 # Mathematics

### Key to Curriculum maps

 Basic numeracy Geometry Sequences Probability Ratios, Proportion, Fractions, Decimals, Percentages Statistics Algebra

### Curriculum map Key Stage 3

 YEAR 7 YEAR 8 YEAR 9 September Continue a given sequence (any) Nth term of a linear sequence Product of Primes HCF & LCM (with Venn diagrams) Standard form Indices Roots Standard form Bounds Error intervals Adding & subtracting decimals Multiplying & dividing integers Multiplying & dividing by powers of 10 Powers and roots Negatives BIDMAS                               Rounding & estimating Negatives BIDMAS October Algebraic notation & Simplifying Index laws Factorising Changing the subject Bisectors Loci Expanding double brackets Factorising quadratics November Factors, multiples, primes, square & cube numbers HCF & LCM Plans and elevations Enlargements Scale diagrams and maps Bearings Direct and inverse Proportion Compound units of speed and density (and pressure) Inequality signs Ordering integers, decimals, fractions Basics of probability Theoretic probability Fibonacci sequence Quadratic sequence December Multiplying & dividing decimals Decimal and fraction equivalents Terminating and recurring decimals Time series graphs Frequency polygons Scatter diagram Constructing lines and angles Label notation for parallel & perpendicular lines Types of angles Label notation for angles Constructing triangles and other shapes January Vertically opposite angles Angles at a point and on a line Sum of angles in a triangle Properties of triangles Properties of quadrilaterals Connection ratios and fractions Divide into a ratio Conversion, comparison, recipes, scaling Compound units of speed Area and circumference Arc length and the area of a sector, Surface area of a right prism Surface area of a cylinder Write as a fraction of Write as a percentage of Finding the percentage change (loss, profit) Increase and decrease by a percentage (5%,10%,20%,…) Generating linear sequence Find the nth term Solve an inequality on a number line Solve linear inequality (including brackets and variable on more than one side) February Ratio notation Simplify a ratio Divide a quantity by a given ratio Alternate and corresponding angles Interior angles in polygons Exterior angles in regular polygons Similarity of shapes Finding missing lengths in similar shapes Congruent shapes Congruent triangles (SSS, SAS, ASA, RHS) Geometrical proof, involving congruence Faces, Edges, Vertices in 3D shapes Nets of 3D shapes March Expression, term, formula, equation, function (variable, coefficient, …) algebraic notation (the ‘rules’ of algebra) Collecting like terms Expanding brackets Substitute positive and negative values Multiplier method Percentage change Reverse percentage questions Simple interest Use the form of y=mx+c Gradients of parallel and perpendicular lines Find the equation of a line through one point with a given gradient two given points Quadratic graphs Intercept, symmetry, pos. or neg. coefficient Units of length, mass, volume, time, money Solving equations (unknown on both sides and brackets involved) Apply solving in geometrical problems Solutions from intersecting graphs Solve linear simultaneous equations April Perimeter of 2D shapes Surface area of cubes and cuboids Area of parallelograms, triangles, trapezia Volume of cuboids Circle definitions Circumference and area of a circle Semi / quarter circles Perimeter and area of compound shapes Volume of cylinder Probabilities of independent combined events Probabilities of dependent combined events Tree diagrams Relative frequency and theoretical probability May Solving equations (incl. use of brackets) with variable on ONE side Linear graphs y=mx+c and ax +by = c Distance time graphs, money rate, ... KS3 recap of transformations Calculating with proper and improper fractions, and mixed numbers Probability with Venn diagrams Frequency trees Possibility space Theoretical vs experimental probability GCSE Percentages June Coordinates Lines parallel to x-axis or y-axis & y = x and y = -x Reflections Translations Rotations Types of data Averages Frequency tables Multiple Bar charts Pie charts Scatter graphs Averages from a table GCSE Pythagoras Range, mode, median, mean Frequency tables Bar charts and vertical line charts Comparative bar charts Pie charts GCSE Trigonometry July Money Management

