Secondary: Key Stage 3

 MathematicsSecondary: Key Stage 368531255023350Curriculum plan 2020-2190000081324001. Curriculum PrinciplesAs mathematics teachers we want our pupils to reach?fluency?in what we are teaching them. In mathematics, fluency requires a deep understanding of concepts and the ability to apply them flexibly and with automaticity. The mathematics curriculum uses multiple representations to help make connections across concepts to help build a deep conceptual understanding. By making consistent use of the same core representations we will scaffold pupils’ thinking to help them understand abstract mathematical concepts. The curriculum will also include intelligent practice that is designed to help pupils develop automaticity in their mathematics.We also aim for our pupils to be able to use the?precise?language?of mathematics, that is distinct from everyday language. The curriculum will do this by explicitly teaching mathematical vocabulary and introducing core sentence structures with which to communicate, express, connect, reason with and apply?mathematical?structures and ideas. Finally, we also aim for our pupils to be able to?think mathematically.?The tasks and activities used in the curriculum teach pupils the components of mathematical thinking: to sort and classify, compare and contrast, specialise and generalise,?to?make conjectures and?to?prove them. ?Below are the set of principles we have used to build this curriculum, with these ambitions for our pupils in mind:Coherence and flexibilityWe strive to support schools by offering a maths curriculum that can fit alongside a range of existing structures. However, complete flexibility over unit ordering is impossible due to the cumulative nature of mathematics and the importance of prior knowledge. We have grouped lessons into units: coherent sequences of 5 or more lessons. Although each lesson can be accessed individually, explicit connections are made to earlier lessons and later lessons in the same unit. This is because the connections between mathematical concepts are so vital to deepening understanding. Knowledge organisationThe units in the maths curriculum are grouped as appropriate for each key stage, with a suggested route organised within year groups. Knowledge selectionOur mathematics lessons cover the full scope of the National Curriculum. We have given more time (both in number of lessons and number of units) to those concepts within the National Curriculum that the evidence tells us are foundational to success in maths. Inclusive and ambitiousWe know the difference it makes when children believe they “can do” maths. We are guided by the principles of the National Curriculum to ensure that every pupil, regardless of starting point, develops their fluency, reasoning and problem solving. Our activities are scaffolded so all children can succeed. Pupils are offered frequent opportunities to be and feel successful in their maths education. We develop conceptual understanding by always building new understanding on what pupils already know, by representing concepts in different ways, and by making connections between concepts. The mathematics curriculum makes consistent use of the same core representations across year groups to help pupils connect prior learning to new learning. These representations are selected to make key mathematical structures and ideas accessible to all pupils, no matter what their starting points. To support every child to communicate mathematically, pupils are introduced to core sentence structures with which to express, connect, reason with and apply?mathematical?structures and ideas.??Pupil engagementYou learn maths by thinking about maths. Our lessons include mathematical tasks which have multiple solutions. Mathematical thinking is woven into the units using scaffolds and prompts such as ‘what is the same and what’s different?’, ‘is it sometimes, always or never true?’ and ‘which could be the odd one out?’. Throughout the curriculum, all pupils have opportunities to sort and classify, compare and contrast, specialise and generalise, to make conjectures and to prove them. Motivation through learningWe believe that mathematics is inherently interesting and that all children?are?entitled?to?a genuine experience of mathematics. The tasks and activities that?pupils?engage with?harness?innate ways of thinking?and develop the habits of mind that?are?drawn?upon when?being?mathematical. Problem solving?is at the heart of every lesson with opportunities to investigate, explore and reason.??2. Subject structure overviewDeveloping deep conceptual understanding requires building on what has been previously understood to develop understanding within a concept and of new concepts. Constructing the curriculum with this principle in mind results in careful sequencing within units, strands, year groups and across key stages to create a coherent progression for pupils. The subject structure shows how knowledge and skills are built up within each strand. The prior knowledge required to access the concepts within each unit will help ensure coherence is maintained when parts of the curriculum are used out of the sequence presented in the following table. Units that are foundational across different strands appear multiple times in the subject structure.Unit title and descriptionLength of unitPrior knowledge requiredNumber7.1Numbers and numeralsDeveloping understanding of a base 10 place value system and exploring number systems with different bases1 weekN/A7.2Axioms and arraysUnderstand how commutativity, associativity