#  # -Maths

 Curriculum Content: Aims and ambitions: Students become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Students reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language  Students can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Year group Topics include By the end of the year, students should be able to: 7 Number Algebra Ratio, proportion and rates of change Geometry and measure Probability  Statistics Assessment: Students will be assessed by min reviews, open book assessments throughout the year and an end of year GCSE style exam paper Number: Manipulate and use basic number skills involving the four operations including decimals and negative numbers. Understand and use fractions and percentages. Understand and use powers and roots. Understand types of numbers and factors. Algebra: Understand linear sequences. Use algebraic methods with respect to expressions and equations.  Draw and understand graphing. Geometry and Measure: Understand properties of 2D shapes and angles. Understand area and perimeter of 2D shapes. Understand volume of 3D shapes. Understand different metric units. Draw and understand transformations. Statistics: Use different averages. Draw and understand different charts and graphs. Ratio, proportion and rates of change: Understand ratio and proportion. Calculate compound measures. Probability: Understand and use probability. 8 Number Algebra Ratio, proportion and rates of change Geometry and measure Probability  Statistics Assessment: Students will be assessed by min reviews, open book assessments throughout the year and an end of year GCSE style exam paper Number: Manipulate and use basic number skills. Understand and use fractions and equivalence.  Understand basic surds Understand basic standard form Understand rules of indices. Understand and use percentages. Algebra: Understand different types of sequences. Use algebraic methods with respect to equations including fractional and simultaneous.  Draw and interpret different types of graphs. Geometry and Measure: Understand properties of 2D shapes and construct different shapes including scale factors. Understand area and perimeter of 2D shapes. Understand volume of 3D shapes. Use basic Pythagoras and trigonometry. Draw and understand transformations. Interpret and draw different elevations. Statistics: Use different averages, and grouped averages Draw and interpret different charts and graphs. Ratio, proportion and rates of change: Understand ratio and proportion, including direct and inverse. Calculate compound measures. Probability: Understand and use probability, including all diagrams. 9 Number Algebra Ratio, proportion and rates of change Geometry and measure Probability  Statistics Assessment: Students will be assessed by min reviews, open book assessments throughout the year and an end of year GCSE style exam paper Number: Manipulate and use all number skills including factors rounding and significant figures. Understand and use fractions and equivalence.  Understand basic surds with different algebraic skills. Understand basic standard form Understand rules of indices. Understand and use percentages. To use number skills in different mathematical areas. Algebra: Understand different types of sequences. Use algebraic methods with respect to equations including fractional and simultaneous.  Draw and interpret different types of graphs. Use algebraic skills in other areas of maths e.g. Geometry and measure. Geometry and Measure: Understand properties of 2D shapes and construct different shapes including scale factors. Understand area and perimeter of 2D shapes. Understand volume of 3D shapes. Use more complex Pythagoras and trigonometry in problem solving. Draw and understand transformations. Interpret and draw different elevations. Statistics: Use different averages, and grouped averages Draw and interpret different charts and graphs. Interpret all graphs and charts. Ratio, proportion and rates of change: Understand ratio and proportion, including direct and inverse. Calculate compound measures. Probability: Understand and use probability, including all diagrams. 10 Number Algebra Ratio, proportion and rates of change Geometry and measure Probability  Statistics Assessment: Students will be assessed by min reviews, open book assessments throughout the year and an end of year GCSE style exam paper Number : Apply systematic listing strategies, including use of the product rule for counting  Estimate powers and roots of any given positive number  Calculate with roots, and with integer {and fractional} indices  Calculate exactly with fractions, {surds} and multiples of π; simplify surd expressions involving squares  Calculate with numbers in standard form A × 10n , where 1 ≤ A < 10 and n is an integer  Change recurring decimals into their corresponding fractions and vice versa  Identify and work with fractions in ratio problems  Apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}. Algebra: Simplify and manipulate algebraic expressions including those involving surds and algebraic fractions. Factorising linear and quadratic expressions  Understand the laws of indices including fractional and negative Interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’ Draw and interpret all  graphs identify and interpret roots, and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square, trigonometry graphs and equations of a circle. Find approximate solutions to equations numerically using iteration translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution  solve linear inequalities in one, or two, variables and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph  Deduce expressions to calculate the n th term of linear and quadratic sequences. To recognise other forms of sequences. Ratio, proportion and rates of change: Compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity including trigonometric ratios  Convert between related compound units  Understand and interpret direct and inverse proportion.  Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion Interpret the gradient at a point on a curve as the instantaneous rate of change Set up, solve and interpret the answers in growth and decay problems, including compound interest. Geometry and measures:  ♣ Interpret and use fractional, and negative, scale factors for enlargements  ♣ Describe combinations of transformations  ♣ Identify and apply circle definitions and to find area and circumference of circles and parts of a circle Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results  Construct and interpret plans and elevations of 3D shapes Interpret and use bearings  Calculate surface areas and volumes of spheres, pyramids, cones and composite solids  Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures  Apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right angled triangles including 3-D. Understand trigonometry in non-right angled triangles Know the exact values of sinθ and cosθ for θ = 0 0 , 300 , 450 , 600 and 900 ; know the exact value of tanθ for θ = 0 0 , 300 , 450 and 600 describe translations as 2D vectors  apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs Probability: Aapply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one  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  Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions  Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams. Statistics:  Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling  Interpret and construct tables and line graphs for time series data  Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use  interpret, analyse and compare the distributions of data sets from univariate empirical distributions applying appropriate statistical methods Apply statistics to describe a population  Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing. 11 Number Algebra Ratio, proportion and rates of change Geometry and measure Probability  Statistics Assessment: Students will be assessed by min reviews, open book assessments throughout the year.  A GCSE mock exam in December consisting of 3 exam papers. A GCSE mock exam in February/March consisting of 3 exam papers. Practise exam papers will also be used for homework throughout the year. Year 10 and 11 are combined. Bold is the higher elements. GCSE Key Information Qualification GCSE Maths Exam Board Edexcel Website Link https://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html Exam Structure and Content We follow the two-year linear Edxcel maths course. There are two different tiers: foundation and higher. Paper 1: Non calculator 1 hour 30 minutes worth 80 marks (33.3% of the final mark) Paper 2: Calculator 1 hour 30 minutes worth 80 marks (33.3% of the final mark) Paper 3: Calculator 1 hour 30 minutes worth 80 marks (33.3% of the final mark) Recommended revision guide REVISE Edexcel GCSE (9-1) Mathematics Higher/foundation Revision Guide PearsonsCPG edxcel revision guide/workbook/exam Practise Papers Exam dates Summer 2020 Paper 1 – non calculator 19th May am Paper 2 – calculator 4th June am Paper 3 – calculator 8th June am Extra-curricular opportunities in UK Maths Challenge GCSE statistics After school revision After school homework club Intervention sessions