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Mathematics Programme of Study

Key Stage 3

 

Year 7

Year 8

Autumn Term 1

  • Whole number calculations
  • Negative numbers
  • Place value & rounding
  • BIDMAS
  • Expressions & formulae
  • Negative numbers
  • Decimal number calculations
  • Place value & rounding
  • BIDMAS
  • Factors & multiples
  • Products of prime numbers 
  • HCF & LCM
  • Straight line graphs
  • Time-series graphs

Autumn Term 2

  • Area & perimeter of 2D shapes
  • Surface area & volume of cuboids
  • Metric & imperial units
  • Operations with fractions
  • Converting between fractions, decimals & percentages
  • Percentage of an amount
  • Percentage increase & decrease
  • Ratio & proportion
  • Metric & imperial units
  • Area & perimeter of 2D shapes
  • Area & Circumference of a circle
  • Arc length & area of sector
  • Properties of 3D shapes
  • Plans & elevations
  • Surface area & volume of prisms
  • Transformations

Spring Term 1

  • Angles on straight line & around a point
  • Angles in triangles, quadrilaterals & polygons
  • Angles in parallel lines
  • Straight line graphs
  • Frequency tables
  • Bar charts, pie charts, line graphs & time series graphs
  • Simplifying algebraic expressions
  • Expanding single & double brackets
  • Factorisation
  • Substitution
  • Rearranging formulae
  • Solving equations (including brackets & unknowns on both sides)
  • Sequences & nth term rule

Spring Term 2

  • Averages & range
  • Line symmetry & rotational symmetry
  • Transformations
  • Probability
  • Sample space
  • Experimental probability
  • Venn diagrams
  • Tree diagrams
  • Construction
  • Loci
  • Bearings

Summer Term 1

  • Solving equations (including brackets & unknowns on both sides)
  • Factors & multiples
  • Sequences & nth term rule
  • Operations with fractions
  • Converting between fractions, decimals & percentages
  • Percentage of an amount
  • Percentage increase & decrease
  • Compound interest & depreciation

Summer Term 2

  • Probability
  • Experimental probability
  • Venn diagrams
  • Constructions & loci
  • Plans & elevations of 3D shapes
  • Review of graphs
  • Stem & leaf diagrams
  • Averages
  • Pie charts
  • Scatter diagrams
  • Dividing numbers according to a ratio
  • Proportions
  • Exchange rates
  • Best buys

Extra-curricular provision 

MathsWatch for consolidation of curriculum, independent learning, homework & revision

MathsWatch for consolidation of curriculum, independent learning, homework & revision

Mathematics Programme of Study: Key Stage 3

Department for Education - Purpose of Study

Working mathematically through the mathematics content, students should be taught to:

Develop fluency

  1. consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots
  2. select and use appropriate calculation strategies to solve increasingly complex problems
  3. use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
  4. substitute values in expressions, rearrange and simplify expressions, and solve equations
  5. move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
  6. develop algebraic and graphical fluency, including understanding linear and simple quadratic functions
  7. use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

  1. extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
  2. extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically
  3. identify variables and express relations between variables algebraically and graphically
  4. make and test conjectures about patterns and relationships; look for proofs or counter- examples
  5. begin to reason deductively in geometry, number and algebra, including using geometrical constructions
  6. interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
  7. explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

  1. develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  2. develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics
  3. begin to model situations mathematically and express the results using a range of formal mathematical representations
  4. select appropriate concepts, methods and techniques to apply to unfamiliar and non- routine problems.

Number

  1. Pupils should be taught to:
  2. understand and use place value for decimals, measures and integers of any size
  3. order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
  4. use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
  5. use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
  6. use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
  7. recognise and use relationships between operations including inverse operations
  8. use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
  9. interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive
  10. or negative integer or zero
  11. work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
  12. define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
  13. interpret fractions and percentages as operators
  14. use standard units of mass, length, time, money and other measures, including with decimal quantities
  15. round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
  16. use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a
  17. use a calculator and other technologies to calculate results accurately and then interpret them appropriately
  18. appreciate the infinite nature of the sets of integers, real and rational numbers.

Algebra

  1. Pupils should be taught to:
  2. use and interpret algebraic notation, including:
    1. ab in place of a × b
    2. 3y in place of y + y + y and 3 × y
    3. a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
    4.  a/b n place of a ÷ b
    5. coefficients written as fractions rather than as decimals
    6. brackets
  3. substitute numerical values into formulae and expressions, including scientific formulae
  4. understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
  5. simplify and manipulate algebraic expressions to maintain equivalence by:
    1. collecting like terms
    2. multiplying a single term over a bracket
    3. taking out common factors
    4. expanding products of two or more binomials
  6. understand and use standard mathematical formulae; rearrange formulae to change the subject
  7. model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
  8. use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
  9. work with coordinates in all four quadrants
  10. recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
  11. interpret mathematical relationships both algebraically and graphically
  12. reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
  13. use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
  14. find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
  15. generate terms of a sequence from either a term-to-term or a position-to-term rule
  16. recognise arithmetic sequences and find the nth term
  17. recognise geometric sequences and appreciate other sequences that arise.