and distributivity underpin our number system and use arrays to represent multiplicative relationships2 weeksN/A7.3Factors and multiplesExplore the composition of integers and use this to understand the idea of factors and multiples2 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbers7.4Order of operationsEstablish a hierarchy for the four operations and use index notation1 week7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersUnderstanding of commutativity, associativity and distributivity7.5Positive and negative numbers Use positive and negative numbers with all four operations3 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersUnderstanding of commutativity, associativity and distributivity7.4 Order of operationsUnderstanding and applying the hierarchy of operations7.13Prime factor decompositionFormalise understanding of the composition of integers 1 week7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbers7.3 Factors and multiplesExpressing integers as a product of two factorsFinding a common multiple of two numbersGeometric representations of integers 7.14Conceptualising and comparing fractionsDevelop understanding of fractions and represent them in different ways2 weeks7.2 Axioms and arrays:Understanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersUse of diagrams to represent multiplication and division7.15Manipulating and calculating with fractionsExtend understanding of applying the four operations on integers to fractions and decimal fractions3 weeks7.2:Understanding of the relationship between division and multiplicationUse of arrays to represent fractions7.14:Knowledge of the different contexts in which a fraction can resultEquivalent fractions7.17PercentagesBuild on understanding of fractions to include percentages. Extend methods developed for calculating with fractions to percentages2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultRepresenting fractions including on a number line Equivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations8.5Accuracy and estimationRounding to the nearest power of 10 and significant figures. Use rounding for estimation. Upper and lower bounds and represent inequalities on a number line2 weeks7.14 Conceptualising and comparing fractionsDecimal notationRepresenting fractions and decimals on a number line9.9Surds and trigonometryUsing surd notation and applying all operations on surds3 weeks7.3 Factors and multiples:Square numbers7.4 Order of operationsApplying the square root function9.12Indices and standard form Index notation and rules including fractional indices Comparing and calculating in standard form3 weeks7.4 Using index notation up to a power of 37.14Representing fractions and decimals on a number lineAlgebra7.2Axioms and arraysUnderstand how commutativity, associativity and distributivity underpin our number system and use arrays to represent multiplicative relationships2 weeksN/A7.4Order of operationsEstablish a hierarchy for the four operations and use index notation1 week7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersCommutativity, associativity and distributivity7.5Positive and negative numbers Use positive and negative numbers with all four operations3 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersCommutativity, associativity and distributivity7.4 Order of operationsUnderstanding and applying the hierarchy of operations7.6Expressions, equations and inequalitiesUse algebraic notation to generalise additive and multiplicative relationships. Form equations and inequalities3 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersCommutativity, associativity and distributivity7.4 Order of operationsUnderstanding and applying the hierarchy of operations8.1SequencesUse algebraic notation to express term to term and position to term rules 2 weeks7.6 Expressions, equations and inequalitiesUsing algebraic notation in different contextsGenerating sequences from geometric patterns8.2Forming and solving equationsExpressions, equations, unknowns, variables. Using algebraic notation to investigate perimeter problems2 weeks7.2 Axioms and arraysUse of arrays to represent integers as a product of two numbersCommutativity, associativity and distributivity7.6 Expressions, equations and inequalitiesUsing algebraic notation in different contexts7.11 Area of 2-D shapesArea and perimeter of rectilinear shapes8.3Forming and solving inequalitiesInequality notation and using algebraic methods to solve inequalities2 weeks7.6 Expressions, equations and inequalitiesUsing algebraic notation in different contexts, including inequality notation8.2 Forming and solving equationsForming and solving linear equations derived from different contexts8.4Linear graphsInequalities on a cartesian plane. Labelling and plotting linear graphs. Familiarity with y=mx+c3 weeks8.1 SequencesExpressing position to term rules algebraically7.10 CoordinatesUsing (x,y) notation to describe position on a coordinate grid9.3Solving linear simultaneous equations algebraicallyUsing algebraic methods to solve simultaneous equations4 weeks8.2 Forming and solving equationsSolving linear equations8.4 Linear graphsPlotting, sketching and interpreting graphs of linear functions9.4Solving linear simultaneous equations graphicallySetting up and solving simultaneous equations graphically2 weeks9.3 Solving linear simultaneous equations algebraicallyUsing algebraic methods to solve simultaneous equations9.10Quadratic expressionsCreating quadratic expressions. Expanding and factorising binomials, plotting quadratic graphs3 weeks7.2 