This section of the site is pretty much permanently in development.
The whole new KS3/KS4 curriculum is listed, but some topic pages are not live or have few links. Keep checking back for more updates! 

Number: Properties and Calculations
PLace Value and Ordering
Multiply and divide by 10, 100, 1000 Understand and use place value for decimals, measures and integers of any size (KS3) Standard form Interpret and compare numbers in standard form (KS3) Calculate with numbers in standard form (KS4) Ordering and inequality notation Order positive & negative integers, use the number line as a model for ordering of the real numbers Use the symbols =, ≠, <, >, ≤, ≥ (KS3 Rounding and Estimation
Rounding to integers and decimal places Round numbers and measures to an appropriate degree of accuracy, such as a number of decimal places or significant figures (KS3) Rounding to significant figures Round numbers and measures to an appropriate degree of accuracy, such as a number of decimal places or significant figures (KS3) Estimation and approximation Use approximation through rounding to estimate answers Calculate possible resulting errors expressed using inequality notation (KS3) Apply and interpret limits of accuracy when rounding or truncating (KS4) Lower and upper bounds (H) Apply and interpret limits of accuracy when rounding or truncating, including upper and lower bounds (KS4 Higher only) Four Operations
Written multiplication methods Use the four operations, including formal written methods, applied to integers (KS3) Short division Use the four operations, including formal written methods, applied to integers (KS3) Operations with negative numbers Use the four operations, including formal written methods, applied to negative integers and decimals (KS3) Order of operations and inverse operations Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals Recognise and use relationships between operations including inverse operations (KS3) Factors, Multiples and Primes
Factors, multiples and primes Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors and common multiples (KS3) Product of primes, HCF and LCM Use the concepts and vocabulary of highest common factor, lowest common multiple and prime factorisation, including using product notation and the unique factorisation property (KS3) Powers and Roots
Square and cube numbers Use integer powers and associated real roots: square, cube and higher (KS3) Integer indices Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 (KS3) Calculate with integer indices (KS4) Working with roots Distinguish between exact representations of roots and their decimal approximations (KS3) Calculate with roots (KS4) Surds and roots (H) Estimate powers and roots of any given positive number Calculate exactly with surds Simplify surd expressions involving squares and rationalise denominators (KS4 Higher only) Fractional indices (H) Calculate with fractional indices (KS4 Higher only) Number: Fractions, Decimals and Percentages
Fraction Calculations
Equivalent fractions and simplifying fractions Improper fractions and mixed numbers Recognise mixed numbers and improper fractions and convert from one form to the other (KS2) Fractions of amounts Recognise, find and write fractions of a discrete set of objects (KS2) Interpret fractions as operators (KS3) Adding and subtracting fractions Use the four operations, including formal written methods, applied to proper and improper fractions and mixed numbers, all both positive and negative (KS3) Multiplying and dividing fractions Use the four operations, including formal written methods, applied to proper and improper fractions and mixed numbers, all both positive and negative (KS3) Decimals and Fractions
Ordering and comparing fractions and decimals Order decimals and fractions (KS3) Work interchangeably with terminating decimals and their corresponding fractions (KS3) Multiplying decimals Use the four operations, including formal written methods, applied to decimals KS3) Dividing decimals Use the four operations, including formal written methods, applied to decimals KS3) Recurring decimals and fractions (H) Change recurring decimals into their corresponding fractions and vice versa (KS4 Higher only) Percentages
Fraction, decimal and percentage equivalence Define percentage as ‘number of parts per hundred’ Interpret percentages as a fraction or a decimal (KS3) Writing and comparing percentages Express one quantity as a percentage of another Compare two quantities using percentages (KS3) Percentages of amounts Interpret percentages as operators (KS3) Percentage increase and decrease Interpret percentage changes as a fraction or a decimal Work with percentages greater than 100% Solve problems involving percentage increase and decrease (KS3) Percentage growth, decay and compound interest Solve problems involving percentage change, including simple interest in financial mathematics (KS3) Set up, solve and interpret the answers in growth and decay problems, including compound interest (KS4) Algebra: Basic Skills
Algebraic Manipulation
Writing expressions using algebra Use and interpret algebraic notation (KS3) Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors (KS3) Translate simple situations or procedures into algebraic expressions or formulae (KS4) Simplify and manipulate algebraic expressions, including those involving surds (KS4) Simplifying algebraic expressions Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms (KS3) Expanding and factorising single brackets Simplify and manipulate algebraic expressions to maintain equivalence by multiplying a single term over a bracket or by taking out common factors (KS3) Laws of indices Simplify expressions involving sums, products and powers, including the laws of indices (KS4) Algebraic fractions (H) Simplify and manipulate algebraic fractions (KS4 Higher only) Equations and identities Know the difference between an equation and an identity (KS4) Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments (KS4) Proof (H) Use algebra to support and construct proofs (KS4 Higher only) Quadratic Expressions
