Balcarras

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.