Our Mathematics curriculum is ambitious, inclusive and carefully sequenced from the Early Years Foundation Stage to Year 6.

It is designed to develop learners who can:

• understand important mathematical concepts;
• recall essential facts;
• calculate accurately;
• select efficient methods;
• reason mathematically;
• solve routine and non-routine problems;
• use precise vocabulary;
• represent ideas in different ways;
• make connections;
• explain and justify thinking;
• recognise and correct errors;
• and apply Mathematics with increasing independence.

St Luke’s uses White Rose Maths as an important resource to support curriculum planning, sequencing, representation and practice.

Teachers and leaders review and adapt White Rose materials in response to:

• the Early Years Foundation Stage;
• the National Curriculum;
• DfE Mathematics guidance;
• learners’ prior knowledge;
• assessment information;
• the needs of each cohort;
• the school’s calculation policy;
• SEND and accessibility;
• available resources;
• and the wider aims of the St Luke’s curriculum.

White Rose Maths supports our curriculum. It does not replace teachers’ professional judgement or the school’s responsibility for ensuring that essential mathematical knowledge is taught, assessed and secured.

The Three National Curriculum Aims

Our Mathematics curriculum develops three connected aims:

• fluency;
• mathematical reasoning;
• and problem-solving.

These aims are developed together rather than treated as separate lesson types.

Fluency

Fluency includes the secure and flexible use of mathematical knowledge.

Learners develop:

• number sense;
• factual recall;
• accurate calculation;
• conceptual understanding;
• procedural fluency;
• efficient strategy selection;
• flexibility with number;
• and confidence in applying known facts.

Fluency does not mean relying only on rote recall or completing large numbers of similar calculations without understanding.

However, conceptual understanding does not remove the need to remember important facts and procedures.

Learners need increasingly automatic recall of essential knowledge, including:

• number bonds;
• addition and subtraction facts;
• multiplication and division facts;
• place-value relationships;
• fraction, decimal and percentage equivalents;
• and frequently used calculation procedures.

When essential knowledge becomes automatic, learners can devote more attention to reasoning and problem-solving.

Mathematical Reasoning

Learners are taught to:

• explain;
• justify;
• compare;
• classify;
• sequence;
• identify relationships;
• make conjectures;
• test examples;
• find counterexamples;
• generalise;
• prove;
• and evaluate the reasoning of others.

Reasoning is not defined simply as writing a sentence after completing a calculation.

Learners need opportunities to think mathematically, select evidence and communicate why an answer or method is valid.

Problem-Solving

Learners apply mathematical knowledge to increasingly varied and unfamiliar situations.

They are taught to:

• understand the problem;
• identify relevant information;
• represent the situation;
• connect the problem with known Mathematics;
• select an approach;
• persist;
• monitor progress;
• check the reasonableness of an answer;
• compare possible solutions;
• and explain conclusions.

Problem-solving is not reserved for learners who complete routine work first. All learners are entitled to solve appropriately challenging problems.

Foundational Mathematical Knowledge

The curriculum gives particular attention to foundational knowledge.

This includes:

• counting;
• cardinality;
• subitising;
• comparison;
• composition of number;
• number bonds;
• place value;
• additive relationships;
• multiplicative relationships;
• multiplication tables;
• fraction knowledge;
• mathematical vocabulary;
• and efficient calculation.

Learners need secure foundations before they can understand more complex Mathematics.

Teachers identify prerequisite knowledge carefully and respond promptly where gaps are found.

Early Mathematics

In the Early Years Foundation Stage, children develop secure foundations in:

• number;
• numerical patterns;
• counting;
• comparison;
• composition;
• subitising;
• shape;
• space;
• measure;
• pattern;
• and spatial reasoning.

Children learn through:

• direct teaching;
• purposeful play;
• practical activity;
• songs and stories;
• routines;
• mathematical discussion;
• and repeated encounters with important concepts.

Early Mathematics is not reduced to numeral recognition or reciting a counting sequence.

Children need to understand quantity, relationships and how numbers are composed.

Teaching for Secure Understanding

Teachers make mathematical structure visible.

They use:

• clear explanation;
• worked examples;
• carefully chosen representations;
• manipulatives;
• diagrams;
• examples and non-examples;
• variation;
• mathematical language;
• guided practice;
• independent practice;
• retrieval;
• and problem-solving.

Teaching helps learners connect:

• concrete experience;
• visual representation;
• spoken explanation;
• and abstract notation.

Concrete, pictorial and abstract representations are not treated as a rigid staircase.

Learners may move flexibly between them when a representation supports understanding, reasoning or explanation.

Practice and Retrieval

Learners need sufficient practice to remember and apply mathematical knowledge.

Practice is designed to develop:

• accuracy;
• recall;
• flexibility;
• efficiency;
• generalisation;
• and independence.

Teachers use retrieval to revisit important prior learning and identify knowledge that is becoming insecure.

Practice should not consist only of disconnected repetition. Examples are selected and ordered carefully so that learners notice mathematical structure and make connections.

Responsive Teaching

Assessment is used throughout lessons to determine whether learners are ready to move on or require further explanation, representation or practice.

Where gaps are identified, teachers may provide:

• immediate clarification;
• alternative representation;
• additional modelling;
• focused practice;
• same-day support;
• small-group teaching;
• pre-teaching;
• structured intervention;
• and additional retrieval.

Support targets the specific missing knowledge.

Learners are not moved through curriculum content simply because a planning sequence specifies the next lesson.

Equally, learners are not denied access to new Mathematics indefinitely. Support is designed to help them secure prerequisites and participate successfully in the main curriculum.

Challenge and Depth

Learners who grasp a concept securely are challenged through greater depth.

This may include:

• more complex relationships;
• unfamiliar contexts;
• multiple representations;
• proof;
• generalisation;
• comparison of methods;
• missing information;
• open problems;
• and more efficient reasoning.

Challenge does not mean moving learners rapidly into the next year group’s curriculum or simply increasing the quantity of calculations.

Mathematics Across the Curriculum

Learners apply Mathematics in subjects such as:

• Science;
• Geography;
• Computing;
• Design and Technology;
• Physical Education;
• and personal financial education.

They may:

• measure;
• collect data;
• interpret graphs;
• calculate;
• compare scale;
• use coordinates;
• investigate pattern;
• or evaluate quantities.

Cross-curricular application strengthens learning when learners already possess the mathematical knowledge required.

By the end of Year 6, learners should possess secure foundations in number, calculation, fractions, measurement, geometry and statistics.

They should be able to reason, solve problems and communicate their mathematical thinking with increasing accuracy, confidence and independence.

Our Mathematics curriculum develops several connected forms of knowledge.

These include:

• conceptual knowledge;
• factual knowledge;
• procedural knowledge;
• representational knowledge;
• and knowledge of mathematical reasoning and problem-solving.

Learners need all of these in order to become successful mathematicians.

Conceptual Knowledge

Conceptual knowledge is understanding mathematical ideas, structures and relationships.

It includes understanding:

• what numbers represent;
• how numbers are composed;
• how place value works;
• how operations are connected;
• why calculation methods work;
• how fractions relate to division and proportion;
• how units measure attributes;
• how shapes are classified;
• and how data represents information.

For example, understanding addition involves more than knowing how to complete a written method.

Learners should understand that addition may involve:

• combining;
• increasing;
• finding a total;
• or identifying a missing part.

Factual Knowledge

Factual knowledge includes mathematical information that learners need to recall accurately and increasingly automatically.

It includes:

• counting sequences;
• number bonds;
• addition and subtraction facts;
• doubles and halves;
• multiplication tables;
• related division facts;
• place-value facts;
• fraction, decimal and percentage equivalents;
• shape properties;
• measurement conversions;
• and mathematical vocabulary.

Secure factual knowledge reduces cognitive demand and supports more complex reasoning.

Procedural Knowledge

Procedural knowledge is knowing how to carry out a mathematical process accurately and efficiently.