Expanding quadratics and other binomials Simplify and manipulate algebraic expressions to maintain equivalence by expanding products of two or more binomials (KS3) Factorising quadratics (a = 1) Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form x² + bx + c, including the difference of two squares (KS4) Factorising quadratics (a not 1) (H) Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax² + bx + c, including the difference of two squares (KS4 Higher only) Completing the square (H) Deduce turning points of quadratic graphs by completing the square (KS4 Higher only) Substitution and Formulae
Substitution Substitute numerical values into formulae and expressions, including scientific formulae (KS3) Formulae Understand and use standard mathematical formulae (KS3) Translate simple situations or procedures into algebraic expressions or formulae (KS4) Changing the subject Rearrange formulae to change the subject (KS3) Algebra: Equations and Inequalities
Linear Equations and Inequalities
Solving twostep linear equations Use algebraic methods to solve linear equations in one variable including all forms that require rearrangement (KS3) Derive an equation, solve the equation and interpret the solution (KS4) Equations with brackets and unknowns both sides Use algebraic methods to solve linear equations in one variable including all forms that require rearrangement (KS3) Representing and solving linear inequalities Solve linear inequalities in one variable (KS4) Represent the solution set on a number line (KS4) Simultaneous Equations
Simultaneous equations (two linear) Solve two linear simultaneous equations in two variables (KS4) Find approximate solutions using a graph (KS4) Derive two simultaneous equations, solve the equations and interpret the solution (KS4) Further simultaneous equations Solve two simultaneous equations, one linear and one quadratic, in two variables (KS4) Solve linear inequalities in two variables Quadratic Equations and Inequalities
Solving quadratic equations by factorising Solve quadratic equations algebraically by factorising (KS4) Quadratics using the formula or completing the square (H) Solve quadratic equations, including those that require rearrangement, by completing the square and by using the quadratic formula (KS4 Higher only) Solving quadratic inequalities (H) Solve quadratic inequalities in one variable (KS4 Higher only) Represent the solution set on a number line, using set notation and on a graph (KS4 Higher only) Iteration
Iteration Find approximate solutions to equations numerically using iteration (KS4 Higher only) Algebra: Sequences, Functions and Graphs
Coordinates
Coordinates Work with coordinates in all four quadrants (KS3) Linear Graphs
Drawing linear graphs Recognise, sketch and produce graphs of linear functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane (KS3) Interpreting and using linear graphs Reduce a given linear equation in two variables to the standard form y = mx + c (KS3) Calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically (KS3) Use linear graphs to estimate values of y for given values of x (KS3) Equation of a line and parallel lines Use the form y = mx + c to identify parallel lines Find the equation of the line through two given points, or through one point with a given gradient Perpendicular lines (H) Use the form y = mx + c to identify perpendicular lines (KS4 Higher only) Graphs of inequalities (H) Solve linear inequalities in one or two variables Represent the solution set using set notation and on a graph (KS4 Higher only) NonLinear Graphs
Quadratic graphs Recognise, sketch and produce graphs of quadratic functions (KS3) Use quadratic graphs to estimate values and to find approximate solutions of simultaneous linear equations (KS3) Identify and interpret roots, intercepts and turning points of quadratic functions graphically (KS4) Cubic and reciprocal graphs Exponential graphs (H) Recognise, sketch & interpret graphs of exponential function y = k^x for positive values of k Plot & interpret exponential graphs in real contexts to find approximate solutions to problems (Both KS4 Higher only) Trigonometric graphs (H) Recognise, sketch and interpret graphs of the trigonometric functions y = sin x, y = cos x and y = tan x for angles of any size (KS4 Higher only) Transformation of graphs (H) Sketch translations and reflections of the graph of a given function (KS4 Higher only) Equation of a circle (H) Recognise and use the equation of a circle with centre at the origin (KS4 Higher only) Find the equation of a tangent to a circle at a given point (KS4 Higher only) Real Life Graphs
Graphs from reallife contexts Find approximate solutions to contextual problems from given graphs of a variety of functions, including piecewise linear, exponential and reciprocal graphs (KS3) Plot and interpret graphs (including reciprocal graphs) and graphs of nonstandard functions in real contexts, to find approximate solutions to problems (KS4) Distancetime and speedtime graphs Plot and interpret graphs to find approximate solutions to simple kinematic problems involving distance, speed and acceleration (KS4) Gradients and areas (H) Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other nonlinear graphs), and interpret results in cases such as distancetime graphs, velocitytime graphs and graphs in financial contexts (KS4 Higher) Sequences and Functions
