Numbers and the number system

• use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple
• use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
• recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions
• Write a number as a product of its prime factors
• Use prime factorisations to find the HCF and LCM of two numbers
• Solve problems using highest common factors or lowest common multiples

Visualizing and constructing

• Identify line and rotational symmetry in polygons
• Understand and use labelling notation for lengths and angles
• Use ruler and protractor to construct triangles, and other shapes, from written descriptions
• Use ruler and compasses to construct triangles when all three sides known

Investigating properties of shapes

• identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
• derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language

Autumn 2

Algebraic proficiency: tinkering

• understand and use the concepts and vocabulary of expressions, equations, formulae and terms
• use and interpret algebraic notation, including: ab in place of a × b, 3y in place of y + y + y and 3 × y, a² in place of a × a, a³ in place of a × a × a, a/b in place of a ÷ b, brackets
• simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket
• where appropriate, interpret simple expressions as functions with inputs and outputs
• substitute numerical values into formulae and expressions
• use conventional notation for priority of operations, including brackets

Algebraic proficiency: visualising

• Use input/output diagrams;
• Use axes and coordinates to specify points in all four quadrants in 2D;
• Identify points with given coordinates and coordinates of a given point in all four quadrants;
• Find the coordinates of points identified by geometrical information in 2D (all four quadrants);
• Draw, label and scale axes;
• Work out time intervals for graph scales;
• Read and interpret straight-line graphs for real-life situations including conversion graphs;
• Draw graphs for real-life situations;
• Interpret distance-time graphs;
• Interpret information presented in a range of linear and non-linear graphs;
• Interpret graphs with negative values on axes;
• Use function machines to find coordinates (i.e. given the input x, find the output y);
• Plot and draw graphs of y = a, x = a, y = x and y = –x;
• Recognise straight-line graphs parallel to the x-axis or the y-axis
• Write the equation of a line parallel to the x-axis or the y-axis

• Investigating angles

• Measure accurately
• Convert between measures
• Solve problems involving measurement

Calculating

• understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)
• apply the four operations, including formal written methods, to integers and decimals
• use conventional notation for priority of operations, including brackets

recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)

Measuring space

• use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
• use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
• change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts

• measure line segments and angles in geometric figures

Proportional reasoning

• use ratio notation, including reduction to simplest form
• divide a given quantity into two parts in a given part:part or part:whole ratio

Exploring fractions, decimals and percentages

• express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
• define percentage as ‘number of parts per hundred’

express one quantity as a percentage of another

Calculating fractions, decimals and percentages

• apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers
• interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
• compare two quantities using percentages
• solve problems involving percentage change, including percentage increase/decrease

Counting and comparing

• order positive and negative integers, decimals and fractions
• use the symbols =, ≠, <, >, ≤, ≥

Summer 1

Checking, approximating and estimating

• round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
• estimate answers; check calculations using approximation and estimation, including answers obtained using technology
• recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)

Pattern sniffing

• Recognise simple arithmetic progressions
• Use a term-to-term rule to generate a linear sequence
• Use a term-to-term rule to generate a non-linear sequence

Solving equations and inequalities

• recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
• solve linear equations in one unknown algebraically

Calculating space

• use standard units of measure and related concepts (length, area, volume/capacity)
• calculate perimeters of 2D shapes
• know and apply formulae to calculate area of triangles, parallelograms, trapezia
• calculate surface area of cuboids
• know and apply formulae to calculate volume of cuboids
• understand and use standard mathematical formulae

Mathematical movement

• work with coordinates in all four quadrants

• understand and use lines parallel to the axes, y = x and y = -x
• solve geometrical problems on coordinate axes
• identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation
• describe translations as 2D vectors

Presentation of data

• interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use

Measuring data

• Find the mode of set of data
• Find the median of a set of data including when there are an even number of numbers in the data set
• Calculate the mean from a frequency table
• Find the mode from a frequency table
• Find the median from a frequency table
• Calculate and understand the range as a measure of spread (or consistency)
• Analyse and compare sets of data, appreciating the limitations of different statistics (mean, median, mode, range)

Numbers – Powers, Root and standard form

• Calculate with positive indices
• Calculate with roots
• Use a calculator to evaluate numerical expressions involving powers
• Use a calculator to evaluate numerical expressions involving roots
• Convert ordinary number to standard form and vice versa
• Calculate with negative indices in the context of standard form
• Add and subtract numbers written in standard form
• Multiply and divide numbers written in standard form
• Use standard form on a scientific calculator including interpreting the standard form display of a scientific calculator