It includes:

• counting procedures;
• calculation strategies;
• written methods;
• measuring;
• drawing and interpreting graphs;
• constructing shapes;
• converting units;
• finding fractions of quantities;
• and solving equations.

Procedures are taught with sufficient conceptual explanation so that learners understand when and why a method works.

Learners also need enough practice for useful procedures to become fluent.

Representational Knowledge

Representational knowledge is understanding how mathematical ideas may be shown in different ways.

Representations may include:

• practical objects;
• fingers;
• ten frames;
• bead strings;
• number tracks;
• number lines;
• part-whole models;
• bar models;
• arrays;
• place-value counters;
• base-ten equipment;
• fraction strips;
• ratio tables;
• graphs;
• diagrams;
• symbols;
• and equations.

Learners are taught that a representation highlights particular mathematical relationships.

They learn to:

• interpret representations;
• connect different representations;
• select a useful representation;
• and recognise the limitations of a model.

Strategic Knowledge

Strategic knowledge is knowing how to approach a mathematical task.

Learners develop knowledge of how to:

• identify what is known;
• identify what is unknown;
• choose a representation;
• select an operation;
• draw on a similar problem;
• break a problem into stages;
• test an idea;
• work systematically;
• check an answer;
• and change approach where necessary.

Knowledge of Mathematical Communication

Learners develop knowledge of how to communicate Mathematics through:

• words;
• symbols;
• equations;
• diagrams;
• tables;
• graphs;
• models;
• gestures;
• and structured explanation.

They learn to use accurate vocabulary and connect spoken, visual and symbolic forms.

Knowledge of Proof and Justification

Learners develop age-appropriate understanding of how mathematical claims can be justified.

They learn that one example may illustrate a claim but does not always prove that it is universally true.

They use:

• examples;
• counterexamples;
• patterns;
• definitions;
• representations;
• logical argument;
• and generalisation

to support or challenge mathematical statements.

Knowledge of Error

Learners develop knowledge of how mathematical errors arise and how they can be analysed.

They learn to:

• identify an incorrect step;
• explain a misconception;
• correct a method;
• compare the error with a valid strategy;
• and use mistakes to strengthen understanding.

Errors are treated as information for teaching rather than as evidence that a learner lacks mathematical ability.

Our Mathematics curriculum is structured around recurring concepts that are introduced in age-appropriate ways and revisited with increasing depth and complexity.

Number Sense

Number sense is a flexible understanding of number and quantity.

It includes:

• counting;
• cardinality;
• subitising;
• comparison;
• composition;
• magnitude;
• estimation;
• number relationships;
• and flexible calculation.

Strong number sense enables learners to reason rather than rely only on memorised procedures.

Counting

Counting involves more than reciting number words.

Learners develop understanding of:

• stable order;
• one-to-one correspondence;
• cardinality;
• abstraction;
• order irrelevance;
• counting forwards;
• counting backwards;
• counting from different starting points;
• and counting in equal steps.

Cardinality

Cardinality is understanding that the final number said when counting represents the total quantity in the set.

Learners connect:

• spoken number;
• quantity;
• numeral;
• and position within the number system.

Subitising

Subitising is recognising a small quantity without counting each item individually.

Learners develop:

• perceptual subitising of familiar small quantities;
• and conceptual subitising by recognising groups and combining them.

Subitising supports composition, number bonds and calculation.

Composition of Number

Composition is understanding that numbers are made from smaller numbers.

Learners develop knowledge such as:

• five can be composed of two and three;
• ten can be composed in different ways;
• a two-digit number is composed of tens and ones;
• and fractions may be composed and decomposed.

Composition underpins addition, subtraction, place value and flexible calculation.

Comparison

Comparison involves recognising whether quantities or values are:

• equal;
• greater;
• less;
• longer;
• shorter;
• heavier;
• lighter;
• or otherwise related.

Learners use comparison language and mathematical symbols accurately.

Place Value

Place value describes the value of a digit according to its position within a number.

Learners develop understanding of:

• ones;
• tens;
• hundreds;
• thousands;
• larger whole numbers;
• tenths;
• hundredths;
• and thousandths.

They learn that our number system is based on powers of ten and that numbers can be composed, partitioned and recombined.

Equality

Equality means that two expressions have the same value.

Learners understand that the equals sign represents equivalence rather than simply signalling that an answer should follow.

They explore equations such as:

• a calculation equal to a value;
• two calculations with the same value;
• and equations containing unknowns in different positions.

Addition and Subtraction

Learners develop understanding of addition and subtraction through structures including:

• aggregation;
• augmentation;
• partitioning;
• reduction;
• difference;
• and inverse relationships.

They learn that addition and subtraction are connected and use known facts to derive new facts.

Multiplication and Division

Learners develop understanding of multiplication and division through:

• equal groups;
• repeated addition;
• arrays;
• scaling;
• grouping;
• sharing;
• factors;
• multiples;
• and inverse relationships.

They learn that multiplication is not only repeated addition and that division may involve either grouping or sharing.

Additive Reasoning

Additive reasoning involves situations in which quantities are combined, separated, compared or changed through addition and subtraction.

Learners identify the structure of the problem rather than relying only on keywords.

Multiplicative Reasoning

Multiplicative reasoning involves relationships based on equal groups, scale, ratio, proportion and multiplication.

It differs fundamentally from additive reasoning.

Learners develop the ability to recognise when a situation involves multiplication rather than repeated addition or simple increase.

Fractions

Learners understand fractions as:

• equal parts of a whole;
• equal parts of a quantity;
• numbers with positions on a number line;
• quotients;
• operators;
• ratios;
• and proportions.

They develop knowledge of:

• numerator;
• denominator;
• equivalence;
• comparison;
• ordering;
• addition and subtraction;
• multiplication;
• and links with decimals and percentages.

Decimals and Percentages

Learners connect decimals and percentages with:

• place value;
• fractions;
• division;
• proportion;
• and measures.

They develop understanding of equivalence and use different representations according to the context.

Ratio and Proportion

Ratio describes a multiplicative relationship between quantities.

Proportion describes equality between ratios or the relationship between a part and a whole.

Learners develop these ideas through:

• scaling;
• recipes;
• maps;
• similar shapes;
• percentages;
• and comparison of quantities.

Algebraic Thinking

Algebraic thinking begins before formal algebraic notation.

Learners develop understanding through:

• pattern;
• generalisation;
• missing numbers;
• equality;
• inverse relationships;
• functions;
• and expressing mathematical structure.

They learn to use symbols to represent unknown or variable quantities.

Measurement

Measurement involves assigning a numerical value to an attribute using an agreed unit.

Learners develop knowledge of:

• length;
• height;
• mass;
• capacity;
• volume;
• time;
• temperature;
• perimeter;
• area;
• money;
• and angles.

They learn to:

• compare;
• estimate;
• select units;
• use instruments;
• read scales;
• convert;
• and calculate.

Geometry

Geometry develops understanding of shape, space, position and movement.

Learners explore:

• two-dimensional shapes;
• three-dimensional shapes;
• properties;
• angles;
• symmetry;
• coordinates;
• translation;
• reflection;
• rotation;
• and spatial relationships.

Spatial Reasoning

Spatial reasoning involves understanding how objects relate, move and fit within space.

It supports:

• geometry;
• measure;
• construction;
• pattern;
• representation;
• and later mathematical learning.

Statistics

Statistics involves collecting, organising, representing and interpreting data.

Learners develop knowledge of:

• categories;
• frequency;
• tables;
• pictograms;
• bar charts;
• line graphs;
• averages;
• and comparison.

They learn that representations should be interpreted critically and that the way data is presented can influence conclusions.

Pattern

Pattern involves recognising regularity, structure or repetition.

Learners learn to:

• identify;
• continue;
• describe;
• represent;
• generalise;
• and explain patterns.

Pattern is central to number, calculation, geometry, algebra and proportional reasoning.

Equivalence

Equivalence means that different representations, expressions or quantities have the same value.

