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+g*y1^%5, d", e" .N4Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.N13Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].N13
N14Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.N5lUse conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.N12fUse standard units of mass, length, time, money and other measures, including with decimal quantities.N12
DF1%Use standard units of mass, length, time, money and other measures, including with decimal quantities.
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. Y5
N13
Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].
G3
N12Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Use standard units of mass, length, time, money and other measures, including with decimal quantities.Y5:Solve problems involving converting between units of time G7
G3
DF7Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.G1
G2HDerive 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).
Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes.Calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm) and square metres (m), and estimate the area of irregular shapesA1#Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" bracketsUse and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.A1
DF3A4Simplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a single term over a bracket
" taking out common factors
" expanding products of 2 or more binomialsA2YSubstitute numerical values into formulae and expressions, including scientific formulae.A6nModel situations or procedures by translating them into algebraic expressions or formulae and by using graphs.yIdentify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.VRecognise mixed numbers and improper fractions and convert from one form to the other.1Interpret fractions and percentages as operators.N11N10"Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.N9
DF5PWork interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as < a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]N9
N10
DF5ZKnow angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.lApply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.G10G3fDraw and measure line segments and angles in geometric figures, including interpreting scale drawings.Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.G7R2+Use scale factors, scale diagrams and maps.A8)Work with coordinates in all 4 quadrants.A13Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs.S2Construct 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.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.N4
SP4N4
DF2Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Select and use appropriate calculation strategies to solve increasingly complex problems.IComplete, read and interpret information in tables, including timetables.hConstruct 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.
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally. S2
RM7S1Describe, 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).
S1
DF7Describe, 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).
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.G5Describe, 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.vIdentify properties of, and describe the results of, translations, rotations and reflections applied to given figures.G8DF6gDevelop algebraic and graphical fluency, including understanding linear and simple quadratic functions.N6PRecognise and use relationships between operations including inverse operations.N6
A7Recognise and use relationships between operations including inverse operations.
Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).oUse algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).A7Recognise and use relationships between operations including inverse operations.
Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Substitute values in expressions, rearrange and simplify expressions, and solve equations.N6
A7
DF3
DF4Use 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.N3Use 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.Square NumbersN7rIdentify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers.
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.Y5
N3Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.DF7
G15Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.G15Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.G3
G9A14SGenerate terms of a sequence from either a termtoterm or a positiontoterm rule.pGenerate and describe linear number sequences.
Use negative numbers in context, and calculate intervals across 0Y6
Y6They should recognise and describe linear number sequences (for example, 3, 3.5, 4, 4.5) including those involving fractions and decimals, and find the termtoterm rule in words (for example, add 0.5).
They should recognise and describe linear number sequences (for example, 3, 3.5, 4, 4.5) including those involving fractions and decimals, and find the termtoterm rule in words (for example, add 0.5).
Generate and describe linear number sequences.Y5
Y6?Multiply and divide numbers mentally, drawing upon known facts.Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000.
Understand and use place value for decimals, measures and integers of any size.Y5
N12Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.N14
N4FDivide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.Y5
N4N14Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
N15
N14
SP1{Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Use approximation through rounding to < estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.Use ratio notation, including reduction to simplest form.
Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.R4
R6uUnderstand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Solve problems involving direct and inverse proportion, including graphical and algebraic representations.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.R6
R9
RM2SP2
SP2
RM6
DF2CDevelop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
Select and use appropriate calculation strategies to solve increasingly complex problems.
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.DF7Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 01 probability scale.P1P3fEnumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams.RM5gBegin to reason deductively in geometry, number and algebra, including using geometrical constructions.RM5
SP4Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.wDevelop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.SP2
SP3Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.DF5 DF5
RM4Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].
Make and test conjectures about patterns and relationships; look for proofs or counterexamples. DF1
DF3(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.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.RM1Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations. RM1
DF5HExtend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].N3
P3hUse 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.
Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams.
N3
P3
SP4Use 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.
Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.R1
N12Change freely between related standard units [for example time, length, area, volume/capacity, mass].