Presentation of data

• Interpret and construct frequency tables
• Construct and interpret frequency table including grouped frequency table for discrete and continuous data
• Construct and interpret bar charts including composite and comparative bar charts and know their appropriate use
• Construct and interpret pie charts and know their appropriate use
• Construct and interpret vertical line charts
• Choose appropriate graphs or charts to represent data
• Plot a scatter diagram of bivariate data
• Interpret a scatter diagram using understanding of correlation 
• Construct a line of best fit on a scatter diagram and use the line of best fit to estimate values
• Understand that correlation does not indicate causation
• Construct and interpret frequency polygons
• Construct and interpret stem and leaf diagrams
• Construct and interpret histograms for grouped data with equal class intervals

Mathematical Movement

• Solve geometrical problems on coordinate axes
• Write the equation of a line parallel to the x-axis or the y-axis
• Identify and draw the lines y = x and y = -x
• Construct and describe reflections in horizontal, vertical and diagonal mirror lines (45° from horizontal)
• Describe a translation as a 2D vector
• Construct and describe rotations using a given angle, direction and centre of rotation
• Solve problems involving rotations, reflections and translations

Measuring data

• Find the mean, median, mode and range of a set of data
• Find the mean, median, mode and range from a frequency table
• Calculate and understand the range as a measure of spread (or consistency)
• Analyse and compare sets of data, appreciating the limitations of different statistics (mean, median, mode, range)
• Find the modal class of set of grouped data
• Find the class containing the median of a set of data
• Calculate an estimate of the mean from a grouped frequency table
• Estimate the range from a grouped frequency table
• Analyse and compare sets of data, appreciating the limitations of different statistics (mean, median, mode, range)
• Choose appropriate statistics to describe a set of data

Understanding risk I

• relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale
• record describe and analyse the frequency of outcomes of probability experiments using tables
• construct theoretical possibility spaces for single experiments with equally likely outcomes and use these to calculate theoretical probabilities
• apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

Visualising and constructing

• Use the centre and scale factor to carry out an enlargement with a positive integer scale factor
• Find the centre and scale factor of an enlargement
• Use scale diagrams, including maps and the concept of scaling in diagrams
• Interpret plans and elevations
• Understand and use bearings
• Construct scale diagrams involving bearings
• Solve geometrical problems using bearings

Calculating

• apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative
• use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

Algebraic proficiency: tinkering

• Use and interpret algebraic notation, including: a² b in place of a × a × b, coefficients written as fractions rather than as decimals
• Simplify an expression involving terms with combinations of variables (e.g. 3a²b + 4ab² + 2a² – a²b)
• Factorise an algebraic expression by taking out common factors
• Simplify expressions using the law of indices for multiplication, division and powers
• Know and use the zero index
• Multiply two linear expressions of the form (x + a)(x + b)
• Multiply two linear expressions of the form (ax + b)(cx + d)
• Expand the expression (x + a)²
• Substitute positive and negative numbers into formulae
• Change the subject of a formula when one and two-step is required
• Distinguish between situations that can be modelled by an expression or a formula
• Create an expression or a formula to describe a situation

Pattern sniffing

• Generate terms of a sequence from a position-to-term rule
• Find the nth term of any linear sequence
• Use the nth term of a sequence to deduce if a given number is in a sequence
• Recognise and use the Fibonacci sequence
• Generate Fibonacci type sequences
• Solve problems involving Fibonacci type sequences
• Explore growing patterns and other problems involving quadratic sequences
• Generate terms of a quadratic sequence from a written rule

Investigating angles

• understand and use alternate and corresponding angles on parallel lines

derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

Proportional reasoning

• Find a relevant multiplier in a situation involving proportion
• Identify direct proportion in a situation
• Solve problems involving unit pricing
• Identify inverse proportion in a situation
• Distinguish between situations involving direct and inverse proportion
• Solve simple problems involving inverse proportion
• Understand and use the connections between ratios and fractions
• Solve problems involving division in a ratio with two or more parts
• Solve simple ratio problems involving comparison
• Solve simple ratio problems involving mixing or concentrations
• Apply understanding of proportion to problems involving recipes
• Solve more complex ratio problems involving mixing or concentrations
• Solve more complex problems involving unit pricing
• Finding missing lengths in similar shapes when information is given as a ratio
• Solve problems combining understanding of fractions and ratio
• Understand and use compound units
• Convert between units of speed
• Calculate average speed
• Convert between compound units of density and pressure

Exploring fractions, decimals and percentages

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8)

Calculating fractions, decimals and percentages

• interpret fractions and percentages as operators
• work with percentages greater than 100%
• solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics
• calculate exactly with fractions

Solving equations and inequalities

• solve linear equations with the unknown on both sides of the equation
• find approximate solutions to linear equations using a graph

Calculating space

• Know circle definitions and properties, including: centre, radius, chord, diameter, circumference
• Calculate the circumference of a circle when radius or diameter is given
• Calculate the perimeter of composite shapes that include sections of a circle
• Calculate the area of a circle when radius or diameter is given
• Calculate the area of composite shapes that include sections of a circle
• Calculate the area of a sector, including calculating exactly with multiples of π
• Calculate the angle of a sector when the arc length and radius are known
• Calculate the volume of a right prism
• Calculate the volume of a cylinder
• Compare lengths, areas and volumes using ratio notation
• Calculate the surface area of a right prism