Learners explore equivalence through:

• equations;
• fractions;
• decimals;
• percentages;
• measures;
• and alternative calculation strategies.

Structure

Mathematical structure is the underlying relationship that connects examples.

Teachers help learners notice structure through:

• representation;
• variation;
• comparison;
• precise questioning;
• and generalisation.

Fluency

Fluency is the accurate, efficient, flexible and increasingly automatic use of mathematical knowledge.

It includes both understanding and recall.

Reasoning

Reasoning is the process of drawing logical conclusions from mathematical knowledge.

Learners explain, justify, compare, generalise and prove.

Problem-Solving

Problem-solving involves applying mathematical knowledge to reach a solution where the method may not be immediately obvious.

Learners learn to represent, plan, monitor, check and evaluate.

Representation

Representations make mathematical relationships visible.

Learners develop increasing independence in selecting and interpreting representations.

Variation

Variation involves changing some features of examples while keeping others constant so that learners notice important mathematical relationships.

It supports conceptual understanding and helps prevent overgeneralisation.

Generalisation

Generalisation involves expressing a relationship that applies beyond individual examples.

Learners may generalise through:

• words;
• diagrams;
• equations;
• or algebraic notation.

Proof

Proof provides a logical justification that a mathematical claim must be true.

At primary level, learners develop proof through representations, examples, counterexamples, definitions and structured argument.

Efficiency

Efficiency involves selecting a method that is accurate, appropriate and economical for the particular calculation or problem.

The most efficient method may vary according to the numbers and context.

Mathematical Resilience

Mathematical resilience involves persisting, seeking another representation, learning from error and recognising that difficulty is a normal part of learning.

Resilience is supported by effective teaching and secure knowledge. It is not an expectation that learners should struggle without appropriate help.

Our Mathematics curriculum is implemented through carefully sequenced teaching that develops conceptual understanding, factual fluency, procedural accuracy, reasoning and problem-solving.

St Luke’s uses White Rose Maths as an important resource to support planning, sequencing, representation and practice.

Teachers and leaders review and adapt White Rose materials so that teaching reflects:

• the Early Years Foundation Stage;
• the National Curriculum;
• DfE Mathematics guidance;
• learners’ prior knowledge;
• assessment information;
• the school’s calculation policy;
• the needs of each cohort;
• SEND and accessibility;
• and the wider aims of the St Luke’s curriculum.

White Rose Maths supports the curriculum but does not replace teachers’ professional judgement.

Teachers select, adapt and supplement resources where necessary to ensure that learners secure the intended mathematical knowledge.

Lesson Design

Mathematics lessons are structured around clear mathematical learning.

Teaching may include:

• retrieval of prior knowledge;
• explicit explanation;
• teacher modelling;
• worked examples;
• use of representations;
• guided practice;
• mathematical discussion;
• independent practice;
• reasoning;
• problem-solving;
• assessment;
• and review.

Teachers identify the essential concept or relationship learners need to understand.

Activities are chosen because they help learners secure that learning rather than simply fill lesson time or complete a worksheet.

Explicit Teaching

Teachers explain new content clearly and in manageable steps.

They model:

• mathematical vocabulary;
• representations;
• calculation strategies;
• written methods;
• reasoning;
• checking;
• and efficient decision-making.

Worked examples are selected carefully so that learners can see both the method and the underlying mathematical structure.

Teachers may compare:

• correct and incorrect examples;
• efficient and inefficient methods;
• different representations;
• related calculations;
• and examples and non-examples.

Representations and Manipulatives

Teachers use manipulatives and visual representations to make mathematical structures visible.

These may include:

• counters;
• cubes;
• ten frames;
• bead strings;
• number tracks;
• number lines;
• part-whole models;
• bar models;
• arrays;
• base-ten equipment;
• place-value counters;
• fraction strips;
• ratio tables;
• diagrams;
• and graphs.

Learners are taught how a representation connects with mathematical language and notation.

Resources are not used as decoration or without explanation.

Teachers make clear:

• what each part represents;
• which relationship is being shown;
• how the representation connects with the calculation;
• and when it may or may not be useful.

Concrete, pictorial and abstract representations are used flexibly.

Learners may return to a familiar representation when it supports deeper reasoning or helps resolve a misconception.

Mathematical Practice

Learners need sufficient practice to secure new knowledge.

Practice may include:

• factual recall;
• oral rehearsal;
• calculation;
• variation;
• completion of worked examples;
• missing-number tasks;
• comparison;
• classification;
• error analysis;
• reasoning;
• and problem-solving.

Practice is selected and sequenced carefully.

Teachers consider:

• which feature changes;
• which feature remains the same;
• what learners are expected to notice;
• which misconception may arise;
• and how examples build towards independence.

Practice should develop understanding and fluency rather than rely only on high-volume repetition.

Fluency and Number Facts

Learners practise essential number facts regularly.

This includes:

• subitising;
• number bonds;
• additive facts;
• doubles and halves;
• multiplication tables;
• related division facts;
• place-value relationships;
• and useful fraction, decimal and percentage equivalents.

Practice may include:

• oral recall;
• low-stakes retrieval;
• games;
• visual representations;
• counting patterns;
• derived facts;
• and application in calculations and problems.

Learners are taught to derive unknown facts from known facts.

For example, they may use:

• a number bond to ten to calculate a related bond to one hundred;
• a known multiplication fact to derive a related division fact;
• or a known double to calculate a near double.

Reasoning

Reasoning is embedded throughout the curriculum.

Learners are encouraged to:

• explain how they know;
• identify what is the same and different;
• compare methods;
• justify a choice;
• identify an error;
• complete a pattern;
• test a claim;
• find a counterexample;
• generalise;
• and prove.

Teachers expect learners to use mathematical evidence rather than rely only on statements such as “I just know.”

Reasoning may be communicated orally, practically, visually or in writing.

The quality of mathematical thinking is prioritised over the length of the written response.

Problem-Solving

Problem-solving is available to all learners.

Teachers select problems that require learners to:

• identify the mathematical structure;
• choose relevant information;
• select an operation;
• use a representation;
• work systematically;
• make connections;
• monitor progress;
• and check the reasonableness of the result.

Learners are taught that problem-solving may involve more than one step or possible approach.

They are given opportunities to compare solutions and discuss efficiency.

Misconceptions and Error

Teachers anticipate common misconceptions and respond promptly.

This may involve:

• presenting an incorrect example;
• asking learners to identify the error;
• using a counterexample;
• returning to a representation;
• revisiting prerequisite knowledge;
• comparing two methods;
• or providing additional guided practice.

Errors are treated as evidence that helps teachers understand learners’ thinking.

Learners are encouraged to explain why an error occurred and how it can be corrected.

Mathematics Across the Curriculum

Mathematical knowledge is applied where appropriate across the curriculum.

Learners may use Mathematics to:

• measure in Science;
• collect and interpret geographical data;
• consider chronology and scale in History;
• calculate within Design and Technology;
• analyse performance in Physical Education;
• use coordinates in Computing;
• and develop financial understanding in PSHE.

Cross-curricular application should reinforce secure mathematical knowledge rather than introduce unfamiliar concepts without appropriate teaching.

Our Mathematics curriculum is sequenced so that learners build secure and connected mathematical knowledge from Nursery to Year 6.

Progression is not understood simply as working with larger numbers or completing more difficult worksheets.

It involves the planned development of:

• conceptual understanding;
• factual recall;
• procedural fluency;
• vocabulary;
• representation;
• reasoning;
• problem-solving;
• efficiency;
• and increasing independence.

Important concepts are revisited in increasingly complex forms.

Early Years Foundation Stage

In Nursery and Reception, children develop secure foundations through:

• counting;
• cardinality;
• one-to-one correspondence;
• subitising;
• comparison;
• composition of number;
• numerical patterns;
• shape;
• space;
• measure;
• pattern;
• and mathematical language.

