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

 Unit 1 – Calculation Working with square, cube and prime numbers and using the 4 operations with fractions. Unit 2 – Number system Use approximations to estimate answers and use this to check the answers to calculations. Rounding numbers to significant figures and understand place value. Unit 3 - Indices Use vocabulary of highest common factor, lowest common multiple and prime factorisation. Apply and use simple laws of indices. Unit 4 – Equations and formulae Substitute values into formulae and expressions, including formulae, powers, roots and algebraic fractions. Expanding products of two binomials. Factorise linear expressions. Construct and rearrange simple formulae. Solve linear equations including use of brackets with unknowns on both sides Unit 5 - Proportion Share in a ratio including where one part is known. Apply ratio to real contexts and problems (conversion, comparison, scaling, mixing, concentrations, best buy problems) Compare lengths, areas and volume using ratio notation Unit 6 – Mensuration Know and apply formulae to calculate area of triangles, parallelograms, trapezia. Know and use Area and Circumference of a circle formulae.Calculate surface area of cuboids. Calculate surface area of right prisms (including cylinders). Know Pythagoras’ theorem and Trigonometric ratios and apply in right-angled triangles and in 2D Figures. Unit 7 – Graphs and sequences Use the form y = mx + c to identify parallel lines. Use a graph to find the approximate solution of a linear equation. Recognise and sketch graphs including real-world contexts. Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions. To deduce expressions to calculate the nth term of linear sequences Unit 8 – Transformations Describe the changes and invariance achieved by combinations of rotations, reflections and translations Unit 9 – Angles Apply the properties of angles at a point, angles on a straight line, vertically opposite angles. Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings. Unit 10 – Probability Design and use frequency trees. Understand and use the term relative frequency. Unit 11 – Statistics Construct and interpret frequency tables, bar charts and pictograms, including composite and dual bar charts. Calculate the median, mean, mode, modal class, and range of different sets of data. Calculate an estimate of the mean for a grouped frequency distribution, knowing why it is an estimate. Find the interval containing the median for a grouped frequency distribution. Interpret, analyse and compare data sets using statistical diagrams, median, mean, mode, modal class and range Identify outliers. Unit 12 – Constructions Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres. Interpret and construct plans and elevations of 3D shapes.

Year 10 Higher

 Unit 1 – Calculation Set up, solve and interpret the answers in growth and decay problems including compound interest. Apply the four operations (including formal written methods) to fractions and mixed numbers. Convert between mixed numbers and improper fractions Unit 2 – Number system Apply and interpret limits of accuracy. Use inequality notation to specify simple error intervals due to truncation or rounding. To be able to add and subtract numbers in standard form. Unit 3 - Indices Prime factorisation, including product notation and unique prime factorisation theorem. Estimate powers and roots of any given positive number. Calculate with fractional and negative indices. Calculate with roots and with integer indices. Simplify and manipulate algebraic expressions involving surds. Unit 4 – Equations and formulae Expanding products of two or more binomials. Factorising and solving quadratic. Expressions including the difference of two squares. Rearrange complex formulae to change the subject. Solve two simultaneous equations find approximate solutions to equations using a graph. Identify the solution sets of linear equations, inequalities, identities in two variables, using the convention of dashed and solid lines. Unit 5 - Proportion Share in a ratio including where one part is known. Apply ratio to real contexts and problems (conversion, comparison, scaling, mixing, concentrations, best buy problems. Solve problems involving direct and inverse proportion both graphically and algebraically. Unit 6 – Mensuration Use compound units such as density and pressure. Calculate Areas and Circumference of Composite shapes. Calculate arc lengths, angles and areas of sectors of circles. Calculate surface area and volume of spheres, pyramids, cones and composite solids. Know Pythagoras’ theorem and Trigonometric ratios and apply in right-angled triangles and in 2D Figures. Know and apply the sine rule and the cosine rule. Know and apply Area = ½ab sin C. Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and column representations of vectors. Unit 7 – Graphs and sequences Plot and interpret graphs of equations: perpendicular lines, reciprocal graphs, sketch translations and reflections of a given function including exponential graphs and find the equation of the line through two given points or through one point with a given gradient. Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square. Calculate exponential functions and the trigonometric functions. Recognise and sketch the graphs of y =sin x, y = cos x and y = tan x. Deduce expressions to calculate the nth term of quadratic sequences. Recognise and use sequences of arithmetic progressions including surds. Unit 8 – Transformations Describe the changes and invariance achieved by combinations of rotations, reflections and translations. Identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement fractional and negative scale factors. Apply the concepts of congruence and similarity including the relationships between lengths, areas and volumes in similar figures. Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic, column representations of vectors Unit 9 – Angles Understand and use alternate and corresponding angles on parallel lines. Derive and use the sum of angles in a triangle (e.g. to derive properties of regular/irregular polygons). Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings. Apply the standard circle theorems. Unit 10 – Probability Use the product rule for counting how many ways something can be done. Use a tree diagram as a method for calculating conditional probabilities. Use a Venn diagram as a method for calculating conditional probabilities. Unit 11 – Statistics Construct and interpret scatter graphs. Identify types of correlation. Identify outliers. Construct and interpret histograms with equal class intervals, cumulative frequency graphs and box plots. Calculate quartiles and inter-quartile range from a small data set, a cumulative frequency diagram or a box plot. Interpret, analyse and compare data sets using box plots, quartiles and inter-quartile range. Compare two diagrams or data sets in order to make decisions about a hypothesis. Unit 12 – Constructions Use the standard ruler and compass constructions. Solve loci problems.