• Calculate the surface area of a cylinder, including calculating exactly with multiples of π
• Know and use Pythagoras’ theorem
• Calculate the hypotenuse of a right-angled triangle using Pythagoras’ theorem in two dimensional figures
• Calculate one of the shorter sides in a right-angled triangle using Pythagoras’ theorem in two dimensional figures
• Solve problems using Pythagoras’ theorem in two dimensional figures

Algebraic proficiency: visualizing

• Know that graphs of functions of the form y = mx + c, x ± y = c and ax ± by = c are linear
• Plot graphs of functions of the form y = mx ± c
• Plot graphs of functions of the form ax ± by = c
• Find the gradient of a straight line on a unit grid
• Find the y-intercept of a straight line
• Sketch linear graphs
• Distinguish between a linear and quadratic graph
• Plot and sketch graphs of quadratic functions of the form y = x² ± c
• Plot and interpret graphs of piece-wise linear functions in real contexts
• Plot and interpret distance-time graphs (speed-time graphs) including approximate solutions to kinematic problems

Understanding Risk II

• List all elements in a combination of sets using a Venn diagram
• List outcomes of an event systematically
• Use a table to list all outcomes of an event
• Use frequency trees to record outcomes of probability experiments
• Construct theoretical possibility spaces for combined experiments with equally likely outcomes
• Calculate probabilities using a possibility space
• Use theoretical and experimental probability to calculate expected outcomes
• List outcomes of combined events using a tree diagram
• Know and use the multiplication and addition law of probability
• Use a tree diagram to solve simple and complex problems involving independent and dependent combined events
• Understand that relative frequency tends towards theoretical probability as sample size increases

• Integers and Place Value
• Decimals
• Indices, powers and roots

• Calculations, checking and rounding
• Indices and roots
• Factors, multiples and primes
• Indices and standard form

• Factors, multiples and primes
• Algebra basics
• Expanding and factorising single brackets
• Substitution and expressions

• Algebra basics
• Equations
• Sequences
• Averages and range

• Tables
• Charts and graphs
• Fractions

• Representing and interpreting data
• Scatter graphs
• Fractions

• Pie charts
• Scatter Graphs
• Fractions, decimals and percentages
• Percentages

• Fractions
• Percentages
• Ratio and proportion

• Equations
• Inequalities

• Polygons, angles and parallel lines
• Pythagoras’ theorem and trigonometry

• Sequences
• Properties of shape, parallel lines and angle facts
• Interior and exterior angles of polygons

• Graphs and real life graphs
• Linear graphs and coordinate geometry
• Quadratic, cubic and other graphs

• Statistics and sampling
• The averages
• Perimeter and area

• Perimeter, area and circles
• 3D forms and volumes
• Accuracy and bounds

• 3D forms and volume
• Real life graphs
• Straight line graphs

• Transformations
• Constructions, loci and bearings

• Transformations
• Ratio

• Solving quadratic and simultaneous equations
• Inequalities
• Probability

• Proportion
• Pythagoras’ theorem and trigonometry
• Probability

• Probability
• Multiplicative reasoning
• Similarity and congruence

• Multiplicative reasoning
• Plans and elevations

• Graphs of trigonometric functions
• Further trigonometry

• Constructions, loci and bearings
•  Quadratic equations: expanding and factorising

• Collecting data

• Data
• Population and sampling Collecting discrete data

Students learn the key definitions of statistical words, how to sample data.

• Planning and collecting data
• Qualitative and discrete data

• Continuous data
• Tabulation
• Measures of central tendency – mode, median and mean

Students will convert raw data to summary statistics, design, construct and present summary tables.

• Measures of dispersion
• Box plots, skewness, calculating and representing outliers

• Scatter graphs
• Time series
• Introduction to probability

Autumn 1

• Plans and elevations
• Construction, loci and bearing
• Quadratic equations: graphs

• Cumulative frequency, box plots and histograms
• Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics

• Circles, cylinders, cones and spheres
• Fractions and reciprocals
• Similarity and congruence in 2D

• Circle theorems
• Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof
• Direct and inverse proportion

• Similarity and congruence in 2D
• Vectors Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations

• Circle geometry
• Graphs of trigonometric functions
• Further trigonometry

• Revision

• geometric proof
• Reciprocal and exponential graphs; Gradient and area under graphs
• Vectors

• Revision

• Revision

• Public exam

• Public exam

• Calculating moving averages, seasonal and cyclic trends

• Simple probability and theoretical probability

• Interpreting index numbers in context and simple calculations
• Binomial distribution 

• Normal distribution and standardised scores
• Quality assurance

• Revision for exam