# Mathematics

Through innovative and enthusiastic teaching and learning of mathematics we aim to pass on our enthusiasm to students of all abilities and interests and we strive to ensure that all students are suitably challenged and engaged in maths, and students who require additional support are effectively supported.

### Topics covered in Maths are detailed below

#### Year 7

 Unit 1 – Calculation Apply the four operations (including formal written methods) to integers and decimals. Apply the four operations (including formal written methods) to simple fractions. Calculate a percentage of a quantity and Know percentage equivalents of decimals with denominators 2, 4, 5, 10 and 25. Unit 2 – Number system Order positive and negative integers and decimals. Multiply and divide by powers of 10. Round numbers to appropriate accuracy, integer or decimal place values. Unit 3 - Indices Apply and use simple laws of indices. Recall and use square numbers up to 15 x 15 and their corresponding roots. Use vocabulary of product notation and unique prime factorisation theorem. Unit 4 – Equations and formulae Form and Solve linear equations in one unknown. To expand and factorise linear expressions. Understand the difference between expressions, equations, formulae and identities. Substitute values into simple expressions and formulae. Unit 5 - Proportion Use ratio notation, including cancelling to the simplest form. Express the division of a quantity into two parts as a ratio. Simplify a ratio in the form 1: n or n:1. Unit 6 – Mensuration Recognise that shapes with the same areas can have different perimeters and vice versa. Calculate volume of cubes and cuboids using standard units. Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints. Know and apply formulae to calculate area of triangles, parallelograms, trapezia. Unit 7 – Graphs and sequences To draw and interpret real life graphs. Use a table of values to plot graphs of linear functions. Find the nth term of linear/quadratic sequences. Recognise sequences including Fibonacci-type sequences, quadratic sequences, and simple geometric progressions. Unit 8 – Transformations Identify, describe and construct congruent shapes, including on coordinate axes, by considering rotation, reflection and translation. Identify, describe and construct similar shapes, including on coordinate axes, by enlargement with positive scale factors. Unit 9 – Angles Apply the properties of angles at a point, angles on a straight line, vertically opposite angles. Derive and use the sum of angles in a triangle, quadrilateral and pentagon to calculate internal and external angles. Identify alternate and corresponding angles on parallel lines. Unit 10 – Probability Design and use a frequency tree and determine the probability of an event. Design and use two-way tables. Construct Venn diagrams based on information provide. Unit 11 – Statistics Calculate the median, mean, mode, and range from a set of discrete data. Construct and interpret line graphs and composite bar charts for grouped and ungrouped data. Construct and interpret simple pie charts. Unit 12 – Constructions Construct triangles and 2-D shapes using given dimensions and angles. Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

#### Year 8

 Unit 1 – Calculation Apply the four operations (including formal written methods) to simple fractions and mixed numbers. Using fractions to solve mathematical problems. Percentage increase and decrease using decimal multipliers. Unit 2 – Number system Convert between improper and proper fractions and Order fractions. Estimate powers and roots of any given positive number. Round numbers to significant figures. Unit 3 - Indices Construct and rearrange simple formulae and expressions including from real world contexts. Use vocabulary of highest common factor, lowest common multiple, prime factorisation, including finding HCF and LCM using products of prime factors. Unit 4 – Equations and formulae Form and Solve linear equations with unknowns on both sides. To expand and factorise positive and negative terms over a simple bracket. Solve fractional equations using balancing method. Construct and rearrange simple formulae and expressions including from real world contexts. Interpreting simple expressions as functions with inputs and outputs. Unit 5 - Proportion Share in a ratio including where one part is known. Use scale factors, scale diagrams and maps. Problems involving direct proportions. Unit 6 – Mensuration Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.). Measure and calculate the area and perimeter of composite rectilinear shapes in centimetres and metres. Calculate volume of cubes and cuboids using standard units. Know and use Area and Circumference of a circle formulae. Unit 7 – Graphs and sequences Recognise and use sequences including Fibonacci-type sequences, quadratic sequences and geometric progressions. To use a table of values and draw straight line, quadratic graphs, simple cubic functions, the reciprocal function. To find the y intercept and gradient of straight-line graphs. Find the equation of a straight line in the form y = mx + c. Unit 8 – Transformations Draw and translate simple shapes on the coordinate plane, and reflect them in the axes. Identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement fractional scale factors. Unit 9 – Angles Understand and use alternate and corresponding angles on parallel lines. Derive and use the sum of angles in a triangle to derive properties of regular/irregular polygons to calculate internal and external angles. Draw and measure bearings. Unit 10 – Probability Display the outcomes of combined or successive events in a two-way table. Construct Venn diagrams based on information provided, including information presented in set notation. Complete a tree diagram to show outcomes and probabilities. Understand and use the term relative frequency. Unit 11 – Statistics Calculate the mean, median, mode and range from a frequency table. Use the averages and range to compare two sets of data and identify outliers. Construct and interpret scatter graphs and identify types of correlation. Unit 12 – Constructions Identify and describe congruent shapes. Interpret and construct plans and elevations of 3D shapes. Use the standard ruler and compass constructions including bisector of a line and angle.