Use standard units of mass, length, time, money and other measures, including with decimal quantities.R1eChange freely between related standard units [for example time, length, area, volume/capacity, mass].G1Derive 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).R10MUse compound units such as speed, unit pricing and density to solve problems.iUse algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.DF3A3
DF7Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.
Use language and properties precisely to analyse numbers, algebraic
expressions, 2D and 3D shapes, probability and statistics.Understand and use standard mathematical formulae; rearrange formulae to change the subject.
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.A5
A6N9Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.N9
N5
N10
R8Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.R8
SP2Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
R8
SP1
SP2Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.SMake and test conjectures about patterns and relationships; look for proofs or counterexamples.
Understand and use the relationship between parallel lines and alternate and corresponding angles.
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.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.G12
RM4
G11
G12?Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of trianglesG7
G6}Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes.
G2Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles.
Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.G6
G9Reduce 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. A11
RM3*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.
Identify variables and express relations between variables algebraically and graphically.sRecognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
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.A9
A11Reduce 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.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]A11
DF5
yRecognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.A9
A6
DF6A9
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs.A6
A13Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use compound units such as speed, unit pricing and density to solve problems.A6
R10Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.RM1
SP1
SP2N5
N6
RM4Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
Recognise and use relationships between operations including inverse operations.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples.nUse a calculator and other technologies to calculate results accurately and then interpret them appropriately.N15
N15
N14
N12_Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Use standard units of mass, length, time, money and other measures, including with decimal quantities.Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.RM7Describe, 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).
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. S1
S2!Describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.S3
RM7Describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.S3Describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.
G9{Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.Use scale factors, scale diagrams and maps.
Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.R2
G3Use scale factors, scale diagrams and maps.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.R2
RM2DF7
RM7Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Substitute values in expressions, rearrange and simplify expressions, and solve equations.A7
DF4}Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.
Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
N2
A3
A7 A12
A10Use 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.
Interpret mathematical relationships both algebraically and graphically.nInterpret and compare numbers in standard form A x 10n 1d"A<10, where n is a positive or negative integer or 0.N8Interpret and compare numbers in standard form A x 10n 1d"A<10, where< n is a positive or negative integer or 0.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.N8
N15Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.A1
N5yUse Pythagoras Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles.G14RM5
DF5Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].Generate terms of a sequence from either a termtoterm or a positiontoterm rule.
Recognise arithmetic sequences and find the nth term.A14
A15HRecognise geometric sequences and appreciate other sequences that arise.A16Generate terms of a sequence from either a termtoterm or a positiontoterm rule.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.A14
DF2A16
A6Recognise geometric sequences and appreciate other sequences that arise.
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.EDerive 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).
Use Pythagoras Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles.G1
G14zUse Pythagoras Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles.
Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Use Pythagoras Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles.G3
G14
RM4
RM5
SP3?Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Interpret fractions and percentages as operators.R6R6
N119Use ratio notation, including reduction to simplest form.Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio.mUnderstand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.Use ratio notation, including reduction to simplest form.
Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio.
Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.
R4
R5
R6
R7jSolve problems involving direct and inverse proportion, including graphical and algebraic representations.R9Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.R7
RM6SP3vBegin to model situations mathematically and express the results using a range of formal mathematical representations. P1
RM7[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 01 probability scale.
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. P4Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 01 probability scale.
Understand that the probabilities of all possible outcomes sum to 1.P1
P2Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.
DF4ZSubstitute values in expressions, rearrange and simplify expressions, and solve equations.DF4
DF6Substitute values in expressions, rearrange and simplify expressions, and solve equations.
Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.SP3
SP4Select and use appropriate calculation strategies to solve increasingly complex problems.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.DF2
SP1
SP3
SP4Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.RM5
SP1
SP3
SP4Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and < techniques to apply to unfamiliar and nonroutine problems.RM1
SP1
SP3
SP4Understand and use place value for decimals, measures and integers of any size.
Interpret and compare numbers in standard form A x 10n 1d"A<10, where n is a positive or negative integer or 0.N1
N81Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes.G7
G2Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]\Understand and use standard mathematical formulae; rearrange formulae to change the subject.A5Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Interpret fractions and percentages as operatorsN4
N11yWork interchangeably with terminating decimals and their corresponding fractions (such as
3.5 and 7/2 or 0.375 and 3/8.)Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
DF2
DF5
R8Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.