Ratio, proportion and rates of change

  1. Pupils should be taught to:
  2. change freely between related standard units [for example time, length, area, volume/capacity, mass]
  3. use scale factors, scale diagrams and maps
  4. express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
  5. use ratio notation, including reduction to simplest form
  6. divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
  7. understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
  8. relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
  9. solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
  10. solve problems involving direct and inverse proportion, including graphical and algebraic representations
  11. use compound units such as speed, unit pricing and density to solve problems.

Geometry and measures

  1. Pupils should be taught to:
  2. derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
  3. calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
  4. draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  5. derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
  6. describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
  7. use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
  8. derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
  9. identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
  10. identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
  11. apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  12. understand and use the relationship between parallel lines and alternate and corresponding angles
  13. derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
  14. apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
  15. use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
  16. use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
  17. interpret mathematical relationships both algebraically and geometrically.

Probability

  1. Pupils should be taught to:
  2. record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
  3. understand that the probabilities of all possible outcomes sum to 1
  4. enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
  5. generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Statistics

  1. Pupils should be taught to:
  2. describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
  3. construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
  4. describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

  

Mathematics Programme of Study: Key Stage 4

 

Year 9

Year 10

Autumn Term 1

Higher Tier

  • Place value and estimating
  • HCF & LCM
  • Zero, negative & fractional indices
  • Standard form
  • Surds
  • Expanding and factorising
  • Solving equations
  • Rearranging formulae
  • Substitution
  • Linear sequences & nth term

Foundation Tier

  • Number calculations
  • Decimal numbers
  • Place value
  • Factors & multiples
  • Squares, cubes & roots
  • Index notation
  • Prime factors
  • Simplifying algebraic expressions
  • Substitution
  • Formulae

Higher Tier

  • Solving quadratic equations
  • Completing the square
  • Solving linear simultaneous equations (including worded questions)
  • Solving linear & quadratic simultaneous equations
  • Solving linear inequalities
  • Probability of compound events
  • Experimental probability
  • Frequency trees
  • Probability tree diagrams

Foundation Tier

  • Coordinates
  • Linear graphs
  • Real-life graphs
  • Distance-time graphs
  • Transformations (translation, reflection, rotation)

Autumn Term 2

Higher Tier

  • Non-linear sequences (geometric, Fibonacci & quadratic)
  • Quadratic expansion and factorisation
  • Stem and leaf diagrams
  • Frequency polygons
  • Scatter graphs
  • Averages & range
  • Two-way tables

Foundation Tier

  • Expanding brackets
  • Factorising
  • Using expressions & formulae
  • Representing data
  • Time series
  • Stem & leaf diagrams
  • Pie charts
  • Scatter graphs
  • Line of best fit

Higher Tier

  • Conditional probability
  • Venn diagrams & set notation
  • Compound interest & depreciation
  • Compound measures (eg speed & density)
  • Direct & inverse proportion

Foundation Tier

  • Transformations (enlargement)
  • Ratios & proportion
  • Direct & inverse proportion

Spring Term 1

Higher Tier

  • Add, subtract, multiply & divide fractions
  • Ratios & proportion
  • Fractions, decimals & percentages
  • Angles properties of triangles & quadrilateral
  • Interior & exterior angles of polygons
  • Pythagoras’ Theorem

Foundation Tier

  • Working with fractions
  • Add, subtract, multiply & divide fractions
  • Converting between fractions, decimals & percentages
  • Percentage of an amount
  • Percentage increase & decrease

Higher Tier

  • Congruent shapes
  • Similar shapes 2D & 3D
  • Graphs of sine, cosine & tangent function

Foundation Tier

  • Pythagoras’ Theorem
  • Trigonometry
  • Probability of single events
  • Finding probabilities of two events using sample space diagrams
  • Experimental probability

Spring Term 2

Higher Tier

  • Trigonometry
  • Linear graphs
  • Real-life graphs
  • Distance-time graphs and velocity-time graphs

Foundation Tier

  • Solving equations (including equations with brackets & unknowns on both sides)
  • Inequalities on a number line
  • Solving inequalities
  • Formulae
  • Sequences & nth term


Higher Tier

  • Area of a triangle using sine rule
  • Sine and cosine rule
  • Sampling (random, stratified, capture-recapture)
  • Cumulative frequency
  • Box plots
  • Histograms
  • Pythagoras & trigonometry in 3D
  • Transformation of graphs

Foundation Tier

  • Venn diagrams
  • Frequency diagrams
  • Probability tree diagrams
  • Percentage of an amount
  • Compound interest
  • Speed, distance & time
  • Direct & inverse proportion

Summer Term 1

Higher Tier

  • Quadratic graphs
  • Cubic & reciprocal graphs
  • Perimeter & area of trapezium & compound shapes
  • Upper and lower bounds
  • Volume & surface area of prisms
  • Area & Circumference of a circle
  • Arc length and area of sectors of circles

Foundation Tier

  • Properties of shapes
  • Angles in parallel lines
  • Angles in triangles
  • Interior & exterior angles in polygons
  • Averages & range

