The broad aim of the mathematics department is to develop in pupils an appreciation and enjoyment of mathematics, and an awareness of its importance in society and in the development of technology.

In particular, the department seeks to:

contribute to pupils’ personal development and overall education;

enable pupils to develop, to the limit of their capability, the mathematical skills and understanding required for their present needs, both in and out of school, and for the future demands of adult life, employment, further study and training.

These aims will be achieved by means of the following objectives:

The development of Mathematical Knowledge and Understanding (learning the basic facts and techniques);

The development of Problem-Solving Skills (interpreting the information given, selecting strategies, processing the data and communicating the solution to the problem);

The development of desirable Social and Personal Qualities (working together and showing initiative);

The appropriate choice of Content and Approach (providing relevant and interesting work)

__(S1-S3 Xmas)__

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.

Pupils will continue to develop their mathematics in the following areas:

**Number, Money and Measure**

- Basic number processes
- Measure
- Patterns and relationships
- Expressions and equations

**Shape position and Movement**

- Properties of 2D shapes and 3D objects
- Angle, symmetry and transformation

**Information Handling**

- Data analysis
- Ideas of chance and uncertainty

The Mathematics is taught in units of work. Context is given to the units that are being taught so that pupils can see that they are not purely learning maths in order to pass examinations. Where opportunities arise, topics are connected to other subject areas in order that pupils can see the relevance of the topics being taught.

__Assessment__

Pupil’s assessment will take on different forms:

**Key questions**: given during the lesson to assess their understanding

**Activities**: grouped or individual tasks

**Formal Assessment:** takes the form of a Topic test covering a number of Units.

**Investigative task**: pupils will be given a problem to solve which will involve them using mathematics from different areas.

__Homework__

Pupils will be set regular homework. This includes

- Revising notes
- Finishing class exercises
- Formal home exercise
- Preparation for Unit Assessments
- Using the internet to access the “mymaths” website.

Literacy Numeracy Health and Well being

Literacy is also addressed as part of the Mathematics curriculum. The ability to interpret the information either verbally or in written form is a key life skill. Pupils will develop their confidence to make the transition from literacy to numerical comprehension and interpretation.

Where opportunities arise we will work closely with other departments to promote a healthy lifestyle.

What must I do to be successful?

Maths is a subject that builds on prior learning. Pupils need to keep practising their skills in order that they can progress with their mathematics. Pupils can ask their teachers for extra work if they require it.

Pupils must always come to class with a pencil, ruler, rubber and a calculator.

# Senior Phase (S4-S6)

**Entrance Requirements: **Pupils will have been advised from assessments and skill development in S1- S3 as to which course would be the most appropriate for their needs.

**Progression: **

This Course or its components may provide progression for the learner to:

- National 5 Mathematics Course
- Skills for Work Courses (SCQF levels 4 or 5)
- Employment and/or training

**Course structure**

**Mathematics: Expressions and Formulae (National 4)**

The general aim of this Unit is to develop skills linked to straightforward mathematical expressions and formulae. These include the manipulation of abstract terms, the simplification of expressions and the evaluation of formulae.

**Mathematics: Relationships (National 4)**

The general aim of this Unit is to develop skills linked to straightforward mathematical relationships. These include solving equations, understanding graphs and working with trigonometric ratios.

**Numeracy (National 4)**

The general aim of this Unit is to develop learners’ numerical and information handling skills to solve straightforward, real-life problems involving number, money, time and measurement. As learners tackle real-life problems, they will decide what numeracy skills to use and how to apply these skills to an appropriate level of accuracy. Learners will also interpret graphical data and use their knowledge and understanding of probability to identify solutions to straightforward real-life problems involving money, time and measurement. Learners will use their solutions to make and explain decisions.

**Mathematics Test (National 4)**

This is the Added Value Unit of the National 4 Mathematics Course. The general aim of this Unit is to enable the learner to provide evidence of added value for the National 4 Mathematics Course through the successful completion of a test which will allow the learner to demonstrate breadth and challenge.