### Curriculum map GCSE (higher level)

 September Year 10 Year 11 Calculations, checking, rounding, product rule Further Trigonometry Indices (including roots and reciprocals) Graphs of trigonometric functions Factors, multiples & primes Collecting data (including sampling & capture-recapture) Standard form and surds Cumulative frequency, box plots and histograms October Algebra: The basics Sketching algebraic graphs Solving linear equations (including setting up and rearranging formulae) Circle Theorems Test and Review Circle Geometry November Sequences Mocks Averages and range Representing and interpreting data Direct and inverse proportion (both numerical and algebraic approach) Scatter graphs Fractions December Gradient and area under (non-linear) graphs and graph transformations Percentages (taught in Y9) Test and Review Higher Level Algebra, functions and proof January Ratio Angles (including polygons and parallel lines) Vectors Pythagoras' Theorem and Trigonometry (taught in Y9) Similarity and congruence, 2D and 3D February Straight line graphs Revision Test and Review Real straight line graphs and coordinate geometry March Quadratic, cubic, reciprocal, exponential and circle graphs Perimeter, area and 3D forms Circles, cylinders, cones and spheres April Exams May Accuracy and bounds Exams Transformations Constructions, loci and bearings June Solving quadratic equations (including linear and non linear simultaneous equations) algebraically Inequalities (linear and quadratic)

### Curriculum map GCSE (Foundation)

 September 10 11 integers & place value Pythag revision and trigonometry multiplicative reasoning decimals probability 1 indices, powers & roots probability 2 October factors, multiples & primes constructions, loci & bearings algebra, the basics quadratic equations, expanding & factorising November Mocks expanding & factorising single brackets expressions & substitution into formulae December tables plans, elevations & nets Charts and Graphs quadratic equations, graphs January Pie Charts circles, cylinders, cones & spheres Scatter Graphs fractions & reciprocals Fractions indices & standard form revision similarity & congruence in 2D Fractions, decimals, percentages vectors February rearranging equations, graphs of cubic & reciprocal functions Revision: Percentages (taught in 9) Revision Stats and sampling March The averages polygons & parallel lines interior & exterior angles of polygons equations April inequalities sequences Exams perimeter & area 3D forms & volume June straight line graphs real life graphs

### Curriculum map A level mathematics

 Pure- 5 hours a fortnight Mechanics- 2 hours a fortnight Statistics- 2 hours a fortnight
 Y12 Y13 Sept Indices and Surds Proof Quadratics Functions and mappings Definitions and Large Data Set Correlation Measures of location Modelling Moments Constant Acceleration Oct Equations and Inequalities Binomial expansion Graphs and transformations Radians Measures of spread Probability Constant Acceleration Forces and friction Nov Coordinate Geometry Trigonometric functions Circles Trigonometry and modelling Representing data Probability Forces Projectiles Dec Algebraic Methods Parametric equations Correlation Normal Distribution Forces Projectiles Jan Binomial expansion Mocks Trigonometric ratios Trigonometric identities Vectors (in mechanics lessons) Differentiation Probability Application of forces Distributions Normal Distribution Feb Mocks Differentiation Differentiation Numerical methods Hypothesis tests Normal Distribution Variable acceleration Application of forces Mar Differentiation Integration Integration Vectors Hypothesis tests Revision of Y12 content Variable acceleration Vectors in kinematics Apr Exponentials and Logarithms Revision and past papers Revision of Y12 content Revision and past papers Revision of Y12 content Revision and past papers May Revision of Y12 content EXAMS

### Curriculum maps Further Maths A level

 Core Pure- 5 hours a fortnight Mechanics- 2 hours a fortnight Statistics- 2 hours a fortnight
 Y12 Y13 Sept Complex Numbers Series Argand Diagrams Methods in calculus Discrete Random Variables Negative Binomial Distribution Momentum and impulse Momentum and impulse Work, energy and power Revision of Y12 collisions Oct Matrices Volumes of revolution Discrete Random Variables Hypothesis Testing- Geometric Work, energy and power Elastic collisions in 2 dimensions Nov Linear Transformations Polar coordinates Poisson Distribution Probability Generating Functions Elastic Collisions Elastic collisions in 2 dimensions Dec Series Hyperbolic Functions Proof by induction Probability Generating Functions Poisson Distribution Revision of Y12 Energy Elastic Collisions Revision for mocks Jan Vectors Mocks Hypothesis Testing- Poisson Methods in differential equations Revision Central Limit Theorem Mocks Elastic springs (Hooke's law) Feb Volumes of revolution Modelling with differential equations Chi-Squared - discrete distributions Central Limit Theorem Revision and past papers Elastic springs (Hooke's law) Mar Revision and past papers Revision and past papers Chi-Squared - discrete distributions Quality of Tests Revision and past papers Revision and past papers Apr Revision and past papers Revision and past papers Chi-Squared - contingency tables Quality of Tests May A2 Complex Numbers REVISION AND EXAMS

### How is Mathematics organised at Balcarras School?

Year 7 (Y7) is split into two bands with each band containing 3 or 4 tutor groups. For the first half term they are taught as a tutor group. After the October half-term they are put into sets based on their raw KS2 results. If a pupil has not taken KS2 exams or their school does not provide the raw scores, we will use the numeracy test that all pupils sit at the end of the first half term to place them.