Understand and use the relationship between parallel lines and alternate and corresponding angles.G10
G11Apply 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.
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
G13
G5iDerive 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.
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 symmetricG12
G5Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles.G6Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.A11Reduce 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.
Interpret mathematical relationships both algebraically and graphically. A11
A108Reduce 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.
Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions. A11
DF6Reduce 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.
Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
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.A11
A9
A12Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
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).A6
S1Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
N5
N15Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.N14
N15Describe, 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)Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures.
Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.G8
G9PUse algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Simplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a single term over a bracket
" taking out common factors
" expanding products of 2 or more binomialsA7
A4Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Substitute values in expressions, rearrange and simplify expressions, and solve equations.A6
DF4+Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a;
" < ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" bracketsN15
N7.Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
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.N8
N12Interpret and compare numbers in standard form A x 10n 1d"A<10, where n is a positive or negative integer or 0.
Use standard units of mass, length, time, money and other measures, including with decimal quantities..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.G4 G13
G14EApply 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.
Use Pythagoras Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles.SGenerate terms of a sequence from either a termtoterm or a position toterm rule.Recognise arithmetic sequences and find the nth term.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.A15
DF3Generate terms of a sequence from either a termtoterm or a position toterm rule.
Recognise arithmetic sequences and find the nth term.Generate terms of a sequence from either a termtoterm or a position toterm rule.
Recognise arithmetic sequences and find the nth term.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples.A14
A15
RM4Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions. G15
RM5Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.N9
N10Use ratio notation, including reduction to simplest form.
Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio.R4
R5Use scale factors, scale diagrams and maps.
Express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1.R2
R3Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.R6
R8
RM2Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
Solve problems involving direct and inverse proportion, including graphical and algebraic representations.RM6
R9DUnderstand that the probabilities of all possible outcomes sum to 1.P2Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.DF3
SP1
SP3
SP4Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.RM7
SP1
SP3
SP4Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.RM2
SP1
SP3
SP4bUse 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.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
N3
RM4Use 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.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.N3
N4
A1
A2}Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Substitute numerical values into formulae and expressions, including scientific formulae.
A4
A3KSimplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a singl< e term over a bracket
" taking out common factors
" expanding products of 2 or more binomials
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.A2
A6
Substitute numerical values into formulae and expressions, including scientific formulae.
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.A4
G16+Simplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a single term over a bracket
" taking out common factors
" expanding products of 2 or more binomials
Interpret mathematical relationships both algebraically and geometrically.DF3
N4Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.DF2YSelect and use appropriate calculation strategies to solve increasingly complex problems.DF2
RM6Select and use appropriate calculation strategies to solve increasingly complex problems.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
DF2
RM6
SP4/Select and use appropriate calculation strategies to solve increasingly complex problems.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.N9
N2Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .R8N9
N2
N10=Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.
Understand and use the relationship between parallel lines and alternate and corresponding anglesG7
G5Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
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.G12
G7DDerive 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.
Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.G13
G9GApply 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.
Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.A9
A12CRecognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
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.
N2
N4
N4
RM1;Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
N4
N14
SP1Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.S3
DF5
RM1
SP2Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs].
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.A7
G16Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Interpret mathematical relationships both algebraically and geometrically.A2
A5
DF3 Substitute numerical values into formulae and expressions, including scientific formulae.
Understand and use standard mathematical formulae; rearrange formulae to change the subject.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
N4
DF2
N14Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions,< and mixed numbers, all both positive and negative.
Select and use appropriate calculation strategies to solve increasingly complex problems.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
N15
N13
N14}Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.N15
R1Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Change freely between related standard units [for example time, length, area, volume/capacity, mass].Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.N4
N6
SP1Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Recognise and use relationships between operations including inverse operations.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.N4
N6Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Recognise and use relationships between operations including inverse operations.GRecognise geometric sequences and appreciate other sequences that ariseR4
R5
R6
R7pDivide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio.
Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.R6
RM6Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
R9
A13
RM2Solve problems involving direct and inverse proportion, including graphical and algebraic representations.
Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.P4
P2Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.