Breadth and challenge will be demonstrated through the use and integration of mathematical ideas and strategies linked to straightforward mathematical expressions, formulae and relationships. This will include the application of algebraic, geometric, trigonometric, statistical and reasoning skills. Numerical skills underpin all aspects of the Course, and the ability to use these without the aid of a calculator will also be assessed.

**Conditions of award**

To achieve the National 4 Mathematics Course, learners must pass all of the required Units, including the Added Value Unit. The required Units are shown in the Course outline section.

National 4 Courses are not graded.

### National 5

**Entry Requirements**

learners would normally be expected to have attained the skills, knowledge and understanding required by:

♦ National 4 Mathematics Course or relevant component Units

**Progression **

This Course may provide progression to:

♦ Higher Mathematics or related

♦ further study, employment or training

**Course structure **

Learners will acquire and apply operational skills necessary for developing mathematical ideas through symbolic representation and diagrams. They will select and apply mathematical techniques and will develop their understanding of the interdependencies within mathematics. Learners will develop mathematical reasoning skills and will gain experience in making informed decisions.

**Mathematics: Expressions and Formulae (National 5) **

The general aim of this Unit is to develop skills linked to mathematical expressions and formulae. These include the manipulation of abstract terms, the simplification of expressions and the evaluation of formulae. The Outcomes cover aspects of number, algebra, geometry and reasoning.

**Mathematics: Relationships (National 5) **

The general aim of this Unit is to develop skills linked to mathematical relationships. These include solving and manipulating equations, working with graphs and carrying out calculations on the lengths and angles of shapes. The Outcomes cover aspects of algebra, geometry, trigonometry and reasoning.

**Mathematics: Applications (National 5) **

The general aim of this Unit is to develop skills linked to applications of mathematics. These include using trigonometry, geometry, number processes and statistics within real-life contexts. The Outcomes cover aspects of these skills and also skills in reasoning.

**Conditions of award **

To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment. The Course assessment is an external exam.

### HIGHER

**Recommended entry **

Learners would normally be expected to have attained the skills, knowledge and understanding required by the National 5 Mathematics Course.

**Progression **

This Course or its Units may provide progression to:

♦ Advanced Higher Mathematics College/University courses

♦ further study, employment and/or training

**Course structure **

This Course will develop, deepen and extend the mathematical skills necessary at this level and beyond.

Learners will acquire and apply operational skills necessary for exploring mathematical ideas through symbolic representation and diagrams. In addition, learners will develop mathematical reasoning skills and will gain experience in making informed decisions.

**Mathematics: Expressions and Functions (Higher) **

The general aim of this Unit is to develop knowledge and skills that involve the manipulation of expressions, the use of vectors and the study of mathematical functions. The Outcomes cover aspects of algebra, geometry and trigonometry, and also skills in mathematical reasoning and modelling.

**Mathematics: Relationships and Calculus (Higher) **

The general aim of this Unit is to develop knowledge and skills that involve solving equations and to introduce both differential calculus and integral calculus. The Outcomes cover aspects of algebra, trigonometry, calculus, and also skills in mathematical reasoning and modelling.

**Mathematics: Applications (Higher) **

The general aim of this Unit is to develop knowledge and skills that involve geometric applications, applications of sequences and applications of calculus. The Outcomes cover aspects of algebra, geometry, calculus, and also skills in mathematical reasoning and modelling.

**Conditions of award **

- To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment. The required Units are shown in the Course outline section. Course assessment will provide the basis for grading attainment in the Course award.