Higher Tier

  • Solving simultaneous equations graphically
  • Representing inequalities graphically
  • Solving quadratic equations graphically
  • Circle theorems

Foundation Tier

  • Properties of 3D shapes
  • Plans & elevations
  • 2D nets of 3D shapes
  • Constructing triangles
  • Identifying congruent triangles
  • Scale drawings
  • Constructions & loci
  • Bearings

Summer Term 2

Higher Tier

  • Plans & elevations of 3D shapes
  • Transformations of 2D shapes
  • Bearings
  • Scale drawings
  • Construction & loci
  • Volume & surface area of cylinders, spheres, pyramids & cones

Foundation Tier

  • Sampling
  • Area & perimeter of 2D shapes
  • Area of compound shapes
  • Surface area of 3D solids
  • Volume of prisms

Higher Tier

  • Rearranging formulae
  • Algebraic fractions (simplifying expressions & solving equations)
  • Surds (rationalising the denominator, expanding brackets)
  • Composite & inverse functions eg f(x), g(x)
  • Vectors

Foundation Tier

  • Expanding double brackets
  • Plotting quadratic graphs
  • Quadratic factorisation
  • Solving quadratic equations
  • Area & Circumference of a circle
  • Volume & surface area of prisms, pyramids, cones & spheres
  • Standard form

Extra-curricular provision 

MathsWatch for consolidation of curriculum, independent learning, homework & revision

MathsWatch for consolidation of curriculum, independent learning, homework & revision

 

Mathematics Programme of Study: Key Stage 4

Department for Education - Purpose of Study

Working mathematically through the mathematics content, students should be taught to:

Develop fluency

  1. consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots
  2. select and use appropriate calculation strategies to solve increasingly complex problems
  3. use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
  4. substitute values in expressions, rearrange and simplify expressions, and solve equations
  5. move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
  6. develop algebraic and graphical fluency, including understanding linear and simple quadratic functions
  7. use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

  1. extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations
  2. extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically
  3. identify variables and express relations between variables algebraically and graphically
  4. make and test conjectures about patterns and relationships; look for proofs or counter- examples
  5. begin to reason deductively in geometry, number and algebra, including using geometrical constructions
  6. interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
  7. explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

  1. develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  2. develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics
  3. begin to model situations mathematically and express the results using a range of formal mathematical representations
  4. select appropriate concepts, methods and techniques to apply to unfamiliar and non- routine problems.

Number

  1. Pupils should be taught to:
  2. understand and use place value for decimals, measures and integers of any size
  3. order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
  4. use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
  5. use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
  6. use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
  7. recognise and use relationships between operations including inverse operations
  8. use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
  9. interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive
  10. or negative integer or zero
  11. work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
  12. define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
  13. interpret fractions and percentages as operators
  14. use standard units of mass, length, time, money and other measures, including with decimal quantities
  15. round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
  16. use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a
  17. use a calculator and other technologies to calculate results accurately and then interpret them appropriately
  18. appreciate the infinite nature of the sets of integers, real and rational numbers.

Algebra

  1. Pupils should be taught to:
  2. use and interpret algebraic notation, including:
    1. ab in place of a × b
    2. 3y in place of y + y + y and 3 × y
    3. a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
    4.  a/b n place of a ÷ b
    5. coefficients written as fractions rather than as decimals
    6. brackets
  3. substitute numerical values into formulae and expressions, including scientific formulae
  4. understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
  5. simplify and manipulate algebraic expressions to maintain equivalence by:
    1. collecting like terms
    2. multiplying a single term over a bracket
    3. taking out common factors
    4. expanding products of two or more binomials
  6. understand and use standard mathematical formulae; rearrange formulae to change the subject
  7. model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
  8. use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
  9. work with coordinates in all four quadrants
  10. recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
  11. interpret mathematical relationships both algebraically and graphically
  12. reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
  13. use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
  14. find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
  15. generate terms of a sequence from either a term-to-term or a position-to-term rule
  16. recognise arithmetic sequences and find the nth term
  17. recognise geometric sequences and appreciate other sequences that arise.

Ratio, proportion and rates of change

  1. Pupils should be taught to:
  2. change freely between related standard units [for example time, length, area, volume/capacity, mass]
  3. use scale factors, scale diagrams and maps
  4. express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
  5. use ratio notation, including reduction to simplest form
  6. divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
  7. understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
  8. relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
  9. solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
  10. solve problems involving direct and inverse proportion, including graphical and algebraic representations
  11. use compound units such as speed, unit pricing and density to solve problems.

Geometry and measures

  1. Pupils should be taught to:
  2. derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
  3. calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
  4. draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  5. derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
  6. describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
  7. use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
  8. derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
  9. identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
  10. identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
  11. apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  12. understand and use the relationship between parallel lines and alternate and corresponding angles
  13. derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
  14. apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
  15. use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
  16. use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
  17. interpret mathematical relationships both algebraically and geometrically.

Probability

  1. Pupils should be taught to:
  2. record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
  3. understand that the probabilities of all possible outcomes sum to 1
  4. enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
  5. generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Statistics

  1. Pupils should be taught to:
  2. describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
  3. construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
  4. describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.