Key Stage 3
Outcomes
- Working Mathematically
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Subject Content
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Number
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Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ?, <, >, ?, ?
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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 propert
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Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
Play Activities 232Examples
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Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
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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
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Interpret and compare numbers in standard form A x 10n 1?A< 10, where n is a positive or negative integer or zero
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Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
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Define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and w
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Interpret fractions and percentages as operators
Play Activities 121Examples
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Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
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Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a< x?b
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Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ?, <, >, ?, ?
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Algebra
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Use and interpret algebraic notation, including:
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Ab in place of a x b
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3y in place of y + y + y and 3 x y
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A2 in place of a x a, a3 in place of a x a x a; a2b in place of a x a x b
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A/b in place of a ÷ b
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Brackets
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Ab in place of a x b
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Substitute numerical values into formulae and expressions, including scientific formulae
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Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
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Simplify and manipulate algebraic expressions to maintain equivalence by:
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Collecting like terms
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Multiplying a single term over a bracket
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Taking out common factors
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Expanding products of two or more binomials
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Collecting like terms
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Understand and use standard mathematical formulae; rearrange formulae to change the subject
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Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
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Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
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Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
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Interpret mathematical relationships both algebraically and graphically
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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
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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
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Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
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Generate terms of a sequence from either a term-to-term or a position-to-term rule
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Recognise arithmetic sequences and find the nth term
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Recognise geometric sequences and appreciate other sequences that arise
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Use and interpret algebraic notation, including:
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Ratio, Proportion & Change
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Use scale factors, scale diagrams and maps
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Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
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Use ratio notation, including reduction to simplest form
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Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
Play Activities 110Examples
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Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
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Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
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Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
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Solve problems involving direct and inverse proportion, including graphical and algebraic representations
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Use compound units such as speed, unit pricing and density to solve problems
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Use scale factors, scale diagrams and maps
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Geometry & Measures
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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)
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Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
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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
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Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
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Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
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Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
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Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
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Understand and use the relationship between parallel lines and alternate and corresponding angles
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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
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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
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Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
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Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
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Interpret mathematical relationships both algebraically and geometrically
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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)
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Probability
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Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
Play Activities 116Examples
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Understand that the probabilities of all possible outcomes sum to 1
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Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
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Statistics
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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,
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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
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Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs
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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,
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Number