Axioms and arraysApplying the distributive property7.6 Expressions, equations and inequalitiesUsing algebraic notation in different contexts, including inequality notation7.10 CoordinatesUsing (x,y) notation to describe position on a coordinate grid8.4 Linear graphsPlotting, sketching and interpreting graphs of linear functions9.11Quadratic equationsSolving quadratic equations. Completing the square and turning points3 weeks9.10 Quadratic expressionsManipulating quadratic expressions8.3 Forming and solving equations Forming and solving linear equations derived from different contextsRatio and proportion7.2Axioms and arraysUnderstand how commutativity, associativity and distributivity underpin our number system and use arrays to represent multiplicative relationships2 weeks7.14Conceptualising and comparing fractionsDevelop understanding of fractions and represent them in different ways2 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersUse of diagrams to represent multiplication and division7.15Manipulating and calculating with fractionsExtend understanding of applying the four operations on integers to fractions and decimal fractions3 weeks7.2: Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent fractions7.14: Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultEquivalent fractions7.16RatioExplore different contexts in which ratio appears and develop use of ratio notation2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultEquivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations7.17PercentagesBuild on understanding of fractions to include percentages. Extend methods developed for calculating with fractions to percentages2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultRepresenting fractions including on a number line Equivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations8.7Ratio, real life graphs, and rates of changeBuilding proportional reasoning in a variety of contexts2 weeks7.16 RatioRatio notation8.4 Linear graphsFinding the gradient and y-intercept of a linear graph8.8Direct and indirect proportionDirect proportion and links to linear graphs and ratio. Inverse proportion in different contexts2 weeks7.16 RatioRatio notation8.4 Linear graphsFinding the gradient and y-intercept of a linear graph9.8Similarity and enlargementSimilarity and ratio. Area and volume of similar shapes2 weeks7.12 Transforming 2-D figuresEnlarging a shape by a given scale factor7.16 RatioExpressing multiplicative relationships using fractions9.9Surds and trigonometryUsing trigonometric ratios to solve problems3 weeks7.3 Factors and multiplesSquare numbers7.4 Order of operations:Square root function9.13Growth and decayExponential growth and decay including compound percentage change and reverse percentage change2 weeks7.17 PercentagesCalculating with percentagesPercentage increase and decrease9.11 Indices and standard formUse index notation and apply index rulesGeometry7.7AnglesDevelop understanding of angle as a measure of turn. Derive geometric properties involving angles and use these to solve problems2 weeksN/A7.8Classifying 2-D shapesUsing geometric properties to sort and classify 2-D shapes2 weeks7.7 AnglesAngle rules including angles around a point, angles in a straight line and angles in parallel lines7.9Constructing triangles and quadrilateralsDevelop understanding of angle properties and 2-D shapes to construct triangles and quadrilaterals 2 weeks7.7 AnglesAngle rules including angles around a point, angles in a straight line and angles in parallel lines7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals7.10CoordinatesExtend understanding of coordinate systems into all four quadrants2 weeks7.5 Positive and negative numbersRepresenting negative numbers using a number line7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals7.11Area of 2-D shapesUnderstand area as a measure of surface and formalise methods for finding the area of different 2-D shapes2 weeks7.2 Axioms and arraysRepresenting integers as a product of two factors using an array7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals7.12Transforming 2-D figuresRotations, reflections, translations and enlargements on a coordinate grid2 weeks7.7 AnglesUnderstand angle as a measure of turn7.10 CoordinatesPlotting points on a coordinate grid in all four quadrants8.12Angles in straight edgesUsing the sum of interior angles of a triangle to explore other polygons. Generalising for interior and exterior angles of polygons4 weeks7.7 AnglesAngle rules including angles around a point, angles in a straight line and angles in parallel lines7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals8.13BearingsConventions and notation of bearings. Calculating with bearings2 weeks7.7 AnglesAngle rules including angles around a point, angles in a straight line and angles in parallel lines7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals8.14CirclesRelationships between diameter and circumference. Area and perimeter of circles including composite shapes2 weeks7.11 Area of 2-D shapesArea as a measure of surface8.15Volume and surface area of prismsCalculating volume of prisms, composite solids. Conversions between units of volume3 weeks7.11 Area of 2-D shapesArea as a measure of surface9.5Constructions, congruence, and lociRuler and compass constructions. Congruence and loci2 weeks7.8 Classifying 2-D shapesProperties of special triangles and quadrilaterals7.9 Constructing triangles and quadrilateralsUse ruler, compasses and protractor to construct triangles and quadrilaterals9.6Pythagoras’s theoremInvestigation