Children explore Mathematics through:

• direct teaching;
• play;
• routines;
• songs;
• stories;
• practical activity;
• outdoor learning;
• and mathematical discussion.

They begin to explain what they notice and represent ideas in different ways.

Key Stage 1

In Key Stage 1, learners develop secure foundations in:

• place value;
• number facts;
• addition and subtraction;
• multiplication and division;
• fractions;
• measurement;
• geometry;
• position and direction;
• and simple statistics.

They learn to:

• use representations;
• calculate;
• compare methods;
• explain reasoning;
• solve simple problems;
• and apply mathematical vocabulary accurately.

Lower Key Stage 2

In Lower Key Stage 2, learners deepen understanding of:

• place value;
• written and mental calculation;
• multiplication and division;
• multiplication tables;
• fractions;
• decimals;
• measurement;
• perimeter and area;
• geometry;
• and statistics.

They become increasingly able to:

• select methods;
• justify decisions;
• interpret problems;
• use bar models and other representations;
• identify patterns;
• and work with increasing accuracy.

Upper Key Stage 2

In Upper Key Stage 2, learners develop increasingly sophisticated understanding of:

• large whole numbers;
• calculation;
• factors and multiples;
• fractions;
• decimals;
• percentages;
• ratio;
• proportion;
• algebra;
• measurement;
• geometry;
• statistics;
• and mathematical relationships.

They are expected to:

• reason with greater depth;
• solve multi-step problems;
• compare approaches;
• justify generalisations;
• interpret increasingly complex information;
• select efficient methods;
• and prepare for secondary Mathematics.

Progression Principles

Progression is guided by the following principles:

• new content builds on secure prerequisite knowledge;
• important concepts are revisited;
• vocabulary becomes increasingly precise;
• representations develop alongside abstraction;
• factual fluency supports complex thinking;
• procedures are connected with conceptual understanding;
• reasoning develops from explanation towards proof;
• problems become increasingly unfamiliar and multi-step;
• and independence increases as support is reduced.

Avoiding Premature Progression

Teachers do not move learners to more complex content before essential foundations are secure.

For example, learners need secure understanding of:

• composition before formal addition;
• place value before written calculation;
• equal groups before multiplication procedures;
• division before fraction equivalence;
• and multiplicative relationships before ratio and proportion.

Where prerequisite knowledge is insecure, teachers revisit and strengthen it.

Depth Before Acceleration

Learners who grasp content rapidly deepen their understanding through:

• varied representations;
• proof;
• generalisation;
• complex reasoning;
• unfamiliar problems;
• comparison of methods;
• and explanation of structure.

They are not routinely accelerated into content from later year groups.

Mathematical vocabulary is taught deliberately and progressively.

Learners need precise language to understand concepts, explain relationships, interpret problems and justify conclusions.

Vocabulary is introduced through:

• clear explanation;
• practical examples;
• representations;
• sentence structures;
• comparison;
• repetition;
• retrieval;
• and application.

Key Vocabulary

Learners develop increasingly secure use of words and phrases such as:

• number;
• numeral;
• digit;
• quantity;
• total;
• sum;
• difference;
• product;
• quotient;
• equal;
• equivalent;
• greater than;
• less than;
• place value;
• partition;
• compose;
• decompose;
• factor;
• multiple;
• array;
• fraction;
• numerator;
• denominator;
• decimal;
• percentage;
• ratio;
• proportion;
• perimeter;
• area;
• volume;
• angle;
• parallel;
• perpendicular;
• symmetry;
• data;
• scale;
• estimate;
• calculate;
• represent;
• reason;
• justify;
• prove;
• and generalise.

Teachers distinguish carefully between mathematical and everyday meanings.

For example:

• “difference” may refer to subtraction or comparison;
• “product” means the result of multiplication;
• “table” may refer to organised data rather than furniture;
• “mean” may refer to an average;
• and “odd” has a precise mathematical meaning.

Mathematical Sentences

Learners are taught to communicate in complete mathematical sentences.

Useful structures may include:

• “I know this because…”
• “The representation shows…”
• “These are equivalent because…”
• “The pattern continues by…”
• “This method is efficient because…”
• “The error occurred when…”
• “The statement is always, sometimes or never true because…”
• “A counterexample is…”
• “I can generalise that…”
• “The relationship between the numbers is…”

Sentence structures support thinking but should not become scripts that limit genuine explanation.

Talk Partners and Discussion

Mathematical talk may involve:

• partner discussion;
• group reasoning;
• whole-class explanation;
• comparison of methods;
• critique of examples;
• and presentation of solutions.

Learners are taught to:

• listen;
• take turns;
• ask for clarification;
• build on an idea;
• disagree respectfully;
• identify evidence;
• and revise their thinking.

Teachers ensure that discussion is purposeful and does not replace individual thought or practice.

Symbols and Notation

Learners develop knowledge of mathematical symbols and notation.

They are taught to connect:

• spoken language;
• practical representations;
• diagrams;
• symbols;
• and equations.

They learn that notation communicates precise relationships.

Teachers model symbols accurately and address misconceptions about:

• the equals sign;
• inequality symbols;
• operation symbols;
• fraction notation;
• decimal points;
• and brackets.

Explaining Methods

Learners are encouraged to explain:

• what they did;
• why the method works;
• why it is appropriate;
• whether another method is possible;
• and how they checked the result.

Over time, explanations should move from descriptions of actions towards clear accounts of mathematical structure.

Reading Mathematical Problems

Learners are taught how to read mathematical language carefully.

They learn to:

• identify the question;
• recognise relevant information;
• distinguish necessary from unnecessary detail;
• interpret mathematical vocabulary;
• identify units;
• notice relationships;
• and represent the situation.

Teachers avoid teaching learners to select operations solely through keywords, because the same word may appear in different mathematical structures.

Assessment in Mathematics is used to determine what learners know, understand and can apply.

It helps teachers identify secure knowledge, misconceptions, missing prerequisites and next steps.

Assessment is ongoing and informs teaching within lessons, across units and over time.

What We Assess

Teachers assess:

• conceptual understanding;
• factual recall;
• calculation;
• procedural accuracy;
• use of representations;
• mathematical vocabulary;
• reasoning;
• problem-solving;
• efficiency;
• and independence.

Sources of Evidence

Assessment may draw on:

• questioning;
• discussion;
• observation;
• practical tasks;
• retrieval;
• mini-whiteboard responses;
• independent work;
• fluency checks;
• reasoning tasks;
• problem-solving;
• quizzes;
• end-of-unit assessments;
• pupil voice;
• and application across the curriculum.

No single assessment is used in isolation.

Day-to-Day Assessment

Teachers check understanding continuously.

They notice whether learners:

• recall facts accurately;
• understand the representation;
• use vocabulary correctly;
• choose an appropriate operation;
• follow a procedure accurately;
• explain why a method works;
• recognise an error;
• transfer learning;
• and work independently.

Teachers use this evidence to decide whether to:

• continue;
• revisit;
• remodel;
• provide further practice;
• change the representation;
• reduce or increase support;
• or deepen the challenge.

Identifying the Barrier

A learner may struggle because of:

• insecure counting;
• weak number sense;
• gaps in place value;
• limited factual recall;
• misunderstanding of an operation;
• inaccurate procedure;
• weak vocabulary;
• difficulty interpreting the problem;
• working-memory demands;
• absence;
• low confidence;
• or an accessibility need.

Assessment identifies the specific barrier rather than labelling the learner as generally weak in Mathematics.

Responsive Teaching

Teachers may respond through:

• immediate feedback;
• additional modelling;
• a simpler representation;
• practical resources;
• guided practice;
• additional factual rehearsal;
• same-day support;
• pre-teaching;
• small-group teaching;
• focused intervention;
• alternative recording;
• assistive technology;
• and increased challenge.

Support should help learners access and succeed within the main curriculum.

