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The Mathematics Department aims to provide a learning experience that challenges, stimulates and supports all pupils as they journey toward achieving their mathematical potential.


About Our Mathematics Department

The Mathematics department at The High School aims to provide a learning experience that challenges, stimulates and supports all pupils as they journey toward achieving their mathematical potential. The department comprises eight highly skilled teachers who work hard to create a learning environment where all pupils can develop confidence, perseverance and a genuine enjoyment for the subject.

We have five classes in each year group. In Transitus, S1 and S2 all classes are given a broad general education in Mathematics based on the Scottish Curriculum for Excellence. From S3 our pupils work toward the Scottish National 5 qualification which will be examined at the end of S4. Over 80% of S5 pupils regularly opt to study Higher Mathematics and the results here are strong, with a pass rate at A – C of around 90%. Advanced Higher Mathematics and Advanced Higher Statistics are popular with S6 pupils. Here, again, the pass rate at A-C is around 90%.

The Mathematics department offers a number of enrichment opportunities throughout the year. Pupils regularly participate in the Scottish Mathematical Council’s Maths Challenge, many achieving Gold awards, the Scottish Enterprising Maths competition and the annual Mathématiques sans Frontières competition. We also enter classes for UK Maths Trust competitions and regularly have individuals who qualify for the follow on rounds such as the Mathematical Olympiad or Kangaroo competitions. Our weekly N-rich Maths club gives pupils a chance to explore some interesting problems whilst our weekly Maths “clinic” provides support for all pupils when they need it.


Mr Stuart Welsh (Head of Department)
Mrs Claire Anderson (Housemistress - Clyde)
Mrs Jane Armstrong
Mrs Elaine Clarke
Dr Danny Hamilton
Mr Tom Lockyer (Transitus Form Teacher)
Mr Gordon MacCorquodale (Housemaster - Moore)
Mr Dougie MacGregor (Transitus Form Teacher)
Mrs Helen Mills (Competitions Coordinator)
Mrs Nicola Morrison (Assistant Housemistress - Bannerman/Learning Support)

Curriculum Information

Mathematics is rich and stimulating. It engages and fascinates learners of all ages, interests and abilities. Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity, and the ability to think in abstract ways. It uses a universal language of numbers and symbols, which allows us to communicate ideas in a concise, unambiguous and rigorous way.

Mathematics is important in everyday life, allowing us to make sense of the world around us and to manage our lives. Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.

All pupils will be presented for National 5 Mathematics at the end of S4. During S3 and S4 the department will prepare pupils thoroughly for the demands of this examination as well as introduce appropriate content from the Higher course.


Course Structure

The National 5 course comprises 3 internally assessed units;

  • Expressions and Formulae
  • Relationships
  • Applications

The end of course certification is based on performance in an externally assessed question paper requiring application of knowledge and skills acquired from across all three units of the course. Skills in using a calculator will be developed and a calculator will be permitted in part of the paper.


Course Aims

The Mathematics department aims to:

  • motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of mathematical and real-life situations.
  • develop confidence in the subject and a positive attitude towards further study in mathematics.
  • develop skills in manipulation of abstract terms in order to solve problems and to generalise.
  • allow learners to interpret, communicate and manage information in mathematical form; skills which are vital to scientific and technological research and development.
  • develop the learner’s skills in using mathematical language and to explore mathematical ideas.
  • develop skills relevant to learning, life and work in an engaging and enjoyable way.


This course will develop learners’ ability to:

  • understand and use mathematical concepts and relationships.
  • select and apply operational skills in algebra, geometry, trigonometry and statistics within mathematical contexts.
  • select and apply skills in numeracy.
  • use mathematical models.
  • use mathematical reasoning skills to interpret information, to select a strategy to solve a problem, and to communicate solutions.

The new Higher Mathematics course enables learners to select and apply mathematical techniques in a variety of mathematical situations.  Learners interpret, communicate and manage information in mathematical form.  The course extends some of the content covered in National 5 and introduces further skills in algebra, geometry and calculus.  An outline of our course structure is provided below.

We teach the course in three units.  Each unit is followed by a minimum competency assessment.  A pass in these assessments is an SQA requirement for full course certification whilst units 1 and 2 are followed by an extended assessment.  50% of the questions in our extended assessment are of A or B difficulty and provide a good indication of pupil progress.  The remaining 50% are at C difficulty level and should be accessible to all pupils.

We cover and assess Unit 1 by mid-October and have Unit 2 completed and assessed before Christmas.  There is an examination standard assessment in January covering Units 1 and 2.  Unit 3 is completed by Easter and is followed by an examination standard assessment covering material from the entire course.


Course Structure 

Our course is arranged as follows:

  • Straight line (App 1.1)
  • Vectors (EF 1.4)
  • Circles (App 1.2)
  • Sequences (App 1.3)

October holiday

Unit assessment plus an extended assessment

  • Logs & Exponentials (EF 1.1)
  • Functions (EF 1.3) 
  • Polynomials (RC 1.1)
  • Differentiation (RC 1.3)

Unit assessment plus an extended assessment

  • Trigonometry (EF 1.2)

Christmas holiday

January Prelim

  • Trig Equations (RC 1.2)
  • Integration (RC 1.4)
  • Optimisation and Area (App 1.4)

Unit assessment plus an extended assessment

Easter holiday

April Prelim


We run a supported study session every Thursday from 15:45 – 16:45 throughout the session.  All Higher pupils are welcome to attend.  Feedback from pupils and parents has always been very positive.

