
KS3Key Stage 3 Standards
Top Mathematicians

Statistics

KS3.S.1.1
Statistics
• Pupils should be taught to:
 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)
 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
 describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs. 

KS3.1495

KS3.1505

KS3.1525

KS3.18110

KS3.27510

KS3.27610

KS3.27710

KS3.27810

KS3.27910

KS3.2805

KS3.2815

KS3.2825

KS3.2835

KS3.2845

KS3.28510

KS3.28610

KS3.28710

KS3.28810

KS3.28910

KS3.2905

KS3.2915

KS3.2925

KS3.2935

KS3.2945

KS3.29520

KS3.2965

KS3.2975

KS3.2985

KS3.2995

KS3.3005

KS3.3015

KS3.3025

KS3.3035

KS3.3045

KS3.3055

KS3.3065

KS3.3075

KS3.3085

KS3.30910

KS3.3105

KS3.3115

KS3.3125


KS3.S.1.1

Number

KS3.NS.1.1
Number
• Pupils should be taught to:
 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 =, â‰ , <, >, â‰¤, â‰¥
 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
 use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
 use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
 recognise and use relationships between operations including inverse operations
 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
 interpret and compare numbers in standard form A x 10n 1 â‰¤ A < 10, where n is a positive or negative integer or zero
 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 one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
 interpret fractions and percentages as operators
 use standard units of mass, length, time, money and other measures, including with decimal quantities
 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 < x â‰¤ b
 use a calculator and other technologies to calculate results accurately and then interpret them appropriately
 appreciate the infinite nature of the sets of integers, real and rational numbers. 

KS3.120

KS3.210

KS3.315

KS3.515

KS3.615

KS3.715

KS3.915

KS3.1020

KS3.1120

KS3.1215

KS3.1310

KS3.1415

KS3.1510

KS3.1620

KS3.1720

KS3.1820

KS3.1915

KS3.2020

KS3.2115

KS3.2220

KS3.2320

KS3.2415

KS3.2510

KS3.265

KS3.2715

KS3.2815

KS3.2915

KS3.3015

KS3.3115

KS3.3220

KS3.335

KS3.345

KS3.3515

KS3.3615

KS3.3715

KS3.3815

KS3.3915

KS3.4015

KS3.4120

KS3.4220

KS3.4315

KS3.4420

KS3.455

KS3.4620

KS3.4720

KS3.4815

KS3.4915

KS3.5015

KS3.5115

KS3.5215

KS3.5315

KS3.5415

KS3.5515

KS3.5615

KS3.575

KS3.5815

KS3.595

KS3.6010

KS3.6115

KS3.6210

KS3.6310

KS3.6415

KS3.6515

KS3.6615

KS3.675

KS3.6810

KS3.6910

KS3.7015

KS3.7110

KS3.7215

KS3.735

KS3.7410

KS3.7510

KS3.7610

KS3.7710

KS3.7810

KS3.7910

KS3.8015

KS3.815

KS3.825

KS3.835

KS3.8415

KS3.8515

KS3.8615

KS3.8715

KS3.8815

KS3.8915

KS3.9020

KS3.915

KS3.925

KS3.935

KS3.945

KS3.955

KS3.9610

KS3.9710

KS3.9810

KS3.9920

KS3.10015

KS3.1015

KS3.1025

KS3.10315

KS3.10415

KS3.10515

KS3.10620

KS3.10720

KS3.10820

KS3.10920

KS3.11015

KS3.11115

KS3.11215

KS3.11315

KS3.11420

KS3.11515

KS3.11615

KS3.11715

KS3.11815


KS3.NS.1.1

Ratios and Proportional Relationships

KS3.RP.1.1
Ratio, proportion and rates of change
• Pupils should be taught to:
 change freely between related standard units [for example time, length, area, volume/capacity, mass]
 use scale factors, scale diagrams and maps
 express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
 use ratio notation, including reduction to simplest form
 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
 understand that a multiplicative relationship between two 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
 solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
 solve problems involving direct and inverse proportion, including graphical and algebraic representations
 use compound units such as speed, unit pricing and density to solve problems. 