Misconceptions

Teachers anticipate and address misconceptions such as:

• believing that the equals sign means “the answer comes next”;
• comparing multi-digit numbers by the final digit;
• assuming multiplication always makes a number larger;
• assuming division always makes a number smaller;
• believing a larger denominator means a larger fraction;
• confusing perimeter and area;
• treating a decimal point as a separator;
• or relying on visual appearance rather than mathematical properties when classifying shapes.

Misconceptions are addressed through explanation, representation, counterexamples and practice.

Feedback

Feedback is timely, specific and linked to the intended learning.

It may be provided through:

• live feedback;
• questioning;
• verbal feedback;
• whole-class feedback;
• worked examples;
• peer discussion;
• and targeted written feedback where necessary.

Learners are given time to respond, correct errors, practise and apply feedback.

Intervention

Intervention is used when learners require support beyond normal classroom adaptation.

It should:

• address a precise gap;
• connect with classroom teaching;
• use familiar representations and language;
• be sufficiently frequent;
• be delivered by trained staff;
• be reviewed regularly;
• and support increasing independence.

Intervention should not become a permanent parallel curriculum.

Subject-Leadership Use of Assessment

Leaders use assessment evidence to identify:

• common misconceptions;
• gaps in foundational knowledge;
• variation between classes;
• fluency weaknesses;
• groups requiring support;
• intervention impact;
• staff development needs;
• resource needs;
• and priorities for curriculum refinement.

The impact of our Mathematics curriculum can be seen in whether learners develop secure knowledge, mathematical confidence and increasing independence.

Over time, learners should demonstrate:

• strong number sense;
• secure factual recall;
• accurate calculation;
• conceptual understanding;
• procedural fluency;
• flexible strategy selection;
• precise vocabulary;
• effective use of representations;
• mathematical reasoning;
• successful problem-solving;
• increasing efficiency;
• resilience;
• and positive mathematical identities.

Evidence of Impact

Impact is evaluated through:

• discussions with learners;
• classroom work;
• fluency assessment;
• reasoning and problem-solving;
• lesson visits;
• assessment information;
• curriculum reviews;
• pupil voice;
• intervention evaluation;
• application across subjects;
• and readiness for the next stage.

No single test, book or piece of work is used in isolation.

Retention and Application

Leaders consider whether learners:

• remember essential knowledge;
• retrieve facts efficiently;
• apply procedures accurately;
• connect current learning with prior learning;
• transfer knowledge to unfamiliar problems;
• and use Mathematics beyond the lesson in which it was taught.

Successful impact involves durable understanding rather than short-term completion of a unit.

Equity

Leaders evaluate the progress and participation of:

• disadvantaged learners;
• learners with SEND;
• learners with English as an additional language;
• learners with speech, language and communication needs;
• learners with low attendance;
• learners joining the school during the year;
• learners with low confidence;
• and learners requiring greater challenge.

They consider whether all learners have equitable access to:

• high-quality teaching;
• manipulatives;
• mathematical discussion;
• fluency practice;
• reasoning;
• problem-solving;
• intervention;
• enrichment;
• and appropriate challenge.

Foundational Knowledge

Particular attention is given to whether learners secure:

• counting;
• subitising;
• number composition;
• place value;
• additive facts;
• multiplicative facts;
• calculation;
• fractions;
• mathematical vocabulary;
• and the prerequisite knowledge needed for future learning.

Where foundations are insecure, leaders evaluate whether support is timely, precise and effective.

Intended Outcome

By the end of Year 6, learners should:

• understand important mathematical concepts;
• recall essential facts;
• calculate accurately and efficiently;
• reason and justify;
• solve increasingly complex problems;
• use appropriate representations;
• communicate with precise vocabulary;
• recognise and correct errors;
• and approach Mathematics with confidence and perseverance.

They should be well prepared for the demands of secondary Mathematics and possess secure numeracy for everyday life.

They should understand that Mathematics is a connected, logical and creative discipline through which they can interpret information, solve problems and make informed decisions.

Our Mathematics curriculum is ambitious for every learner.

All learners are entitled to develop secure mathematical foundations, participate in reasoning and problem-solving, and experience success.

Teachers identify barriers carefully and adapt teaching without unnecessarily reducing expectations or narrowing curriculum entitlement.

A learner may require support with:

• counting;
• number sense;
• factual recall;
• place value;
• mathematical vocabulary;
• working memory;
• visual processing;
• spatial reasoning;
• attention;
• fine-motor control;
• interpreting questions;
• recording;
• confidence;
• or applying knowledge independently.

Support is matched to the specific barrier rather than based on a general label of being weak in Mathematics.

Learners with SEND

Learners with SEND may benefit from:

• smaller teaching steps;
• explicit modelling;
• additional repetition;
• carefully selected manipulatives;
• visual representations;
• reduced visual clutter;
• pre-teaching;
• repeated retrieval;
• consistent mathematical language;
• worked examples;
• alternative recording methods;
• additional processing time;
• assistive technology;
• carefully structured adult support;
• and specialist advice where appropriate.

Adaptations should preserve the important mathematical idea.

For example, a learner may record a calculation using:

• practical equipment;
• symbols;
• a diagram;
• a verbal explanation;
• a digital tool;
• or an adult scribe

while still demonstrating the intended mathematical understanding.

Learners with Speech, Language and Communication Needs

Mathematics places significant language demands on learners.

Support may include:

• explicit vocabulary teaching;
• clear and concise instructions;
• visual prompts;
• sentence structures;
• oral rehearsal;
• gestures;
• examples and non-examples;
• repeated explanation;
• reduced linguistic complexity where it does not alter the Mathematics;
• and opportunities to demonstrate understanding practically.

Teachers distinguish between difficulty understanding the Mathematics and difficulty expressing mathematical thinking verbally or in writing.

Learners with English as an Additional Language

Learners with English as an additional language may require support with:

• mathematical vocabulary;
• comparative language;
• positional language;
• multi-step instructions;
• word problems;
• unfamiliar contexts;
• and words with different everyday and mathematical meanings.

Teachers support access through:

• visual representations;
• practical equipment;
• clear modelling;
• diagrams;
• sentence structures;
• bilingual resources where appropriate;
• oral rehearsal;
• and links with mathematical knowledge developed in another language.

Mathematical knowledge already secured in a home language is recognised as an asset.

Learning English as an additional language is not treated as a mathematical difficulty.

Learners with Physical or Sensory Needs

Learners may require:

• larger manipulatives;
• high-contrast resources;
• tactile representations;
• adapted rulers or measuring tools;
• enlarged graphs;
• accessible digital resources;
• specialist seating;
• alternative recording;
• audio description;
• additional positioning support;
• or assistance with handling equipment.

Teachers work with the SENCo, families and relevant professionals to identify appropriate adjustments.

Disadvantaged Learners

Leaders ensure that disadvantaged learners have equitable access to:

• high-quality teaching;
• manipulatives;
• fluency practice;
• reasoning;
• problem-solving;
• intervention;
• mathematical games;
• home-learning resources;
• clubs;
• competitions;
• and wider enrichment.

Where learners have limited access to mathematical resources or support beyond school, additional opportunities are provided without lowering expectations.

Learners with Low Mathematical Confidence

Learners with low confidence may be supported through:

• carefully sequenced success;
• predictable routines;
• additional rehearsal;
• use of familiar representations;
• opportunities to explain thinking without public pressure;
• constructive feedback;
• error analysis;
• and recognition of progress.

Teachers avoid language that suggests mathematical ability is fixed.

Learners are taught that success develops through secure knowledge, practice, support and perseverance.

Learners Requiring Greater Challenge

Learners who demonstrate secure understanding are challenged through:

• unfamiliar problems;
• deeper reasoning;
• proof;
• generalisation;
• multiple representations;
• comparison of methods;
• missing information;
• open-ended tasks;
• increased constraints;
• and greater independence.

Challenge should deepen understanding rather than simply increase the number of questions or move learners prematurely into later curriculum content.

Avoiding Over-Scaffolding

Scaffolds are selected carefully and reduced as knowledge becomes secure.