Being placed in a lower set does not mean that a pupil is not good at mathematics; it merely reflects their relative position on entry in an intake of nearly 200 pupils. Some pupils and parents find the initial setting to be a worry, especially if a child was one of the best mathematicians in a small primary school but we have found that the only fair way to allocate starting sets is to use the KS2 raw score and rank pupils. It is our aim to stretch and challenge pupils in all sets and at all abilities.

Again this year, pupils who have started at Balcarras in the bottom set in Y7 have achieved grade 8 at GCSE in Y11.

During Y7, changes are made between sets if it is clear that a student is wrongly placed.

All Y7 pupils take a common examination and this, together with performance in class work and homework throughout the year, forms the basis of set allocation for Y8 within two parallel half-year bands. In Y9 pupils are placed in sets 1-9 as a full year group. In Y10 and Y11 we go back to two parallel half-year bands. Within each band pupils are setted for mathematics based on their exam and class work. We always enter students into the highest level paper that we believe will maximize their grade in external examinations

## Key Stage 3

Follow the kangaroo maths Key Stage 3 Framework for Teaching Mathematics, with a strong mastery approach. In accordance with the National Strategy we aim to develop both mental and written mathematical skills.

The scheme mirrors the requirements of the national curriculum and includes number and algebra, geometry and measures, statistics together with mathematical processes and applications.

Being in smaller set groupings, aided by Teaching Assistants where appropriate, supports the least able.

We set and internally assess KS3 SAT examinations to determine setting for Y10.

## GCSE

All students follow a course of study that can lead to a GCSE examination in mathematics. We follow the Edexcel specification and pupils sit three formal examinations at the end of the course. There is no coursework in mathematics. The examinations include elements of ‘functional skills’ and the final grade will be between 9 and 1, with foundation students able to achieve a maximum of a grade 5.

Results are consistently well above the national average and amongst the highest in the county.

In June 2019, 90.5% of the students in Y11 achieved an 9 - 4 grade in mathematics with 47.1% of pupils gaining a grade 7 or better and 11.4% achieving a grade 9.

 2019 90.5% 9-4 in Maths 2018 89.7% 2017 94.8% 2016 86.1% A*-C in Maths 2015 91.3% 2014 90.5% 2013 93.6% 2012 95% 2011 90%

### GCSE Mathematics 2019 ## A level

Advanced level mathematics is growing in popularity and is relevant to most career choices. We offer units in Pure Maths, Mechanics, Statistics and Decision Maths. Balcarras School has an enviable reputation for A Level success.

In 2019, at A Level, 21 students achieved an A* grade and over 80% achieved at least a grade A. This gave the department an ALPS grade 1 making it the best mathematics department in the country (including grammar schools and independent schools). In A Level Further maths 85% achieved at least a grade A. Many of these students went on to study maths at some of the best universities in the country.

• Mathematics was the most applied for subject in the sixth form in 2017, 2018 and 2019
• Balcarras is one of the few schools in the county that offers both A level Mathematics and A level Further Mathematics

### What equipment will be needed?

In maths lessons you will need to have a pen, pencil and rubber together with mathematical drawing instruments (e.g. compass, ruler and protractor).

We expect all students to bring and use a scientific calculator and this is essential for two of the examinations papers. The school has mathematical equipment and calculators for sale and these can be purchased from any maths teacher.

• Items of equipment will be on sale during the new Y7 induction meeting in June
• A fixed price pack includes a calculator and all the equipment needed

### Does the school take part in any mathematical competitions?

Yes. We regularly enter students for the UKMT Mathematical Challenges at Junior, Intermediate and Senior Levels as well as the regional Team Mathematics Challenges. We run a maths club for Y11, 12 and 13 pupils every Thursday lunchtime which prepares students for the Maths Challenges and also for STEP/ MAT exams prior to University applications. 