KS3.15315

KS3.1545

KS3.1555

KS3.15610

KS3.15710

KS3.15815

KS3.15910

KS3.17815

KS3.17915

KS3.18015

KS3.18415

KS3.18515

KS3.825

KS3.835

KS3.8415

KS3.8515

KS3.8615

KS3.8715

KS3.8815

KS3.8915

KS3.9020

KS3.915

KS3.925

KS3.935

KS3.1015

KS3.1025

KS3.11715

KS3.11815

KS3.1925

KS3.19315

KS3.1945

KS3.19510

KS3.1965

KS3.1975

KS3.1985

KS3.1995

KS3.20015

KS3.2015

KS3.20215

KS3.20315

KS3.20420

KS3.2055

KS3.20615

KS3.20715

KS3.20810

KS3.20920

KS3.21010

KS3.21115

KS3.21215


KS3.RP.1.1

Geometry

KS3.G.1.1
Geometry and measures
• Pupils should be taught to:
 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)
 calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes
 draw and measure line segments and angles in geometric figures, including interpreting scale drawings
 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
 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
 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
 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
 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 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
 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
 use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving rightangled triangles
 use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D
 interpret mathematical relationships both algebraically and geometrically. 

KS3.1695

KS3.21315

KS3.21415

KS3.21510

KS3.2165

KS3.21715

KS3.21815

KS3.2195

KS3.2205

KS3.2215

KS3.2225

KS3.22310

KS3.2245

KS3.2255

KS3.2265

KS3.2275

KS3.2285

KS3.2295

KS3.2305

KS3.2315

KS3.2325

KS3.2335

KS3.2345

KS3.2355

KS3.2365

KS3.2375

KS3.2385

KS3.2395

KS3.2405

KS3.2415

KS3.2425

KS3.2435

KS3.2445

KS3.2455

KS3.2465

KS3.24710

KS3.24810

KS3.24910

KS3.25010

KS3.2515

KS3.2525

KS3.2535

KS3.2545

KS3.2555

KS3.2565

KS3.2575

KS3.2585

KS3.2595

KS3.2605

KS3.2615

KS3.2625

KS3.2635

KS3.10415


KS3.G.1.1

Algebra

KS3.OA.1.1
Algebra
• Pupils should be taught to:
 use and interpret algebraic notation, including:
• ab in place of a x b
• 3y in place of y + y + y and 3 x y
• aÂ² in place of a x a, aÂ³ in place of a x a x a; aÂ²b in place of a x a x b
• a/b in place of a Ã· b
• coefficients written as fractions rather than as decimals
• brackets
 substitute numerical values into formulae and expressions, including scientific formulae
 understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
 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 two or more binomials
 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
 use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
 work with coordinates in all four quadrants
 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
 interpret 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
 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
 find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs
 generate terms of a sequence from either a termtoterm or a positiontoterm rule
 recognise arithmetic sequences and find the nth term
 recognise geometric sequences and appreciate other sequences that arise. 

KS3.1195

KS3.1205

KS3.12110

KS3.1225

KS3.1235

KS3.12410

KS3.12515

KS3.1265

KS3.12715

KS3.1285

KS3.12910

KS3.1305

KS3.13115

KS3.13210

KS3.1335

KS3.1345

KS3.13510

KS3.1365

KS3.13710

KS3.1385

KS3.1395

KS3.14010

KS3.14110

KS3.14210

KS3.14315

KS3.14410

KS3.1455

KS3.14720

KS3.14810

KS3.1495

KS3.1505

KS3.1515

KS3.1525

KS3.15315

KS3.1545

KS3.1555

KS3.15610

KS3.15710

KS3.15815

KS3.15910

KS3.16010

KS3.1615

KS3.1625

KS3.16310

KS3.16415

KS3.1655

KS3.16610

KS3.1675

KS3.1685

KS3.1695

KS3.17010

KS3.17110

KS3.17215

KS3.17310

KS3.17415

KS3.17510

KS3.17610

KS3.17710

KS3.17815

KS3.17915

KS3.18015

KS3.18110

KS3.1825

KS3.1835

KS3.18415

KS3.18515

KS3.1865

KS3.1875

KS3.18815

KS3.18915

KS3.19015

KS3.19115

KS3.1620

KS3.4315

KS3.455

KS3.4620

KS3.4720

KS3.575

KS3.6310

KS3.6910

KS3.7015

KS3.8415

KS3.8615

KS3.11715


KS3.OA.1.1

Probability

KS3.SP.1.1
Probability
• Pupils should be taught to:
 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
 understand that the probabilities of all possible outcomes sum to 1
 enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
 generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. 

KS3.26415

KS3.2655

KS3.2665

KS3.26710

KS3.2685

KS3.26915

KS3.2705

KS3.2715

KS3.2725

KS3.2735

KS3.2745


KS3.SP.1.1