Linear sequences Generate terms of a sequence from either a termtoterm or a positiontoterm rule (KS3) Recognise arithmetic sequences and find the nth term (KS3) Recognising other sequences Recognise geometric and other sequences (KS3) Recognise and use sequences of triangular, square and cube numbers, Fibonacci type sequences, quadratic sequences, and simple geometric progressions where n is an integer, and r is a positive rational number (KS4) Nth term of a quadratic sequence (H) Deduce expressions to calculate the nth term of quadratic sequences (KS4 Higher only) Geometric progressions with surds (H) Recognise and use simple geometric progressions where n is an integer, and r is a surd (KS4 Higher only) Simple functions Where appropriate, interpret simple expressions as functions with inputs and outputs (KS4) Inverse and composite functions Interpret the reverse process as the ‘inverse function’ Interpret the succession of two functions as a ‘composite function’ (KS4 Higher only) Proportion, ratio and Rates of Change
Proportion
Simple direct proportion Solve problems involving direct proportion, including graphical and algebraic representations (KS3) Simple inverse proportion Solve problems involving inverse proportion, including graphical and algebraic representations (KS3) Interpreting proportion equations Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y Interpret equations that describe direct and inverse proportion (KS4) Constructing proportion equations Construct equations that describe direct and inverse proportion (KS4 Higher only) Proportion graphs Interpret the gradient of a straight line graph as a rate of change Recognise and interpret graphs that illustrate direct and inverse proportion (KS4) Instantaneous and average rates of change Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts (KS4 Higher only) Ratio
Working with ratio 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 (KS3) Ratios and fractions 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 Identify and work with fractions in ratio problems (KS4) Shape: Calculations and Measures
Units, Measurements and Drawings
Standard units of measurement Use standard units of mass, length, time, money and other measures, including with decimal quantities Change freely between related standard units, such as time, length, area, volume/capacity, mass (KS3) Compound measures Use compound units such as speed, unit pricing and density to solve problems (KS3) Convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts (KS4) Scale drawings and bearings Use scale factors, scale diagrams and maps (KS3) Draw and measure line segments and angles in geometric figures, including interpreting scale drawings (KS3) Interpret and use bearings (KS4) Area And Volume
Area of rectangles, triangles & parallelograms Derive and apply formulae to calculate and solve problems involving perimeter and area of triangles and parallelograms (KS3) Area of trapezia and compound shapes Derive and apply formulae to calculate the area of trapezia Calculate and solve problems involving areas of composite shapes (KS3) Volume of cuboids and simple prisms Derive and apply formulae to calculate and solve problems involving volume of cuboids (including cubes) and other prisms (KS3) Circumference and area of circles Calculate and solve problems involving perimeters of circles, areas of circles and composite shapes (KS3) Arc length and area of a sector Calculate arc lengths, angles and areas of sectors of circles (KS4) Volume and surface area of cylinders Derive and apply formulae to calculate and solve problems involving volume of cylinders Use the properties of faces and surfaces of cylinders to solve problems in 3D (KS3) Volume of cones, spheres and pyramids Calculate surface areas and volumes of spheres, pyramids, cones and composite solids (KS4) Surface area of cones, spheres and pyramids Calculate surface areas and volumes of spheres, pyramids, cones and composite solids (KS4) Pythagoras and Trigonometry
Pythagoras’ theorem Use Pythagoras’ Theorem to solve problems involving rightangled triangles (KS3) Apply Pythagoras’ Theorem to find lengths in rightangled triangles and in twodimensional figures (KS4) Trigonometry in rightangled triangles Use trigonometric ratios in similar triangles to solve problems involving rightangled triangles (KS3) Apply trigonometric ratios to find angles and lengths in rightangled triangles and in twodimensional figures (KS4) Exact trigonometric values Know the exact values of sin θ cos θ and tan θ for θ = 0, 30, 45, 60, 90 degrees (KS4) Pythagoras and trigonometry in 3D Apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in rightangled triangles (and, where possible, general triangles) in three dimensional figures (KS4 Higher only) Sine and cosine rules (H) Know and apply the sine rule and cosine rule to find unknown lengths and angles (KS4 Higher only) Area of triangle using 1/2 ab sin C (H) Know and apply area = 1/2 ab sin C to calculate the area, sides or angles of any triangle (KS4 Higher only) Shape: Properties and Constructions
Transformations, Congruence and Similarity