The Mathematics Department has a comprehensive range of resources available to your child through Fronter, the school’s virtual learning environment.  Resources include: practice unit assessments; topic specific practice; practice extended assessments; past prelims and practice exams.  There is also a forum on Fronter where pupils can post questions and have them answered by a member of the Maths department.  I would strongly encourage pupils to make use of Fronter throughout the session.

Scholar is an online resource provided by Heriot Watt University.  Your child has log-in details for Scholar and can access course notes, animations, interactivities, and online tests.

Our online revision tutorials have proved very popular with pupils and parents in the past and we fully intend to continue these in the run-up to the final examination in May.  We will contact parents nearer the time with more details of this. 

Advanced Higher is the SQA’s highest level of National Course. It is very demanding. Advanced Higher extends students’ knowledge and skills beyond Higher. Students will face new academic and personal challenges, requiring them to develop their knowledge and abilities, and to think and work independently.

Two Advanced Highers are offered: Advanced Higher Mathematics or Advanced Higher Applied Mathematics (Statistics). It is recommended you check university preferences before making your choice. It is often possible to take both courses.


Advanced Higher Mathematics

The Advanced Higher Mathematics Course extends learners’ mathematical knowledge in algebra, geometry and calculus. It includes matrix algebra, complex numbers and vectors and formalises the concept of mathematical proof. 

Advanced Higher Mathematics emphasises the need for candidates to undertake extended thinking and decision making, to solve problems and integrate mathematical knowledge. The course offers candidates, in an interesting and enjoyable manner, an enhanced awareness of the range and power of mathematics 

This course is suitable for anyone with an A Grade in Higher Mathematics and recommended for those considering a future in Engineering, Physics or Mathematical Sciences. The decision to take this course should not be taken lightly, or by anyone without a keen interest and high level of ability in the subject. It is a rigorous and intellectually demanding course which requires many hours of private study every week.


Advanced Higher Applied Mathematics (Statistics)

This is a specialist course in probability and statistics. This course is suitable for anyone with an A Grade in Higher Mathematics. Highly recommended for those considering further study or employment in the areas of mathematics, biological and social sciences, medicine, accounting, business and management and an ability to indulge in logical thought is essential. Graphic calculator skills are also beneficial. 

Topics covered includes conditional probability theory, bivariate analysis, sampling theory, estimation and confidence intervals, hypothesis testing, properties of functions, binomial, Poisson, normal and t-distributions, further differentiation and integration, control charts and matrices.


Advanced Higher Mathematics of Mechanics

This is a specialist course where learners’ will acquire and apply the skills necessary for exploring ideas in mechanics.  Through this course we study linear and parabolic motion, force, energy and periodic motion; we also consider some of the mathematical techniques from the Advanced Higher Mathematics course which are relevant to the study of mechanics.

Mechanics is widely used in developments in Physics, Technology and Engineering.  As such this course is recommended for those who are considering a future in one of these fields.

This course is suitable for anyone with an A Grade in Higher Mathematics and it is desirable that learners’ have some experience of Higher Physics; however this is not a requirement and no previous knowledge of mechanics required.


In deciding on which AH Mathematics course to take pupils should consider their future and which course is going to be the more useful to them. Please be discouraged from the thought that Maths is familiar, Statistics and Mechanics are new, and so the safe option is to stay with Mathematics. It may be helpful to get some advice from Sixth Year pupils who are currently taking each course. 

Mathematics - Online Profiles using Fronter (for Parents of Pupils in Transitus-S2)        

The Mathematics department uses Fronter to record and monitor progress. Your child has an individual login and can access their information from any computer using the “Fronter” link on the High School website.

We have divided the Mathematics syllabus into individual goals so that we are able to give you and your child feedback on specific learning outcomes which may require attention. This process allows pupils to see exactly what they should be working on in order to improve and helps them to feel more in control of their learning.

The goals system for Mathematics can be accessed through Fronter by choosing the appropriate year group from the Mathematics home page and by clicking the “goals” button on the left hand side menu bar. This will display the goals set for your child. We have included examples for the majority of goals so that you can see the type of question your child will be expected to answer. More goals will appear as we progress with the course and, following class assessment, your child’s teacher will highlight either “Excellent”, “Room for Improvement” or “Consolidation Essential” as required.

Where appropriate, a teacher may add comments to the conversation attached to a goal. Comments could include advice on how to tackle a particular goal or specific revision work to be attempted. Most goals have a reference to suggested consolidation material and additional resources are available from your child’s teacher as required. If your child has not performed as well as they would have liked for a specific goal, they can, following suitable revision, ask their teacher if they can be re-assessed on that goal. If they are successful, their teacher will update the profile accordingly. In this way pupils can work toward excellence in every goal and you can quickly and easily monitor their progress. In most cases goals from previous years will still be available to view and pupils should aim to upgrade these in the same way.

We would recommend that you check this profile every 3 to 4 weeks as it will be updated following each assessment. We hope that you will find this a useful system of feedback, which can be reviewed at any time during the session.