Teachers consider whether:

• manipulatives;
• sentence structures;
• adult prompts;
• worked examples;
• step-by-step guides;
• and visual models

are supporting independence or creating unnecessary dependence.

Inclusion in Mathematics means enabling every learner to engage with important mathematical ideas, not removing the reasoning or complexity from the subject.

In Nursery and Reception, children develop the foundations of Mathematics primarily through the areas of Mathematics and the wider EYFS curriculum.

Mathematical learning is supported through:

• direct teaching;
• purposeful play;
• adult interaction;
• stories;
• songs;
• routines;
• practical exploration;
• outdoor learning;
• and repeated encounters with important concepts.

The EYFS curriculum gives particular attention to:

• number;
• numerical patterns;
• shape;
• space;
• measure;
• pattern;
• and spatial reasoning.

Nursery

In Nursery, children develop early understanding of:

• quantity;
• counting;
• one-to-one correspondence;
• cardinality;
• comparison;
• subitising;
• composition of small numbers;
• pattern;
• shape;
• size;
• position;
• length;
• mass;
• capacity;
• and time.

Children may explore Mathematics through:

• counting objects;
• distributing resources;
• singing number songs;
• comparing groups;
• matching;
• sorting;
• building;
• filling and emptying;
• making patterns;
• completing puzzles;
• cooking;
• and discussing daily routines.

Adults model mathematical language and help children notice relationships.

They may ask:

• How many are there?
• How do you know?
• Can you show it another way?
• Which group has more?
• What is the same?
• What is different?
• How could you make five?
• What comes next?
• Which one is longer?
• Will this fit?
• How could we check?

Reception

In Reception, learners deepen their understanding of number and numerical patterns.

They develop:

• accurate counting;
• cardinality;
• subitising;
• composition of numbers;
• comparison;
• number bonds;
• one more and one less;
• doubling;
• sharing;
• grouping;
• odd and even patterns;
• shape;
• measure;
• pattern;
• and spatial reasoning.

Learners are encouraged to:

• represent quantities;
• explain what they notice;
• compare arrangements;
• identify patterns;
• use mathematical language;
• and apply knowledge in practical situations.

Number Sense

Early Mathematics prioritises deep understanding of small numbers.

Learners should not be rushed into calculations with larger numbers before they understand:

• quantity;
• composition;
• comparison;
• and the relationships between numbers.

For example, secure understanding of five includes recognising that it can be composed as:

• four and one;
• three and two;
• five and zero;
• or other equivalent arrangements.

This knowledge supports later addition and subtraction.

Subitising

Children are given repeated opportunities to recognise small quantities without counting each item individually.

They encounter quantities through:

• fingers;
• dice;
• dot patterns;
• ten frames;
• objects;
• and different arrangements.

Adults encourage children to explain how they saw the quantity.

Mathematical Language

Children develop words and phrases such as:

• more;
• fewer;
• equal;
• same;
• different;
• altogether;
• first;
• next;
• before;
• after;
• behind;
• beside;
• under;
• above;
• longer;
• shorter;
• heavier;
• lighter;
• full;
• empty;
• pattern;
• shape;
• and number.

Language is connected directly to practical experience.

The Learning Environment

The indoor and outdoor environments provide opportunities to apply Mathematics through:

• construction;
• role play;
• sand and water;
• cooking;
• gardening;
• loose parts;
• puzzles;
• maps;
• obstacle courses;
• creative activities;
• and routines such as registration and snack time.

Mathematical opportunities are purposeful and supported by knowledgeable adult interaction.

Transition into Year 1

Information about each learner’s:

• counting;
• cardinality;
• subitising;
• number composition;
• comparison;
• mathematical language;
• pattern;
• shape;
• spatial reasoning;
• confidence;
• and support needs

is shared carefully between Reception and Year 1.

This ensures that Year 1 teaching builds from secure knowledge of prior learning.

Our Mathematics curriculum helps learners understand that Mathematics is a global, creative and evolving human discipline.

Learners encounter mathematical ideas, systems and contributions from different cultures, periods and communities.

Mathematics as a Human Endeavour

Learners understand that mathematical knowledge has developed through the work of many people across the world.

They may encounter contributions connected with:

• number systems;
• zero;
• algebra;
• geometry;
• measurement;
• astronomy;
• navigation;
• statistics;
• computing;
• engineering;
• architecture;
• and financial systems.

Teachers avoid presenting Mathematics as the work of only a small number of isolated individuals.

Mathematical development often involves:

• collaboration;
• translation;
• refinement;
• challenge;
• application;
• and the sharing of ideas across cultures.

Mathematicians and Related Careers

Learners should encounter a broad range of people who use Mathematics, including:

• mathematicians;
• statisticians;
• engineers;
• architects;
• computer scientists;
• economists;
• actuaries;
• data analysts;
• accountants;
• doctors;
• researchers;
• surveyors;
• designers;
• and scientists.

Curriculum content and displays should include:

• women mathematicians;
• Black and minority ethnic mathematicians;
• disabled mathematicians;
• mathematicians from different countries;
• contemporary professionals;
• and people whose contributions have historically received less recognition.

Cultural Breadth

Learners may explore how different societies have developed and used:

• numerals;
• calendars;
• measurement systems;
• geometric designs;
• pattern;
• symmetry;
• architecture;
• trade;
• navigation;
• and data.

Cultural examples should deepen mathematical understanding rather than become decorative or tokenistic additions.

For example, a pattern may be studied for its:

• symmetry;
• transformation;
• tessellation;
• ratio;
• or geometric structure,

as well as its cultural context.

Representation in Problems

Teachers review contexts used in mathematical problems so that learners encounter:

• different family structures;
• varied occupations;
• diverse names;
• different communities;
• inclusive images;
• and experiences beyond a narrow cultural or social norm.

Contexts should be relevant and respectful without distracting from the mathematical structure.

Financial and Everyday Contexts

Learners apply Mathematics to authentic situations involving:

• money;
• budgeting;
• saving;
• spending;
• comparing value;
• time;
• travel;
• measurement;
• data;
• and decision-making.

Problems should reflect realistic situations and support learners to understand how Mathematics influences everyday life.

Challenging Stereotypes

The curriculum challenges beliefs such as:

• some people are naturally mathematical and others are not;
• speed is the main sign of ability;
• Mathematics is primarily for boys;
• practical Mathematics is less valuable than abstract Mathematics;
• or making an error means a learner cannot succeed.

Learners encounter a wide range of mathematical role models and pathways.

Every learner should recognise that Mathematics belongs to them.

Enrichment gives learners opportunities to apply Mathematics in engaging, collaborative and unfamiliar contexts.

Opportunities may include:

• Mathematics clubs;
• problem-solving challenges;
• competitions;
• puzzle events;
• enterprise projects;
• financial education;
• coding;
• STEM activities;
• architecture projects;
• data investigations;
• outdoor Mathematics;
• family workshops;
• mathematical trails;
• themed Mathematics events;
• and links with businesses, universities or community organisations.

Enrichment complements, rather than replaces, the planned curriculum.

Mathematical Challenges

Learners may participate in challenges that require them to:

• work systematically;
• identify patterns;
• make conjectures;
• justify conclusions;
• solve collaboratively;
• communicate methods;
• and persist with unfamiliar problems.

Challenges should be accessible to a broad range of learners.

They should not be limited only to those who calculate most quickly.

Enterprise and Financial Education

Enterprise activities may help learners apply Mathematics through:

• budgeting;
• costing;
• pricing;
• calculating change;
• comparing value;
• profit and loss;
• data collection;
• forecasting;
• measurement;
• and evaluation.

Enterprise should include meaningful mathematical thinking rather than only selling a product.

Learners may consider:

• available funds;
• material costs;
• price per item;
• projected income;
• actual income;
• waste;
• affordability;
• and ethical decisions.

Outdoor Mathematics

Outdoor learning may support:

• measurement;
• shape;
• scale;
• position;
• direction;
• data collection;
• estimation;
• pattern;
• and problem-solving.

