 # Mathematics

Much of our everyday lives and work has mathematics at its heart. It encompasses applying mathematical techniques to routine procedures, problem solving, presenting arguments which may be justified by proofs alongside interpreting solutions in the context of the problem at hand. At St Mary’s we aim to provide an expertly devised varied curriculum which teaches techniques whilst engaging and inspiring students to apply these skills to real life problems which extend to other subject areas. Additionally we offer chances for enrichment through lunchtime clubs, external group competitions as well as individual challenges which are conducted internationally.  We offer a regular lunchtime help club where students of all ages and abilities are encouraged to seek any support or help with individual questions or topic areas.

Key Stage 3

 Key Stage 3 In Key Stage 3 pupils follow the programs of study prescribed by the National Curriculum. They learn new techniques in each of the set areas of Number & Measure, Geometry, Algebra, Statistics, Probability, Ratio and proportion and Rates of Change and apply these to problems. We challenge and extend their thinking often going beyond that set out below. The pupils are encouraged to explain their thinking and to set this down on paper. They meet simple proofs and are encouraged to develop their talents of reasoning, interpretation and problem solving in the context of real life problems. More detail as to the content is set out below. Year 7 Secure Skills Include Number & Measure: ·         Factors, Multiples, Squares, Square Roots, Primes and Divisibility tests. Powers and roots. Finding HCF and LCM logically. ·         Simple estimation and rounding to decimal places and significant figures. ·         Multiplication – standard methods up to 4 digit by 2 digit. ·         Negative numbers including +/-/x/÷and order of operations. ·         Conversion between metric units. ·         Time including time in decimal form. ·         Fractions, decimals, and percentage problems. Geometry: ·         Angle facts. ·         Properties of 2D and 3D shapes. ·         Area and perimeter of rectangles, triangles, parallelograms and composite shapes. ·         Volume and surface area of cubes and cuboids. ·         Metric and Imperial Units and their connections. ·         Reflective and rotational symmetry in shapes, transformations & formal constructions. ·         Coordinates and straight line graphs. Algebra: ·         Using letters in place of unknowns & variables and simplifying expressions. Create and use formulae. ·         Solving simple equations. ·         Generate sequences from term-to-term and position to term rules.   Statistics: ·         Work confidently with discrete data. Representing and interpreting data in graphical form. Comparing two data sets. Ratio, Proportion and Rates of Change: ·         Understand the relationship between ratio and proportion. ·         Solve proportional and ratio problems. Year 8 Secure Skills Include Number & Measure: ·         Use integer powers of 2, 3, 4, 5 and their associated roots. ·         Four rules of fractions and negative numbers and questions involving BIDMAS. ·         Multiply and divide an integer by a decimal and a decimal by a decimal. ·         Prime factor form including application to highest common factor and lowest common multiple. ·         Use multipliers to calculate a percentage increase/decrease.   Geometry: ·         Angles associated with parallel lines. ·         The sums of the interior and exterior angles of regular/irregular polygons. ·         Transform 2-D shapes by simple combinations of rotations, reflections, enlargements and translations, on paper and using ICT. ·         Formal constructions and loci, both by reasoning and by using ICT, to produce shapes and paths. ·         Use bearings including the eight compass point bearings and three-figure bearings. ·         Extend area to trapezium; calculate areas of compound shapes. Algebra: ·         Recognise and plot equations of the form y = mx + c correspond to straight-line graphs. ·          Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. ·         Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets). ·         Begin to work with inequalities such as listing integer values that satisfy -4 ≤ x< 3 and appreciating all the real values of x that satisfy this. ·         Use linear expressions to describe the nth term of a linear sequence. Probability: ·         Find and record all mutually exclusive outcomes for single events and two successive events in a systematic way, using two-way tables, tree diagrams and Venn diagrams. Statistics: ·         Scatter graphs and linear correlation. ·         Understand what is meant by a sample. ·         Design questionnaires. ·         Produce and interpret stem and leaf diagrams, pie charts, bar charts and frequency diagrams. ·         Averages from a frequency table. ·         Compare two or more sets of data. Ratio, Proportion and Rates of Change: ·         Use Scale drawings and map scales. ·         Use the unitary method to solve simple word problems involving ratio and direct proportion. ·         Divide a quantity into two or more parts in a given ratio, find missing quantities from a ratio and express a ratio in the form 1: n Year 9 Secure Skills Include Number & Measure: ·         Cancel common factors before multiplying or dividing fractions. ·         Multiply and divide by decimals. ·         Use a calculator efficiently to perform complex calculations with numbers of any size including fractions and negative numbers, knowing not to round during intermediate steps of a calculation; use p and sign change keys, function keys for powers, roots and fractions, brackets and the memory.  Interpret the display in context. ·         Estimate square roots and cube roots. Geometry: ·         Extend angles in polygons work. ·         Convert between area and volume measures (mm2 to cm2, cm2 to m2, mm3 to cm3, cm3 to m3, and vice versa). ·         Find the circumference and area of a circle. ·         Calculate the surface area and volume of right prisms. ·         Understand congruence. ·         Visualise and use 2-D representations of 3-D objects; including plans and elevations. ·         Enlarge 2-D shapes, given a centre of enlargement and any scale factor, on paper and using ICT; identify the scale factor of an enlargement and recognise that enlargements preserve angle but not length. ·         Pythagoras’ Theorem. ·         Trigonometry in right-angled triangles Algebra: ·         Find the inverse of a linear function. ·         Construct and solve linear equations with integer coefficients. ·         Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20. ·         Solve problems involving direct proportion using algebraic methods. ·         Generate points and plot graphs of linear functions where y is given implicitly in terms of x, e.g. ay + bx = 0, y + bx + c = 0. ·         Distance–time graphs. ·         Factorise by common factors. ·         Use formulae from mathematics and other subjects. ·         List integer values that satisfy a given inequality and represent inequalities on number lines.   Probability: ·         Use frequency trees and link to probabilities.   Statistics: ·         Work confidently with continuous data including: grouping data, estimating the mean, modal class and the interval containing the median. Ratio, Proportion and Rates of Change: ·         Find percentage changes. ·         Calculate simple interest, VAT, discounts, pay rises and simple compound interest. ·         Interpret and use ratio in a range of contexts, including solving word problems. ·         Extend working with map scales.
Key Stage 4
Key Stage 4
In Key Stage 4 students follow the prescribed National Curriculum which is assessed by Edexcel Examination Board. Students are entered for either Higher Level leading to grades 4 – 9 or Foundation level leading to grades 1 – 5. The vast majority of the course builds upon and extends the skills learned at KS3, but students do encounter and develop new areas of mathematics. Particular emphasis is to be able to confidently:

