1. National Curriculum 2014 (UK)
2. Mathematics

Key Stage 3

Outcomes

• Working Mathematically
  • Develop Fluency
    • Substitute values in expressions, rearrange and simplify expressions, and solve equations
      Play Activities 5
      Examples
    • Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics
      Play Activities 6
      Examples
• Subject Content
  • Number
    • Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ?, <, >, ?, ?
      Play Activities 5
      Examples
    • 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
      Play Activities 6
      Examples
    • 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 232
      Examples
    • Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
      Play Activities 22
      Examples
    • 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
      Play Activities 96
      Examples
    • Interpret and compare numbers in standard form A x 10n 1?A< 10, where n is a positive or negative integer or zero
      Play Activities 51
      Examples
    • Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
      Play Activities 5
      Examples
    • 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
      Play Activities 42
      Examples
    • Interpret fractions and percentages as operators
      Play Activities 121
      Examples
    • Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
      Play Activities 16
      Examples
    • Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a< x?b
      Play Activities 10
      Examples
  • Algebra
    • Use and interpret algebraic notation, including:
      • Ab in place of a x b
        Play Activities 5
        Examples
      • 3y in place of y + y + y and 3 x y
        Play Activities 3
        Examples
      • 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
        Play Activities 8
        Examples
      • A/b in place of a ÷ b
        Play Activities 5
        Examples
      • Brackets
        Play Activities 3
        Examples
    • Substitute numerical values into formulae and expressions, including scientific formulae
      Play Activities 25
      Examples
    • Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
      Play Activities 3
      Examples
    • Simplify and manipulate algebraic expressions to maintain equivalence by:
      • Collecting like terms
        Play Activities 13
        Examples
      • Multiplying a single term over a bracket
        Play Activities 4
        Examples
      • Taking out common factors
        Play Activities 2
        Examples
      • Expanding products of two or more binomials
        Play Activities 4
        Examples
    • Understand and use standard mathematical formulae; rearrange formulae to change the subject
      Play Activities 16
      Examples
    • Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
      Play Activities 32
      Examples
    • Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
      Play Activities 20
      Examples
    • 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
      Play Activities 17
      Examples
    • Interpret mathematical relationships both algebraically and graphically
      Play Activities 3
      Examples
    • 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
      Play Activities 15
      Examples
    • 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
      Play Activities 11
      Examples
    • Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
      Play Activities 11
      Examples
    • Generate terms of a sequence from either a term-to-term or a position-to-term rule
      Play Activities 8
      Examples
    • Recognise arithmetic sequences and find the nth term
      Play Activities 80
      Examples
    • Recognise geometric sequences and appreciate other sequences that arise
      Play Activities 13
      Examples
  • Ratio, Proportion & Change
    • Use scale factors, scale diagrams and maps
      Play Activities 12
      Examples
    • Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
      Play Activities 23
      Examples
    • Use ratio notation, including reduction to simplest form
      Play Activities 99
      Examples
    • 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 110
      Examples
    • Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
      Play Activities 21
      Examples
    • Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
      Play Activities 3
      Examples
    • Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
      Play Activities 41
      Examples
    • Solve problems involving direct and inverse proportion, including graphical and algebraic representations
      Play Activities 6
      Examples
    • Use compound units such as speed, unit pricing and density to solve problems
      Play Activities 45
      Examples
  • Geometry & Measures
    • 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)
      Play Activities 36
      Examples
    • Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
      Play Activities 50
      Examples
    • 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
      Play Activities 6
      Examples
    • Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
      Play Activities 4
      Examples
    • Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
      Play Activities 36
      Examples
    • Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
      Play Activities 48
      Examples
    • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
      Play Activities 10
      Examples
    • Understand and use the relationship between parallel lines and alternate and corresponding angles
      Play Activities 16
      Examples
    • 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
      Play Activities 16
      Examples
    • 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
      Play Activities 31
      Examples
    • Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
      Play Activities 3
      Examples
    • Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
      Play Activities 5
      Examples
    • Interpret mathematical relationships both algebraically and geometrically
      Play Activities 5
      Examples
  • Probability
    • 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 116
      Examples
    • Understand that the probabilities of all possible outcomes sum to 1
      Play Activities 4
      Examples
  • Statistics
    • 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,
      Play Activities 64
      Examples
    • 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
      Play Activities 28
      Examples
    • Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs
      Play Activities 4
      Examples