Understand that the probabilities of all possible outcomes sum to 1.RM2Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically. RM2
DF2Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Select and use appropriate calculation strategies to solve increasingly complex problemsDF2
RM1
SP1oSelect and use appropriate calculation strategies to solve increasingly complex problems.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
RM5
SP3
SP4CBegin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.
DF7
RM3
SP4?Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
Identify variables and express relations between variables algebraically and graphically.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.RM2
RM5
SP1Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
DF3
RM4
SP3AUse algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.N1
N2
N4Understand and use place value for decimals, measures and integers of any size.
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.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. N7
N15/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.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.Change freely between related standard units [for example time, length, area, volume/capacity, mass].
Use standard units of mass, length, time, money and other measures, including with decimal quantities.
R1
R2Change freely between related standard units [for example time, length, area, volume/capacity, mass].
Use scale factors, scale diagrams and maps.A1
A2
DF3
DF4
AUse and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b < in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Substitute numerical values into formulae and expressions, including scientific formulae.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Substitute values in expressions, rearrange and simplify expressions, and solve equationsN7
A1Use 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.
Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" bracketsA6
A2Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Substitute numerical values into formulae and expressions, including scientific formulae.G11aUnderstand and use the relationship between parallel lines and alternate and corresponding anglesG7
G12DDerive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
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.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
G9
G13
RM4Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids.
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.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples. N1
N2
Understand and use place value for decimals, measures and integers of any size.
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .N11
N4
R3>Interpret fractions and percentages as operators.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1.
N9
N10
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.N9
N10
DF5
A8
A9A8
A9
A10Work with coordinates in all 4 quadrants.
Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
Interpret mathematical relationships both algebraically and graphically.A13
A12
RM3Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs.
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.
Identify variables and express relations between variables algebraically and graphically.N4
N1Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Understand and use place value for decimals, measures and integers of any size.N4
N14
N12
SP2Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Use standard units of mass, length, time, money and other measures, including with decimal quantities.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
S1
RM7Describe, 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).
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.A2
A7
A6
DF3Substitute numerical values into formulae and expressions, including scientific formulae.
Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.N4
N142Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Use< approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.SP1
SP4Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.DF2
SP1Select and use appropriate calculation strategies to solve increasingly complex problems.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.A155Recognise arithmetic sequences and find the nth term.A14
A15
RM1Generate terms of a sequence from either a termtoterm or a positiontoterm rule.
Recognise arithmetic sequences and find the nth term.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.G1
G15aDerive 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).
Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.R4
R2gUse ratio notation, including reduction to simplest form.
Use scale factors, scale diagrams and maps.
R5
R7Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio.
Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.N10
R8
R9
RM2
R6uSolve problems involving direct and inverse proportion, including graphical and algebraic representations.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.P1
P2
P4Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 01 probability scale.
Understand that the probabilities of all possible outcomes sum to 1.
Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.
DF2
RM6
SP2CSelect and use appropriate calculation strategies to solve increasingly complex problems.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
RM5
SP3
SP4
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
N1
N2.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.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.N12
R1Use standard units of mass, length, time, money and other measures, including with decimal quantities.
Change freely between related standard units [for example time, length, area, volume/capacity, mass].Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes.R3bExpress 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1.!Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%yWork interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
G10
G6Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.
Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles. G5
DF7BDescribe, 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.
Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.R1
A12
RM3
`Change freely between related standard units [for example time, length, area, volume/capacity, mass].
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.
Identify variables and express relations between variables algebraically and graphically.DF6
A6Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.N1
N4Understand and use place value for decimals, measures and integers of any size.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
DF2
N14
SP3ZSelect and use appropriate calculation strategies to solve increasingly complex problems.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
DF2
N14
SP1fSelect and use appropriate calculation strategies to solve increasingly complex problems.
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.N6
N6
A7
SP1
DF2Develop their mathematic< al knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Select and use appropriate calculation strategies to solve increasingly complex problems.RGenerate terms of a sequence from either a termtoterm or a positiontoterm ruleGenerate terms of a sequence from either a termtoterm or a positiontoterm rule
Recognise arithmetic sequences and find the nth term.Generate terms of a sequence from either a termtoterm or a positiontoterm rule
Recognise arithmetic sequences and find the nth term.