Translations, rotations and reflections Identify properties of, and describe the results of translations, rotations and reflections applied to given figures (KS3) Describe translations as 2D vectors (KS4) Enlargement by positive scale factor Construct similar shapes by enlargement, with and without coordinate grids (KS3) Interpret and use fractional scale factors for enlargements (KS4) Enlargement by negative scale factor Interpret and use negative scale factors for enlargements (KS4 Higher only) Comparing lengths, areas and volumes Compare lengths, areas and volumes using ratio notation and/or scale factors (KS4) Invariance (H) Describe the changes and invariance achieved by combinations of rotations, reflections and translations (KS4 Higher only) Congruence and similarity Know and use the criteria for congruence of triangles (KS3) Identify and construct congruent triangles (KS3) Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides and use known results to obtain simple proofs (KS3) Apply the concepts of congruence and similarity, including relationships between lengths, in similar figures (KS4) Similar areas and volumes (H) Apply the concepts of congruence and similarity, including the relationships between areas and volumes in similar figures (KS4 Higher only) Shape and Angle Properties (2D)
Angles in parallel lines Understand and use the relationship between parallel lines and alternate and corresponding angles (KS3) Angles around a point, on a line & in a triangle Apply the properties of angles at a point, angles at a point on a straight line and vertically opposite angles (KS3) Derive and use the sum of angles in a triangle (KS3) Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles (KS3) Properties of triangles Use the standard conventions for labelling the sides and angles of triangle ABC (KS3) Derive and illustrate properties of triangles (for example, equal lengths and angles) using appropriate language and technologies (KS3) Properties of quadrilaterals Derive and illustrate properties of quadrilaterals and other plane figures (for example, equal lengths and angles) using appropriate language and technologies (KS3) Properties and angles in polygons Describe, sketch and draw using conventional terms and notations: regular polygons, and other polygons that are reflectively and rotationally symmetric (KS3) Deduce the angle sum in any polygon, and to derive properties of regular polygons (KS3) Circle properties Derive and illustrate properties of circles using appropriate language and technologies (KS3) Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment (KS4) Circle theorems (H) Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results (KS4 Higher only) Shape And Angle Properties (3d)
Faces, vertices and edges Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D (KS3) Plans and elevations Construct and interpret plans and elevations of 3D shapes Constructions
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 (KS3) Shape: Vectors
Vectors
Vector calculations Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors (KS4) Vector proofs (H) Use vectors to construct geometric arguments and proofs (KS4 Higher only) Probability
Probability Basics
The probability scale 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 (KS3) Understand that the probabilities of all possible outcomes sum to 1 (KS3) Mutually exclusive events Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one Simple sets and Venn diagrams Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams (KS3) Theoretical and Experimental
Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities (KS3) Use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size (KS4) Independent and Conditional
Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions (KS4) Calculate and interpret conditional probabilities through representation using expected frequencies with twoway tables, tree diagrams and Venn diagrams (KS4 Higher only) Statistics
Presenting Data
Simple charts and graphs Construct and interpret frequency tables, bar charts and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data (KS3) Pie charts Construct and interpret pie charts for categorical data (KS3) Timeseries graphs Interpret and construct tables and line graphs for time series data (KS4) Scatter graphs Describe relationships between two variables and illustrate using scatter graphs (KS3) Recognise correlation and know that it does not indicate causation (KS4) Draw estimated lines of best fit, make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of so doing Cumulative frequency and box plots (H) Construct and interpret cumulative frequency graphs, and know their appropriate use (KS4 Higher only) Use box plots to interpret, analyse and compare the distributions of data sets (KS4 Higher only) Histograms (H) Construct and interpret histograms with equal and unequal class intervals and know their appropriate use (KS4 Higher only) Processing Data
Ungrouped data  averages and spread Describe, interpret and compare singlevariable distributions through measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) (KS3) Grouped data  averages and spread Describe, interpret and compare singlevariable grouped distributions through measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) (KS3) Interpret, analyse and compare distributions through appropriate measures of central tendency (including modal class) (KS4) Quartiles and interquartile range (KS4 Higher only) Interpret, analyse and compare distributions using quartiles and interquartile range (KS4) Data collection and sampling
Sampling (KS4) Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling (KS4) Apply statistics to describe a population (KS4) 
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