Learners may:

• measure distances;
• investigate symmetry;
• collect environmental data;
• create scale drawings;
• follow coordinate or directional routes;
• estimate height;
• or analyse patterns in the environment.

Activities are linked to clear mathematical learning.

Technology and Computing

Digital tools may support:

• representation;
• data handling;
• coding;
• graphing;
• geometry;
• simulation;
• and checking.

Technology is used when it strengthens understanding or enables purposeful application.

It should not replace essential mental, written or practical mathematical knowledge.

Family Engagement

The school may provide:

• calculation workshops;
• number-fact guidance;
• multiplication-table support;
• early-number sessions;
• problem-solving events;
• and information about White Rose Maths.

Family guidance should help parents and carers understand current methods and avoid unnecessary conflict between school and home approaches.

Pupil Leadership

Learners may contribute through roles such as:

• Mathematics Ambassadors;
• puzzle leaders;
• peer explainers;
• competition organisers;
• resource monitors;
• enterprise-team members;
• and contributors to mathematical displays or newsletters.

Peer support is carefully structured so that misconceptions are not reinforced.

Equitable Participation

Leaders review who participates in:

• clubs;
• challenges;
• competitions;
• workshops;
• enterprise;
• and leadership roles.

Disadvantaged learners, learners with SEND and learners with low confidence should have equitable access to wider mathematical opportunities.

Mathematics contributes strongly to learners’ personal development.

Through mathematical learning, learners develop:

• confidence;
• resilience;
• perseverance;
• patience;
• curiosity;
• precision;
• independence;
• logical thinking;
• collaboration;
• responsibility;
• and openness to alternative methods.

Mathematics teaches learners that difficulty is a normal part of learning.

They develop resilience by:

• trying a representation;
• breaking a problem into stages;
• checking a method;
• identifying an error;
• listening to another explanation;
• revising an approach;
• and continuing with appropriate support.

Resilience does not mean leaving learners to struggle without guidance.

Effective teaching provides the knowledge, representations and feedback learners need to make progress.

Responsible Use of Mathematics

Learners explore how Mathematics can influence:

• personal finance;
• public information;
• healthcare;
• technology;
• environmental decisions;
• voting and polling;
• economics;
• design;
• and access to resources.

They learn that data and statistics can be used responsibly or misleadingly.

Learners are encouraged to question:

• how information was collected;
• whether a graph is presented fairly;
• whether a sample is representative;
• whether an average is meaningful;
• and whether a conclusion is supported by the data.

British Values

Mathematics contributes to learners’ understanding of democracy, the rule of law, individual liberty, mutual respect and tolerance of different faiths and beliefs through:

• collaborative decision-making;
• agreed mathematical conventions;
• fair use of data;
• financial choice;
• respectful comparison of methods;
• reasoned disagreement;
• and recognition of mathematical contributions from different cultures.

Our school values are developed meaningfully through Mathematics.

Kindness

Learners listen patiently, explain ideas supportively, share resources and help create a classroom where mistakes can be discussed safely.

Respect

Learners respect different methods, mathematical evidence, agreed conventions and the contributions of others.

Confidence

Learners develop confidence by explaining thinking, using representations, solving problems, correcting errors and recognising their progress.

Excellence

Learners pursue excellence through secure knowledge, precise vocabulary, accurate calculation, careful reasoning and purposeful checking.

Mathematics supports our vision to Believe, Achieve and Thrive by helping learners believe in themselves as mathematicians, achieve through secure knowledge and disciplined thinking, and thrive as confident, resourceful and numerate members of society.

Families can support Mathematics by helping learners notice number, pattern, shape, measure and problem-solving in everyday life.

The most valuable support is regular, encouraging and connected to the methods learners are being taught in school.

Developing Positive Attitudes

Families are encouraged to avoid statements such as:

• “I was never good at Maths.”
• “Maths is too hard.”
• “Some people just cannot do Maths.”
• “You should know this already.”
• or “You are only good at Maths if you are fast.”

Instead, helpful language may include:

• “Let us think about what you already know.”
• “Can you show it another way?”
• “Which part is difficult?”
• “What representation could help?”
• “How could you check?”
• “Mistakes help us see what needs more practice.”
• and “You are becoming more confident with this.”

Everyday Mathematics

Families can support Mathematics through everyday activities such as:

• counting;
• shopping;
• cooking;
• telling the time;
• reading timetables;
• measuring;
• comparing prices;
• planning journeys;
• sharing;
• estimating;
• budgeting;
• looking at shapes;
• interpreting graphs;
• and discussing sports scores.

These experiences help learners recognise that Mathematics is useful and relevant.

Number Facts

Learners benefit from regular practice of:

• number bonds;
• doubles and halves;
• addition and subtraction facts;
• multiplication tables;
• related division facts;
• place-value relationships;
• and fraction, decimal and percentage equivalents.

Practice can be kept short and varied through:

• oral questions;
• card games;
• dice games;
• matching activities;
• quick quizzes;
• online practice approved by the school;
• and applying facts to calculations.

Understanding and recall should develop together.

Multiplication Tables

Families can support multiplication-table knowledge by encouraging learners to:

• count in equal steps;
• recognise patterns;
• use arrays;
• connect multiplication and division;
• derive unknown facts from known facts;
• practise little and often;
• and explain how they know.

For example, a learner may use a secure (5 \times 6) fact to derive (10 \times 6), or use (7 \times 8) to identify (56 \div 7).

Mathematical Talk

Useful questions include:

• How did you work it out?
• What do you notice?
• Can you represent it?
• Is there another method?
• Which method is most efficient?
• How do you know the answer is reasonable?
• What is the same?
• What is different?
• Can you prove it?
• Where did the error occur?
• What fact could help?

Families do not need to recreate a formal Mathematics lesson.

A short conversation about method and reasoning is often more useful than completing a large number of repetitive questions.

Supporting Current Calculation Methods

Families are encouraged to use the school’s calculation guidance when supporting written methods.

Methods may differ from those adults remember from their own schooling.

Where a learner is unsure, families should:

• encourage the learner to explain the taught method;
• refer to school guidance;
• avoid introducing several conflicting methods at once;
• and contact the class teacher where clarification is needed.

The aim is to support understanding and confidence.

Using Manipulatives and Drawings

Everyday objects may help learners represent Mathematics.

These may include:

• buttons;
• counters;
• coins;
• pasta;
• blocks;
• number lines;
• drawings;
• arrays;
• bar models;
• and place-value charts.

Using equipment is not a sign of weakness. Representations can support learners of all ages to explain and test mathematical relationships.

Supporting Problem-Solving

Families can encourage learners to:

• read the problem carefully;
• identify what is known;
• identify what must be found;
• draw or model the situation;
• choose an operation;
• estimate;
• solve;
• and check.

Adults should avoid immediately giving the operation or completing the problem for the learner.

Online Mathematics

Families should use school-recommended digital resources where possible.

Online activities should:

• reflect taught methods;
• be age appropriate;
• protect personal information;
• support meaningful practice;
• and avoid creating unnecessary pressure through public rankings or excessive time limits.

Seeking Support

Families should contact the class teacher where they are concerned about:

• counting;
• number recognition;
• number facts;
• multiplication tables;
• place value;
• calculation;
• mathematical vocabulary;
• understanding of problems;
• confidence;
• anxiety;
• or progress.

The school can help identify the specific knowledge requiring further teaching or practice.

Our Mathematics curriculum is planned so that learners build secure and connected knowledge from the Early Years Foundation Stage to Year 6.

The summaries below should be read alongside the whole-school Mathematics overview, calculation policy, progression documents and year-group curriculum maps.

Nursery

Children develop early understanding of:

• counting;
• one-to-one correspondence;
• cardinality;
• subitising;
• comparison;
• composition of small numbers;
• pattern;
• shape;
• space;
• measure;
• and mathematical vocabulary.