Make and test conjectures about patterns and relationships; look for proofs or counterexamplesA16
RM1Recognise geometric sequences and appreciate other sequences that arise.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations. DF5
DF75Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.R5R7
RM2Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.N11
N9Interpret fractions and percentages as operators.
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
SP2
R9Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Solve problems involving direct and inverse proportion, including graphical and algebraic representations.P1
DF3
SP1
SP2
SP4Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics..
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.RM4
SP1
SP3
SP4Make and test conjectures about patterns and relationships; look for proofs or counterexamples
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.
SP1
SP3
SP4^Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.
RM5
SP1
SP4OBegin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.Y5
N4
N1MMultiply and divide whole numbers and those involving decimals by 10, 100 and 1,000.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Understand and use place value for decimals, measures and integers of any size.N2
N4JOrder positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.LSimplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a single term over a bracket
" taking out common factors
" expanding products of 2 or more binomials
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.
A6
DF3Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.Simplify and manipulate algebraic expressions to maintain equivalence by:
" collecting like terms
" multiplying a single term over a bracket
" taking out common factors
" expanding products of 2 or more binomials
RM1
SP4Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.xWork interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8.)N10
DF5
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]G10
G7!Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.
Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.bUnderstand and use the relationship between parallel lines and alternate and corresponding angles.G7
DF75Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.A9
A10Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian pl< ane.
Interpret mathematical relationships both algebraically and graphicallyExtend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Select and use appropriate calculation strategies to solve increasingly complex problems.N4
4Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Substitute numerical values into formulae and expressions, including scientific formulaeN5
N15
A2S2
S1Construct 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.
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).S2
A7
N6Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Recognise and use relationships between operations including inverse operations.A6
DF3
SP3OModel situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.A1
A14wUse and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Generate terms of a sequence from either a termtoterm or a positiontoterm rule.A15
RM4Recognise arithmetic sequences and find the nth term.
Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
SP4
DF2
RM6/Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.
Select and use appropriate calculation strategies to solve increasingly complex problems.
Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8.)
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%eUse ratio notation, including reduction to simplest form.
Use scale factors, scale diagrams and maps.Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio.R6
R7Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.
Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.
SP2
SP3
RM7pDevelop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.DF2
RM2
RM5
SP4Select and use appropriate calculation strategies to solve increasingly complex problems.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.[Select and use appropriate calculation strategies to solve increasingly complex problems.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.DF2
RM2
SP4DF3
DF4
RM1
SP2Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Substitute values in expressions, rearrange and simplify expressions, and solve equations.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.DF5
RM2
SP3
DF5
RM3
SP1
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
Identify variables and express relations between variables algebraically and graphically.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.N4
N2JUse the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .G3
R1Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Change freely between related standard units [for example time, length, area, volume/capacity, mass].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)A1
A6Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place o< f y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" brackets
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.A2
DF5Substitute numerical values into formulae and expressions, including scientific formulae.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]A6
A2
DF4#Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Substitute numerical values into formulae and expressions, including scientific formulae.
Substitute values in expressions, rearrange and simplify expressions, and solve equations.Y5 zIdentify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.
Y6
Y5
N4Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
Add and subtract fractions with the same denominator, and denominators that are multiples of the same number.
Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.N9
N1Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Understand and use place value for decimals, measures and integers of any size.
N10
N9Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).G3
G6Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles.G3
G5
G7
RM5^Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
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.
Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.A2
DF6Substitute numerical values into formulae and expressions, including scientific formulae.
Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions.A9
A13
RM3
SP3Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.
Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs.
Identify variables and express relations between variables algebraically and graphically.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
G5
G8
QDescribe, 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.
Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures.G5
G8 G15
DF7Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.
Use language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.G15
G1aUse the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D.
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).N4
DF1gUse the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.
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.R3
N10Express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1.
Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.Use ratio notation, including reduction to simplest form.
Divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio.DF7
P1ZUse language and properties precisely to analyse numbers, algebraic expressions, 2D and 3D shapes, probability and statistics.
