Mathematics
Welcome to Maths
We believe in a maths curriculum that is creative and engaging with the national curriculum at its core. All children are to have access to this curriculum and to make progress in lessons, irrespective of their starting point. Children need to develop the necessary skills to make them “deep thinkers” acquiring maths skills that can be recalled quickly and transferred and applied in different contexts. They need to be able to make rich connections across the areas of maths and use their knowledge in other subjects.
The maths department is made up of collaborative team of 11 maths specialists that are passionate about teaching their subject. We believe in a maths curriculum that is creative and engaging with the national curriculum at its core. All children are to have access to this curriculum and to make progress in lessons, irrespective of their starting point. Children need to develop the necessary skills to make them “deep thinkers” acquiring maths skills that can be recalled quickly and transferred and applied in different contexts. They need to be able to make rich connections across the areas of maths and use their knowledge in other subjects.
Balcarras Maths Department Endpoints
Maths is the foundation for understanding the world and we want our children to know the purpose behind their learning and to apply their knowledge to their everyday lives. We expect all pupils to have mastered by the end of each year.
Year 7 
Year 8 
Year 9 
Year 10 
Year 11 
Multiply Decimals 
Negative Number Calculations 
Standard Form conversions 
Divide decimals 
Standard form calculations 
Round to whole number, nearest 10 
Round to decimal places 
Three rules of indices 
Round to significant figures 
Estimation 
Find all factors and multiples of a number 
Write number as product of prime factors 

Use PFF to find HCF and LCM 

Fraction means equal parts, equivalent fractions 
F/D/% conversions 

Mixed Number Calculations 

Measure an angle 

Construct perp bisector 


Collect like terms 
Expand single brackets 
Expand double bracket 
Factorise with common factors 
Solve quadratics by factorising 
Sub +ve values into expressions 


Sub negative values into a formula 
Formulae for Cones and Spheres 
Angles in Triangle sum to 180 
Angles in simple polygons

Vertically opposite angles 
Angles of regular polygons 
Angle in parallel lines 
Find F/V/E for 3d shapes 
Plan of a 3D shape 
Pythagoras Find hypotenuse 
Pythagoras Find any side 
SOHCAHTOA 
Convert metric units of length 
Calculate Speed given distance and time 


Speed, Density, Pressure 
Ratio write, equivalent 
Share in a ratio 
Direct Proportion 
Combined Ratio and Proportion problems 
Inverse Proportion 
Solve 1 step equations 
Solve 2 step equation 
Solve Equation – unknown both sides 
Solve Equations with brackets and unknowns on both sides 
Solve simultaneous equations 
Area of rectangle and triangle 
Diameter is twice radius 
Area and Circumference of a circle 
Area and circumference of semi and quarter circles 
Volume and surface area of a cylinder 
Find simple percentages of an amount (non calc) 
Find percentages using a multiplier 
% increase, decrease using multiplier 
Repeated % changes using multiplier 
Reverse percentages 
Plot Coordinates in 4 quadrants 
Plot x=a, y = b 
Plot y=mx+c 
Gradient and y intercept 
Plot quadratic equations 
Rotate, Reflect and Translate 2D shapes 
Enlargement 
Translate with a vector and combine transformations 
Describe single transformation 
Vector algebra 
Averages from discrete data 
Use frequency Tables 

Averages from frequency tables 

Draw Bar Chart 
Dual and Composite Bar Charts 
Scatter diagram and correlation 
Interpret Scatter diagram 
Construct a Pie Chart 

Find nth term of an increasing arithmetic sequence with positive terms 
nth term for any arithmetic sequence 
generate a sequence given nth term 
Rearrange Formulae 


Represent inequalities on a number line 
Solve linear inequality 
Use inequalities to write an error interval 


Recognise Similar and Congruent shapes 
Find volume of a right prism 
Proof of Congruency 

Write probability as a fraction 
Probability for independent events 
Probability for dependent events 
Venn Diagrams 
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 



October 

November 
Factors and Multiples 


December 



January 



February 

March 

April 

May 

June 





July 
Curriculum map GCSE (higher level)
September 
Year 10 
Year 11 
October 

Solving linear equations (including setting up and rearranging formulae) 

Test and Review 

November 
Mocks 

Direct and inverse proportion (both numerical and algebraic approach) 

December 

Gradient and area under (nonlinear) graphs and graph transformations 

Test and Review 

January 

Revision 

Test and Review  
Exams 

Exams 

Solving quadratic equations (including linear and non linear simultaneous equations) algebraically 


Curriculum map GCSE (Foundation)
September 
10 
11 
October 



November 

Mocks 

December 

January 



February 

rearranging equations, graphs of cubic & reciprocal functions 

Revision 



March 

April 





Exams 

June 


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 

ChiSquared  discrete distributions 
Central Limit Theorem 

Revision and past papers 
Elastic springs (Hooke's law) 
Mar 
Revision and past papers 
Revision and past papers 

ChiSquared  discrete distributions 
Quality of Tests 

Revision and past papers 
Revision and past papers 
Apr 
Revision and past papers 
Revision and past papers 

ChiSquared  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 halfterm 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 halfyear bands.
In Y9 pupils are placed in sets 19 as a full year group. In Y10 and Y11 we go back to two parallel halfyear 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% 94 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.