetry. • Recognise tessellations and extend to enlargement from a point where secure.
Vocabulary:
Career examples: Cryptographer; robotics engineer; animator |
Topics:
Knowledge:
Skills: • Consolidate FDP conversion, calculation and problem solving at the level needed by the class. • Apply mathematics to real-life, multi-step and investigative contexts and explain reasoning. • Construct triangles, perpendicular bisectors and angle bisectors accurately. • Use scale drawings and interpret or draw nets, plans, elevations and isometric representations. • Recognise 3D-shape properties and explore volume.
Vocabulary:
Career examples: Product designer |
Topics:
Knowledge:
Skills: • Use probability language and scales; compare equally likely and mutually exclusive outcomes. • Express and compare probability as fractions, decimals and percentages; use Venn diagrams where appropriate. • Continue sequences, describe term-to-term rules and generate terms. • Connect sequences to algebraic expressions and nth-term rules where secure. • Express and simplify ratios, divide in a given ratio and solve direct-proportion problems.
Vocabulary:
Career examples: Game designer; music producer; pharmacist |
Topics:
Knowledge:
Skills: • Multiply and divide decimals using mental and written methods. • Use calculator functions and BIDMAS accurately and check answers by estimation. • Compare unit prices, proportional deals and best value. • Interpret bills, tickets, timetables and data and select efficient methods for multi-step problems. • Plan budgets and explore income, expenditure, saving, profit, loss and financial choices.
Vocabulary:
Career examples: Event planner; entrepreneur / business founder |
Year 8
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Autumn Term: |
Autumn Term: |
Spring Term: |
Spring Term: |
Summer Term: |
Summer Term: |
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Topics:
Knowledge:
Skills: • Compare and order positive and negative numbers, decimals and fractions; revisit the four operations. • Use factors, multiples, primes, HCF, LCM, prime factor decomposition, roots and indices. • Round and estimate using decimal places and significant figures; interpret upper and lower bounds. • Use inequality notation and represent intervals on number lines. • Collect like terms, simplify expressions, expand brackets, factorise and substitute into formulae. • Write and rearrange formulae, extending to algebraic fractions where secure.
Vocabulary:
Career examples: Cybersecurity specialist; software engineer |
Topics:
Knowledge:
Skills: • Calculate angles in lines, triangles, quadrilaterals, parallel lines and polygons; use congruence and proof where secure. • Convert units and calculate perimeter and area of polygons and compound shapes. • Calculate circumference and area of circles and convert between units of area. • Plan data collection; construct and interpret diagrams; calculate averages and spread; evaluate bias and reliability. • Use scatter diagrams, correlation and grouped data where appropriate. • Generate sequences from rules and find nth-term rules, including graphical and geometric sequences.
Vocabulary:
Career examples: Structural engineer; quantity surveyor; sport statistician; animation designer |
Topics:
Knowledge:
Skills: • Order FDP values and complete all four operations with fractions. • Find fractions and percentages of amounts and calculate percentage increase or decrease. • Write and interpret numbers in standard form using powers of ten. • Use BIDMAS and efficient mental strategies in multi-step problems and justify method choice. • Construct triangles, perpendiculars, bisectors and loci using ruler, compass and protractor. • Use scale drawings and bearings in map-based problems.
Vocabulary:
Career examples: Financial analyst; air traffic controller; surveyor |
Topics:
Knowledge:
Skills: • Plot coordinates and draw or interpret linear, real-life, time-series and conversion graphs. • State or interpret equations of lines and extend to gradients and quadratic graphs where secure. • Use formal written methods, BIDMAS and calculators with decimals and negative values. • Estimate and check results for reasonableness. • Solve one-step, two-step and multi-step equations, including brackets and fractions where appropriate. • Construct equations, use trial and improvement, and represent inequality solutions on number lines.
Vocabulary: Career examples: Game designer; pharmacist; aerospace engineer |
Topics:
Knowledge:
Skills: • Simplify and compare ratios, divide quantities in a ratio and find unknowns in direct proportion. • Explore inverse proportion and use rates and compound units such as speed, density and unit price. • Reflect, rotate, translate and enlarge shapes; combine transformations. • Describe congruent and similar shapes using centres and scale factors. • List outcomes systematically and calculate theoretical and experimental probabilities. • Use tree diagrams and Venn diagrams and compare experimental results with theory.
Vocabulary:
Career examples: Sports nutritionist; game artist; risk analyst |
Topics:
Knowledge:
Skills: • Identify 3D-shape properties and interpret isometric drawings, plans and elevations. • Use nets and calculate surface area and volume of cuboids and prisms. • Revisit simplifying, expanding, factorising, substitution and equation solving. • Apply fractions, decimals, percentages, ratio, calculators and compound units in investigations. • Explore budgeting, saving, borrowing, interest, repayment, investment and financial decisions. • Use interleaved problem solving to prepare for the next stage of the curriculum.