Year 11 Foundation

 Unit 1 – Calculation Work with terminating decimals and their corresponding fractions. Interpret percentages and percentage changes as a fraction or decimal multiplicatively. Solve problems involving percentage change, increase/decrease, original value and simple interest/financial. Unit 2 – Number system Apply hierarchy of operations (to include brackets, powers, roots and reciprocals). Calculate, convert and interpret standard form Ax10n. Apply and interpret limits of accuracy. Use inequality notation to specify simple error intervals due to truncation or rounding Unit 3 - Indices Prime factorisation, including product notation and unique prime factorisation theorem. Use and apply Laws of Indices. Unit 4 – Equations and formulae Factorising and solving quadratic expressions including the difference of two squares. Rearrange complex formulae to change the subject. Solve two simultaneous equations. Identify the solution sets of linear equations, inequalities, identities in two variables. Represent solutions on a number line. Set up and solve linear equations in mathematical and non-mathematical contexts, and Interpret solutions in context. Unit 5 - Proportion Use and understand proportion as equality of ratios. Solve problems involving direct and inverse proportion both graphically and algebraically Unit 6 – Mensuration Calculate Areas and Circumference of Composite shapes. Know and apply formulae to calculate volume of cuboids and other right prisms (including cylinders). Calculate arc lengths, angles and areas of sectors of circles. Use compound units such as density and pressure Unit 7 – Graphs and sequences 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. Unit 8 – Transformations Identify, describe and construct similar shapes, including on coordinate axes, by enlargement, fractional scale factors. Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures. Apply addition and subtraction of vectors and multiplication of vectors by a scalar. Unit 9 – Angles Understand and use alternate and corresponding angles on parallel lines. Derive and use the sum of angles in a triangle (e.g. to derive properties of regular/irregular polygons). Unit 10 – Probability Complete a tree diagram to show outcomes and probabilities. Use a Venn diagram as a method for calculating probabilities Unit 11 – Statistics Construct and interpret pie charts, vertical line charts and scatter graphs. Understand that correlation does not indicate causation. Draw a line of best fit by eye for data with strong enough correlation, and use it to estimate unknown values when appropriate. Understand outliers and make decisions whether or not to include them when drawing a line of best fit. Plot and interpret time-series graphs Unit 12 – Constructions Use the standard ruler and compass constructions. (SSS, SAS, ASA, RHS triangles). 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 11 Higher

 Unit 1 – Calculation Convert recurring decimals into corresponding fractions and vice versa. Set up solve and interpret Growth and Decay problems. Unit 2 – Number system Use limits of accuracy in calculating with upper and lower bounds. To calculate with numbers in standard form. Unit 3 - Indices Calculate exactly with surds, simplifying expressions that involve squares. Rationalise the denominator. Unit 4 – Equations and formulae Express exponential growth or decay as a formula. Find approximate solutions to equations numerically using iteration. Solve linear inequalities, and quadratic inequalities, represent the solution set on a number line. Algebraic proof. Set up and solve simultaneous equations including linear/quadratic. Interpret the reverse process as the ‘inverse function’. Unit 5 - Proportion Construct and interpret equations that describe direct and inverse proportions Be able to calculate with proportionality and inversely proportionality involving squares and roots. Recognise and interpret graphs that illustrate direct and inverse proportion Unit 6 – Mensuration Calculate or estimate gradients of graphs and areas under graphs. Interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts. Surface area and volume of composite solids. Trigonometric Ratios and Pythagoras’ theorem in 3D figures. Unit 7 – Graphs and sequences Apply the concepts of average and instantaneous rate of change (gradients of chords or tangents) in numerical, algebraic and graphical contexts. Interpret the gradient at a point on a curve as the instantaneous rate of change. Recognise use and find the equation of a circle with centre at the origin, including. Transform the graph of any function f(x): f(x) + a, f(x + b), af(x) and f(ax) where a and b are integers. Recognise transformations of functions and be able to express a transformed function in algebraic form. Apply transformations to the graphs of sine and cosine functions. Unit 8 – Transformations Apply vector methods for simple geometric proofs. Recognise when lines are parallel using vectors. Unit 9 – Angles Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results. Describe the changes and invariance achieved by combinations of rotations, reflections and translations. Unit 10 – Probability Solve more difficult probability problems using a variety of appropriate methods. Derive and apply the formula: P(A and B)=P(A given B)P(B) Unit 11 – Statistics Construct and interpret histograms with equal and unequal class intervals, cumulative frequency graphs and box plots. Find an estimate of the median or other information from a histogram. Calculate quartiles and inter-quartile range from a small data set, a cumulative frequency diagram or a box plot. Interpret, analyse and compare data sets using box plots, quartiles and inter-quartile range. Plot and interpret time-series graphs. Unit 12 – Constructions Use these to construct given figures and loci problems and know that the perpendicular distance from a point to a line is the shortest distance to the line.