on tilted squares. Introduction to surd notation and finding missing sides2 weeks7.11 Area of 2-D shapesFinding the area of triangles and rectilinear shapes9.8Similarity and enlargementSimilarity and ratio. Area and volume of similar shapes2 weeks7.12 Transforming 2-D figuresEnlarging a shape by a given scale factor7.16 RatioExpressing multiplicative relationships using fractions9.9Surds and trigonometryUsing trigonometric ratios to solve problems3 weeks7.16 RatioExpressing multiplicative relationships using fractionsStatistics and probability7.14Conceptualising and comparing fractionsDevelop understanding of fractions and attach represent them in different ways2 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent integers as a product of two numbersUse of diagrams to represent multiplication and division7.15Manipulating and calculating with fractionsExtend understanding of applying the four operations on integers to fractions and decimal fractions3 weeks7.2 Axioms and arraysUnderstanding of the relationship between division and multiplicationUse of arrays to represent fractions7.14 Conceptualising and comparing fractions:Knowledge of the different contexts in which a fraction can resultEquivalent fractions7.16RatioExplore different contexts in which ratio appears and develop use of ratio notation2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultEquivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations7.17PercentagesBuild on understanding of fractions to include percentages. Extend methods developed for fractions to percentages2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultRepresenting fractions including on a number line Equivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations8.9Univariate dataUnderstanding mean, median, mode and range in different contexts and using different representations. Exploring collection of discrete and continuous data3 weeks7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations7.16 RatioExpressing multiplicative relationships using fractions8.10Bivariate dataConstructing scatter graphs and analysing shape, including examining clusters, outliers, and correlation2 weeks8.4 Linear graphsPlotting, sketching and interpreting graphs of linear functions8.8 Univariate dataCalculating statistical measures of univariate data including mean, mode, median and range9.1ProbabilityTheoretical and experimental probability. Probability of single and combined events2 weeks7.14 Conceptualising and comparing fractionsKnowledge of the different contexts in which a fraction can resultRepresenting fractions including on a number line Equivalent fractions7.15 Manipulating and calculating with fractionsCalculating with fractions using all four operations9.2Sets and Venn and diagramsVenn diagrams, samples spaces, two-way tables and tree diagrams3 weeks9.1 ProbabilityExpressing the probability of a single event and combined events using fractional notation3. Suggested sequenceThe following tables show our suggested sequence of the curriculum across year 7 to 9. This sequencing ensures that knowledge and skills are built up according to the progression within each strand while also giving opportunities for pupils to engage with a variety of mathematics within each year group. The sequencing within each strand in the previous section shows how units can be taken out of this suggested sequence and the prior knowledge required indicates dependencies between the different strands.Year 7 Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Week 10Week 11Week 12AutumnMaking generalisations about the number system 1Making generalisations about the number system 27.1 Numbers and numerals7.2 Axioms and arrays7.3 Factors and multiples7.4 Order of operations7.5 Positive and negative numbers7.6 Expressions, equations and inequalitiesSpring2-D geometryThe Cartesian plane7.7 Angles7.8 Classifying 2-D shapes7.9 Constructing triangles and quadrilaterals7.10 Coordinates7.11 Area of 2-D shapes7.12 Transforming 2-D figuresSummerFractionsRatio and proportion7.13 Prime factor decomposition7.14 Conceptualising and comparing fractions7.15 Manipulating and calculating with fractions7.16 Ratio7.17 Percentages7.18 Different number systemsYear 8Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Week 10Week 11Week 12AutumnEquations and inequalities 1Equations and inequalities 28.1 Sequences8.2 Forming and solving equations8.3 Forming and solving inequalities8.4 Linear graphs8.5 Accuracy and estimation8.6 Mixed algebra problemsSpringProportional reasoningRepresentations and reasoning with data8.7a Ratio8.7 Ratio, real life graphs and rate of change8.8 Direct and inverse proportion8.9 Univariate data8.10 Bivariate data8.11 Famous maths problemsSummerAnglesArea, volume and surface area8.12 Angles in straight edges8.13 Bearings8.14 Circles and composite shapes8.15a Area review8.15 Volume andSurface area of prismsYear 9Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Week 10Week 11Week 12AutumnProbabilityLinear simultaneous equations9.1a FDP review9.1 Probability9.2 Sets and Venn diagrams9.3 Solving algebraically9.4 Solving graphicallySpringGeometry of trianglesRatio and proportion9.5a Angle review9.5 Constructions, congruence and loci9.6 Pythagoras’ Theorem9.7 Famous maths problems9.8a Ratio review9.8 Similarity and enlargement9.9 Surds and trigonometrySummerQuadraticsReasoning with number9.10 Quadratic expressions9.11 Quadratic equations9.12 Indices and standard form9.13 Growth and decay9.13b Finance ................
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