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 01 probability scale.rExtend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Begin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.RM1
RM5
SP2DF1
RM2
SP3
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.
Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.DF5
RM1
SP1
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fr< actions and decimals, and equations and graphs]
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.N2
N1Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, `", <, >, d", e" .
Understand and use place value for decimals, measures and integers of any size.ASimplify and manipulate algebraic expressions to maintain equivalence by: " collecting like terms " multiplying a single term over a bracket " taking out common factors " expanding products of 2 or more binomials
A4
A2Simplify and manipulate algebraic expressions to maintain equivalence by: " collecting like terms " multiplying a single term over a bracket " taking out common factors " expanding products of 2 or more binomials Substitute numerical values into formulae and expressions, including scientific formulae.
A2
A5
N6
Substitute numerical values into formulae and expressions, including scientific formulae.
Understand and use standard mathematical formulae; rearrange formulae to change the subject.
Recognise and use relationships between operations including inverse operations.A6
A1Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use and interpret algebraic notation, including:
" ab in place of a b
" 3y in place of y + y + y and 3 y
" a in place of a a, a in place of a a a; ab in place of a a b
" a/b in place of a b
" coefficients written as fractions rather than as decimals
" bracketsN11 /Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8).
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]Define percentage as number of parts per hundred , interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematicsApply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles.
Understand and use the relationship between parallel lines and alternate and corresponding angles.G6
G7@Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles. Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.G12
G3Derive 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. Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.A8
A10tWork with coordinates in all 4 quadrants.
Interpret mathematical relationships both algebraically and graphically.A6
RM1Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations.Work with coordinates in all 4 quadrants.
Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.A10
A11Interpret mathematical relationships both algebraically and graphically. 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 N4
N14
Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures].
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xd"b.N15
DF2Use a calculator and other technologies to calculate results accurately and then interpret them appropriately.
Select and use appropriate calculation strategies to solve increasingly complex problems.Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, an<d pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data. 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). 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).
Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.A3jUnderstand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.A7
DF3
DF46Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.
Substitute values in expressions, rearrange and simplify expressions, and solve equations.Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement).
Substitute values in expressions, rearrange and simplify expressions, and solve equations.A6
A7Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.
Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement). RM4
N7"Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
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.N7
DF3)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.
Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate gridsGenerate terms of a sequence from either a termtoterm or a position toterm rule.
Recognise arithmetic sequences and find the nth term.UGenerate terms of a sequence from either a termtoterm or a position toterm rule. IDerive 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). Calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes.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). RM2
SP1
SP2
SP3
SP4yExtend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.Select and use appropriate calculation strategies to solve increasingly complex problems
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Begin to model situations mathematically and express the results using a range of formal mathematical representations.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.
DF2
SP1
SP4DSelect and use appropriate calculation strategies to solve increasingly complex problems
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems. .
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.QBegin to reason deductively in geometry, number and algebra, including using geometrical constructions.
Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.SP2
SP4Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics.
Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems.Select and use appropriate calculation strategies to solve increasingly complex problems.
Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.,Maths Department Key Stage 3 Schemes of WorkWPlease select the textbook you are using from the tabs at the bottom or the link below.SetBook7x17x27x37y17y27y37y48x18x28x38y18y28y38y49x19x29x39x49y19y29y39y41A1C1B2C2B2A3C3B3ASu1Su21A Topic 1B Topic1C Topic2A Topic2B Topic 2C Topics 3A TopicsThe nth term formula3B Topic3C TopicAutumn 1Autumn 2Spring 1Spring 2Summer 1Summer 2CH1 Whole numbers and decimalsCH2 Measure, perimeter and areaCH3 Expressions and formulaeEnd of half term testCH4 Fractions, decimals and %sCH5 Angles and 2D shapes
CH6 GraphsCH7 CalculationsCH8 StatisticsCH9 TransformationsCH10 EquationsCH11 Factors and multiplesCH12 ConstructionsCH13 SequencesCH14 CalculationsCH15 Ratio and proportionCH16 ProbabilityCH17 Everyday mathsAYears 7 and 8  end of half term test. Year 9  end of year test.*Overview of schedule of work by half term:
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