Vocabulary:
Career examples: Architect; entrepreneur / business founder |
British Values in Mathematics
British values are embedded through mathematical discussion, collabortion, reasoning, and the application of mathematics to real-life contexts across Years 5-8.
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British value |
Where it is addressed |
How it is developed |
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Democracy |
Statistics and data: surveys, questionnaires, averages, graphs, bias and reliability (Years 6-8); investigations and group problem solving (Years 5-8). |
Pupils contribute questions and ideas, compare different methods and interpretations, listen to others and reach reasoned conclusions. Data collection highlights the importance of fair questions and representative evidence. |
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The rule of law |
Formal methods; BIDMAS and algebraic conventions; angle, shape and probability rules; safe use of mathematical equipment; Money Matters. |
Pupils see how agreed rules and conventions support accuracy, fairness and safety. They follow constraints, check solutions and consider the consequences when mathematical or financial rules are not applied correctly. |
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Individual liberty |
Problem solving and investigations; choice of representations and calculation methods; calculator and estimation work; budgeting, saving and spending in Money Matters. |
Pupils make informed choices, select efficient strategies, take ownership of their work and explain or revise decisions. Financial contexts develop independence, responsible choice and awareness of risk and value. |
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Mutual respect and tolerance of different faiths and beliefs |
Learning-partner discussion; peer review; global and community data; metric and imperial measures; Roman numerals; patterns and tessellations; probability and data interpretation. |
Pupils challenge ideas politely, value different valid approaches and work collaboratively. Diverse contexts are explored without stereotyping, and pupils recognise that mathematics has developed across different cultures, communities and traditions. |
Careers in Mathematics Curriculum
Career links are made explicit through the mathematical knowledge and skills taught in each term.
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Term |
Year 5 |
Year 6 |
Year 7 |
Year 8 |
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Autumn |
• Game designer - coordinates, sequences and transformations • Carpenter - fractions, measurement, area and perimeter |
• Software engineer - number and algorithms • Cybersecurity analyst - factors and primes • Pharmacist - fractions and decimals • Sport statistician - data and averages • Civil engineer - measures and perimeter • Air traffic controller - time and angles • Marketing analyst - percentages and data |
• Quantity surveyor - measurement and area • Sports performance analyst - FDP and graphs • Software developer - algebra and formulae • Transport planner - graphs and measures • Data analyst - statistics • Accountant - calculations • Architect - angles and shapes |
• Cybersecurity specialist - number structure and indices • Software engineer - algebra and formulae • Structural engineer - angles and proof • Quantity surveyor - perimeter, area and circles • Sport statistician - data • Animation designer - sequences |
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Spring |
• Event planner - graphs, timetables and percentages • Architect - angles, polygons and accuracy |
• Meteorologist - negative values and data • Graphic designer - shape and symmetry • Architect - perimeter and area • Chef - ratio and proportion • Data journalist - graphs • Medical researcher - FDP and data • Robotics programmer - sequences and BIDMAS • Surveyor - angles and coordinates • Game designer - transformations |
• Cryptographer - factors and primes • Robotics engineer - equations • Animator - transformations • Product designer - constructions and 3D shapes |
• Financial analyst - FDP and standard form • Air traffic controller - bearings • Surveyor - constructions and scale • Game designer - graphs • Pharmacist - accurate calculations and equations • Aerospace engineer - equations and graphs |
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Summer |
• Chef - unit conversion, capacity and volume • Entrepreneur / business founder - budgeting, pricing and value |
• Transport planner - timetables and time-distance graphs • Aerospace engineer - scale and volume • Economist - data and monetary value • Entrepreneur / business founder - budgeting and finance |
• Game designer - probability • Music producer - sequences • Pharmacist - ratio and proportion • Event planner - decimals, timetables and best value • Entrepreneur / business founder - budgets and financial choices |
• Sports nutritionist - ratio and compound units • Game artist - transformations • Risk analyst - probability • Architect - 3D shapes, surface area and volume • Entrepreneur / business founder - financial decisions |
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Aspect |
How it is developed in mathematics |
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Spiritual |
Pupils experience curiosity, creativity and satisfaction through investigations, problem solving and more than one valid method. Sequences, symmetry, tessellations, geometry and 2D/3D representations encourage appreciation of pattern and mathematical structure, while reflection on challenge builds confidence and perseverance. |
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Moral |
Pupils present calculations and data honestly, check the reliability and possible bias of evidence, and discuss fair interpretations. Probability is applied without stereotyping. Money Matters develops responsible thinking about saving, spending, borrowing, interest, profit, loss and the consequences of financial choices. |
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Social |
Learning partners, group investigations and class discussion develop listening, turn-taking, cooperation and constructive disagreement. Pupils explain reasoning, compare approaches, review one another's work respectfully and use peer support to help everyone participate and progress. |
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Cultural |
Pupils explore mathematics in different times, places and communities through Roman numerals, metric and imperial systems, global data, maps, timetables, patterns and tessellations. Career and real-life contexts show the shared importance of mathematics across cultures and society. |