·         Accurately recall facts and carry out routine procedures or set tasks requiring multi-step solutions.

·         Present arguments and proofs.

·         Make deductions, inferences and draw conclusions from mathematical information from mathematical information.

·         Interpret and communicate information accurately in the context of the given problem.

·         Evaluate methods used and results obtained.

·         Evaluate solutions to identify how they may have been affected by assumptions made.

Assessment is by three separate 1 ½ hour written examinations at the end of the course. Paper 1 is non-calculator and Papers 2 & 3 require the use of a scientific calculator. The three papers are equally weighted.

Those topic areas which are totally new to the tiers of entry are:

 Foundation Vectors ·         Vectors in 2D, writing as column vectors. ·         Simple vector journeys. Trigonometry ·         Use of Sine, cosine and tangent in right-angled triangles. ·         Learning values of the trigonometrical functions of the special angles. Congruent and Similar Triangles. Compound Interest. Solving Quadratic and Simultaneous Equations. Indices and Standard Form. Upper and Lower Bounds. Graphs. Set notation and its application to probability. Direct and Inverse Proportion. Compound measures. Higher Vectors ·         Vectors in 2D, magnitude and direction. ·         Vector journeys. ·         Collinear points and parallel vectors. Circle Theorems Upper and Lower Bounds and calculations with these. Trigonometry ·         Use of Sine, cosine and tangent in right-angled triangles. ·         Learning values of the trigonometrical functions of the special angles. ·         Sine rule and cosine rule. ·         Extend to 3D problems. Systematic listing strategies ·         Use of factorial notation. Functions ·         Input, output and composite functions. ·         Inverse functions. ·         Transforming graphs of functions. Growth and Decay Set Theory and its applications to probability. Numerical Methods Pre-calculus methods for finding gradient of a curve and the area between a curve and the x axis. ·         Applications of this to velocity-time and distance-time graphs. Time series and moving averages.
 Exam Board: AQA ( Specification 8300) For further details on the syllabus content please visit: AQA | GCSE | Mathematics | Specification at a glance   Good websites for support Dr Frost- all students have a login Corbett Maths- free to use for all
Key Stage 5
 Key Stage 5 Students who opt to study either Mathematics or Further Mathematics follow the Edexcel syllabus for both. These exciting subjects extend the knowledge and reasoning acquired thus far and challenge the students’ application and evaluation to a greater and much deeper level. The A level Mathematics course builds upon the three areas of Pure Mathematics, Statistics and Mechanics. The students will expand their knowledge of Proof Algebra and functions Coordinate geometry in the (x,y) plane Sequences and Series Trigonometry Exponentials and Logarithms Differentiation Integration Vectors Quantities and units in mechanics Kinematics Forces and Newton’s laws Moments Statistical Sampling Data presentation and interpretation Probability Statistical Distributions Statistical Hypotheses Testing Assessment is by three 2hour examination papers at the end of the course. In Further Mathematics the students will delve into fewer topic areas but far more deeply. They will meet Complex numbers Series Volumes of Revolution Proof Matrices Further Algebra and Functions Further Calculus Further Vectors Polar Coordinates Hyperbolic Functions Differential Equations Further Trigonometry Conics Differential Methods Numerical Methods Momentum and Impulse Work, Energy and Power Elastic springs and strings Elastic collisions Assessment is by four 1 ½ hour examination papers at the end of the course. Exam Board: For A level Mathematics the Exam board is Edexcel. The subject code is 9MA0. For A level Further Mathematics the exam board is also Edexcel.  The subject code is 9FM0. For further details please visit:  https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html Good Websites for support Dr Frost Physics and Maths Tutor