Reception

Learners develop:

• secure counting;
• cardinality;
• subitising;
• composition of numbers;
• comparison;
• number bonds;
• numerical patterns;
• one more and one less;
• doubling;
• sharing;
• grouping;
• shape;
• measure;
• and spatial reasoning.

Year 1

Learners develop:

• place value within 100;
• counting;
• addition and subtraction;
• number bonds;
• early multiplication and division;
• fractions;
• measurement;
• money;
• time;
• shape;
• position;
• and mathematical reasoning.

Year 2

Learners develop:

• place value;
• addition and subtraction facts;
• calculation;
• multiplication and division;
• fractions;
• measurement;
• money;
• time;
• two-dimensional and three-dimensional shape;
• position and direction;
• statistics;
• and problem-solving.

Year 3

Learners develop:

• place value;
• addition and subtraction;
• multiplication and division;
• multiplication tables;
• fractions;
• measurement;
• money;
• time;
• perimeter;
• shape;
• angles;
• and statistics.

Year 4

Learners deepen:

• place value;
• written and mental calculation;
• multiplication-table knowledge;
• multiplication and division;
• fractions;
• decimals;
• measurement;
• perimeter and area;
• geometry;
• position;
• and statistics.

Year 5

Learners develop:

• place value with larger numbers;
• calculation;
• factors and multiples;
• fractions;
• decimals;
• percentages;
• measurement;
• perimeter, area and volume;
• geometry;
• coordinates;
• translation;
• reflection;
• and statistics.

Year 6

Learners draw together knowledge from across the Mathematics curriculum.

They develop:

• place value;
• efficient calculation;
• fractions;
• decimals;
• percentages;
• ratio;
• proportion;
• algebra;
• measurement;
• geometry;
• statistics;
• multi-step problem-solving;
• proof;
• generalisation;
• and readiness for secondary Mathematics.

Year-Group Curriculum Links

The page should link to:

• Nursery Mathematics overview;
• Reception Mathematics overview;
• Year 1 Mathematics overview;
• Year 2 Mathematics overview;
• Year 3 Mathematics overview;
• Year 4 Mathematics overview;
• Year 5 Mathematics overview;
• Year 6 Mathematics overview;
• whole-school calculation policy;
• fluency progression;
• reasoning progression;
• and problem-solving progression.

The following documents provide further information about Mathematics at St Luke’s.

Core Mathematics Documents

• Whole-School Mathematics Curriculum Overview
• Mathematics Progression from Nursery to Year 6
• Calculation Policy
• Number and Place Value Progression
• Addition and Subtraction Progression
• Multiplication and Division Progression
• Fractions, Decimals and Percentages Progression
• Ratio and Proportion Progression
• Algebra Progression
• Measurement Progression
• Geometry Progression
• Statistics Progression
• Mathematical Vocabulary Progression
• Fluency Progression
• Reasoning Progression
• Problem-Solving Progression
• Manipulatives and Representations Guidance
• Mathematics Assessment Guidance
• Mathematics Intervention Framework
• Mathematics Across the Curriculum Guidance
• White Rose Curriculum Overview
• Mathematics Policy

Mathematics is led and monitored carefully to ensure that learners develop secure foundations, connected understanding and increasing independence.

The Mathematics leader works with:

• teachers;
• teaching assistants;
• senior leaders;
• the Early Years Foundation Stage team;
• the SENCo;
• curriculum leaders;
• governors;
• families;
• and external advisers where appropriate.

Leadership responsibilities include:

• reviewing curriculum sequencing;
• adapting White Rose materials where necessary;
• maintaining the calculation policy;
• monitoring early number;
• evaluating factual fluency;
• reviewing multiplication-table provision;
• monitoring use of representations;
• evaluating reasoning and problem-solving;
• reviewing mathematical vocabulary;
• supporting staff subject knowledge;
• identifying professional development needs;
• reviewing assessment;
• monitoring intervention;
• evaluating Mathematics across the curriculum;
• speaking with learners;
• reviewing books and lessons;
• and evaluating improvement actions.

Monitoring Mathematics

Leaders may monitor through:

• lesson visits;
• discussions with learners;
• book review;
• fluency checks;
• assessment analysis;
• review of representations;
• planning review;
• teacher discussion;
• pupil voice;
• intervention evaluation;
• and application across the wider curriculum.

Monitoring focuses on what learners understand, remember and can apply.

It should not rely only on the quantity of completed pages or whether every class is on the same White Rose lesson.

Key Questions for Leaders

Leaders consider:

• Are foundational concepts identified clearly?
• Do learners develop secure number sense?
• Are number facts taught and practised systematically?
• Do learners understand the Mathematics behind procedures?
• Are written methods taught consistently?
• Are representations selected purposefully?
• Can learners connect concrete, visual and abstract forms?
• Is mathematical vocabulary taught accurately?
• Are reasoning and problem-solving available to all learners?
• Are learners expected to explain and justify?
• Are misconceptions anticipated and addressed?
• Does assessment identify specific gaps?
• Is responsive teaching timely?
• Are interventions connected to classroom teaching?
• Are scaffolds reduced as learners become secure?
• Are learners with SEND accessing ambitious Mathematics?
• Are disadvantaged learners receiving effective support?
• Are confident mathematicians challenged through depth?
• Is White Rose adapted where cohort needs require it?
• Are learners prepared for the next stage?

Staff Development

Professional development may include:

• early number;
• number sense;
• subitising;
• factual fluency;
• multiplication tables;
• representations and manipulatives;
• written calculation;
• fractions;
• mathematical vocabulary;
• reasoning;
• problem-solving;
• responsive teaching;
• SEND and accessibility;
• assessment;
• and subject leadership.

New staff receive clear induction into:

• the school’s calculation policy;
• White Rose use and adaptation;
• agreed representations;
• fluency expectations;
• assessment;
• and intervention approaches.

Assessment and Moderation

Leaders support reliable assessment through:

• shared curriculum expectations;
• comparison of learner work;
• discussion of misconceptions;
• review of reasoning and problem-solving;
• analysis of factual fluency;
• and moderation within and beyond the school where appropriate.

Intervention Review

Intervention is reviewed to establish whether it:

• addresses a precise mathematical gap;
• uses familiar language and representations;
• complements classroom teaching;
• is delivered consistently;
• improves application;
• reduces dependency;
• and supports successful participation in whole-class learning.

Governor Oversight

Governors receive strategic information about:

• curriculum quality;
• attainment and progress;
• foundational knowledge;
• vulnerable groups;
• intervention impact;
• staff development;
• resource needs;
• and improvement priorities.

Information is presented without identifying individual learners.

Further information about Mathematics at St Luke’s is available through the curriculum pages and documents linked above.

Parents and carers can request:

• more detailed information about Mathematics in a particular year group;
• copies of curriculum overviews;
• the calculation policy;
• information about White Rose Maths;
• support with early number;
• number-bond guidance;
• multiplication-table support;
• explanations of written methods;
• fraction guidance;
• problem-solving support;
• information about Mathematics assessment;
• details of intervention;
• accessible versions of curriculum documents;
• and information about workshops or mathematical events.

Please contact the class teacher or school office through the contact details provided on the school website.

Families are encouraged to raise concerns promptly if a learner:

• struggles to count accurately;
• has difficulty recognising quantities;
• cannot recall important number facts;
• misunderstands place value;
• relies heavily on counting for simple calculations;
• finds mathematical language difficult;
• avoids problem-solving;
• becomes anxious about Mathematics;
• or is not making expected progress.

The school will review whether support is needed with:

• number sense;
• factual recall;
• place value;
• calculation;
• language;
• representation;
• reasoning;
• problem-solving;
• working memory;
• confidence;
• or access to suitable resources.

Paper copies of curriculum information can be provided on request.

The school welcomes constructive feedback about the accessibility and usefulness of its Mathematics information. Published content is reviewed regularly to ensure that it remains accurate, clear and consistent with the curriculum learners receive.