#### Year 9

 Unit 1 – Calculation Work with terminating decimals and their corresponding fractions. Calculate with fractions. Calculate percentage change and reverse percentages. Unit 2 – Number system Calculate, convert and interpret standard form Ax10n . Use positive integer powers and associated real roots (square, cube and higher). Use inequality notation to specify simple error intervals due to truncation or rounding. Unit 3 - Indices Calculate with fractional indices. Simplify algebraic expressions using multiplication and division of integers powers. Unit 4 – Equations and formulae Solve two linear simultaneous equations algebraically and graphically. Expand and factorise products of two binomials. Substitute values into complex expressions and formulae involving powers and roots. Unit 5 - Proportion Apply ratio to real contexts and problems (conversion, comparison, scaling, mixing, concentrations, best buy problems). Compare lengths, areas and volume using ratio notation. Problems involving direct and inverse proportion. Unit 6 – Mensuration Change freely between related standard units in numerical contexts. Investigate Pythagoras’ theorem and Trigonometric ratios and apply in right-angled triangles. Calculate arc lengths, angles and areas of sectors of circles. Unit 7 – Graphs and sequences Deduce expressions to calculate the nth term of linear sequences including quadratic sequences. Use the form y = mx + c to identify parallel/perpendicular lines; find the equation of the line through two given points or through one point with a given gradient. Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function and identify and interpret roots, and exponential graphs. Unit 8 – Transformations Identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement negative scale factors. Describe the changes and invariance achieved by combinations of rotations, reflections and translations. Unit 9 – Angles Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides. Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings. Unit 10 – Probability Use a tree diagram as a method for calculating conditional probabilities. Use a Venn diagram as a method for calculating conditional probabilities. Estimate probabilities by considering relative frequency. Unit 11 – Statistics Calculate an estimate of the mean for a grouped frequency distribution, knowing why it is an estimate. Draw line of best fit and estimate from scatter graph and understand that correlation does not indicate causation. Plot and interpret time-series graphs. Use a time-series graph to predict a subsequent value. Unit 12 – Constructions Use the standard ruler and compass constructions and use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line.

#### Year 10 Foundation

 Algebra 2 Recognise and use relationships between operations, use conventional notation for priority of operations, including brackets and powers. Calculate with roots and with integer indices. Simplify and manipulate algebraic expressions. Using a calculator Use positive integer powers and associated square roots. Work interchangeably with terminating decimals and their corresponding fractions. Measure Change freely between related standard units (E.g. time, length). Use compound units such as speed. Use standard units of measure and related concepts. Use standard units of time. Processing, representing and interpreting data Interpret and construct charts and diagrams including bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data. Sequences Generate terms of a sequence from either a term-to-term or position-to-term rule. Deduce expressions to calculate the nth term of linear sequences. Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences and simple geometric progressions. Perimeter and area of 2D shapes Know and apply formulae to calculate area of triangles, parallelograms, trapezium. Calculate perimeters of 2D shapes and composite shapes. Graphs 1 Work with coordinates in all four quadrants. Plot graphs of equations that correspond to straight line graphs in the coordinate plane in the form y=mx + c. Identify and interpret gradients and intercepts of linear functions graphically and algebraically. Averages and range Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency & spread. Pythagoras Theorem Know the formulae for Pythagoras’ theorem, a2 + b2 = c2, apply to find lengths in right-angled triangles in two dimensional figures. Circles Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. Know the formulae: Circumference of a circle = 2πr = πd, Area of a circle = πr2 Constructions and Loci Draw diagrams from written description. Use the standard ruler and compass constructions. Use these to construct given figures and solve loci problems. Percentages Order decimals and fractions. Knowledge and understanding of terms used in household finance. Interpret fractions and percentages as operators. 3D shapes Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres. Construct and interpret plans and elevations of 3D shapes. Use standard units of measure and related concepts. Know and apply formulae to calculate volume of cuboids and other right prisms (including cylinders). Equations and inequalities Use and interpret algebraic notation, including: ab in place of a x b; 3y in place of y + y + y and 3 x y; a/b in place of a ÷ b; brackets. Solve linear equations. Use the symbols <, >, ≤, ≥ and solve linear inequalities.

#### Year 10 Higher

 Construction and Loci Measure line segments in geometric figures, including interpreting maps and scale drawings. Use the standard ruler and compass constructions. Use these to construct given figures and solve loci problems. Probability Record, describe and analyse the frequency of outcomes of probability experiments using tables. Relate relative expected frequencies to theoretical probability, using appropriate language and the 0-1 probability scale. Construct theoretical possibility spaces for single and combined experiments. Calculate the probability of independent events. Calculate and interpret conditional probabilities through representation using expected frequencies, with two-way tables, tree diagrams and Venn diagrams. Circle Geometry Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results. Graphs Work with coordinates in all four quadrants. Plot graphs of equations that correspond to straight-line graphs in the coordinate plane. Find the equation of the line through two given points or through one point with a given gradient. Identify and interpret gradients and intercepts of linear functions graphically and algebraically. Calculate gradients of graphs and interpret results in cases such as distance-time graphs. Transformations Identify, describe and construct congruent and similar shapes. Describe the changes and invariance achieved by combinations of rotations, reflections and translations. Describe translations as 2D vectors. Processing, Representing and Interpreting Data Interpret and construct tables, charts and diagrams, including frequency tables, bar charts and pie charts for categorical data. Vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use. Use and interpret scatter graphs of bivariate data. Make predictions (interpolate and extrapolate). Inequalities and Formulae Substitute numerical values into formulae and expressions, including scientific formulae. Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors. Understand and use standard mathematical formulae; rearrange formulae to change the subject. Solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line. Pythagoras and Trigonometry (2D and 3D) Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors. Know the formulae for: Pythagoras’ theorem, a2 + b2 = c2, and the trigonometric ratios. Apply them to find angles and lengths in right-angled triangles in two dimensional figures and, where possible, general triangles in two- and three-dimensional figures. More Graphs and Equations Find approximate solutions to equations numerically using iteration. Plot and interpret graphs (including reciprocal graphs and exponential graphs). Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y =1/x with x ≠ 0, and exponential functions y = kx for positive values. Area and Volume 2 Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders). Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2. Calculate arc lengths, angles and areas of sectors of circles. Use standard units of measure and related concepts. Change freely between related standard units.

#### Year 11 Foundation

 Graphs 2 Plot graphs of equations that correspond to straight-line graphs. Recognise, sketch and interpret linear functions and quadratic functions. Find approximate solutions to quadratic equations using a graph. Transformations Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS). Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement. Ratio and Proportion Identify and work with fractions in ratio problems. Use ratio notation, including reduction to simplest form. Divide a given quantity into two parts. Solve problems involving direct proportion. Scatter diagrams Interpret and construct tables, charts and diagrams. Use and interpret scatter graphs of bivariate data. Probability Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees. Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale. Apply the property that the probabilities of an exhaustive set of outcomes sum to 1. Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams. Formulae and Functions Substitute numerical values into formulae and expressions. Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors. Rearrange formulae to change the subject. Sequences 2 Generate terms of a sequence from term-to-term or position-to-term rule. Recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions. Deduce expressions to calculate the nth term of linear sequences. Quadratic Equations Simplify and manipulate algebraic expressions by: collecting like terms; expanding and factorising; expanding products of two binomials; factorising quadratic expressions of the form ×2 + bx + c, including the difference of two squares; Solve quadratic equations algebraically by factorising. Number 2 Calculate with roots and with integer indices. Calculate with and interpret standard form A x 10n, where 1 ⩽ A < 10 and n is an integer. Round numbers and measures to an appropriate degree of accuracy. Area and Volume 2 Identify and apply circle definitions and properties. Know and apply formulae to calculate: area of triangles, parallelograms, trapezia volumes of cuboids and other right prisms (including cylinders). Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate. Calculate arc lengths, angles and areas of sectors of circles. Calculate exactly with multiples of π. Simultaneous Equations Solve two simultaneous equations in two variables (linear / linear) algebraically; find approximate solutions using a graph. Derive two simultaneous equations, solve the equations and interpret the solution. Trigonometry Know the trigonometric ratios sin, cos and tan; apply them to find angles and lengths in right-angled triangles in two dimensional figures; Know the exact values of sin and cos for = 0°, 30°, 45°, 60° and 90°; know the exact value of tan for  = 0°, 30°, 45° and 60°