### ADVANCED HIGHER

**Recommended entry **

Entry to this Course is at the discretion of the centre. However, learners would normally be expected to have attained the skills, knowledge and understanding required by the following or equivalent qualifications and/or experience:

Higher Mathematics Course

**Core Skills **

Achievement of this Course gives automatic certification of the following:

Complete Core Skill: Using Graphical Information at SCQF level 6

Complete Core Skill: Using Number at SCQF level 6

**Progression **

This Course or its Units may provide progression to:

other qualifications in Mathematics or related areas

further study, employment and/or training

Further details are provided in the Rationale section. April 2015, version 1.1 3

**Equality and inclusion **

This Course Specification has been designed to ensure that there are no unnecessary barriers to learning or assessment. The individual needs of learners should be taken into account when planning learning experiences, selecting assessment methods or considering alternative evidence. For further information, please refer to the *Course Support Notes *and the *Course Assessment Specification. *April 2015, version 1.1 4

**Rationale **

All new and revised National Courses reflect Curriculum for Excellence values, purposes and principles. They offer flexibility, provide more time for learning, more focus on skills and applying learning, and scope for personalisation and choice.

In this Course, and its component Units, there will be an emphasis on skills development and the application of those skills. Assessment approaches will be proportionate, fit for purpose and will promote best practice, enabling learners to achieve the highest standards they can.

This Course provides learners with opportunities to continue to acquire and develop the attributes and capabilities of the four capacities, as well as skills for learning, skills for life and skills for work.

All Courses provide opportunities for learners to develop breadth, challenge and application, but the focus and balance of the assessment will be appropriate for the subject area.

**Relationship between the Course and Curriculum for Excellence values, purposes and principles **

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 to 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.

Because mathematics is rich and stimulating, it engages and fascinates learners of all ages, interests and abilities. Learning in 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 prove and communicate ideas in a concise, unambiguous and rigorous way.

Mathematics equips us with many of the skills required for life, learning and work. Understanding the part that mathematics plays in almost all aspects of life is crucial. This reinforces the need for mathematics to play an integral part in lifelong learning and be appreciated for the richness it brings.

This Course allows learners to acquire and develop the attributes and capabilities of the four capacities. For example, success in mathematical learning and activity leads to increased confidence as an individual, being able to think logically helps towards being a responsible citizen, and being able to understand, use and communicate mathematical ideas will assist in becoming an effective contributor.

**Purpose and aims of the Course **

Mathematics helps us to make sense of the world around us. It is the study of relationships, patterns, proofs and the properties of numbers. Mathematics takes a reasoned approach to thinking and is characterised by order and the use of carefully designed terms and processes. Mathematics can be used to model real-life situations and can equip us with the skills we need to interpret and analyse information, simplify April 2015, version 1.1 5

and solve problems, assess risk, and make informed decisions. Mathematics at Advanced Higher provides the foundation for many developments in the sciences and in technology as well as having its own intrinsic value.

This Course is designed to enthuse, motivate, and challenge learners by enabling them to:

select and apply complex mathematical techniques in a variety of mathematical situations, both practical and abstract

extend and apply skills in problem solving and logical thinking

extending skills in interpreting, analysing, communicating and managing information in mathematical form, while exploring more advanced techniques

clarify their thinking through the process of rigorous proof

The Course develops and expands a range of mathematical skills. It allows the learner to develop further skills in calculus and algebra. Areas such as number theory (which helps keep the internet secure), complex numbers (the uses of which are ubiquitous, ranging from the solution of equations to the description of electronic circuits) and matrices (used in game theory and economics) are introduced. The learner’s mathematical thinking will also benefit from examples of rigorous proof.

**Information about typical learners who might do the Course **

This Course is suitable for learners who are secure in their attainment of the Higher Mathematics Course or an equivalent qualification.

Learners will develop skills in selecting and applying complex mathematical techniques in a variety of situations requiring knowledge of mathematics. These skills will enable progression to further learning and to employment. The abstract content of the Course will greatly benefit students who wish to pursue a career in pure mathematics and the more practical aspects of the Course will benefit those intending to study any of the many courses which utilise mathematics.

On successful completion of this Course, learners could progress to a course in higher education such as a degree or Higher National Diploma. These could be in mathematics or in a mathematics-related area. There are many careers where mathematical skills are important, and this level would be useful in areas of science, engineering and technology, through the use of mathematical modelling. There are applications in computer technology, encryption security, equipment design, and in the design and analysis of experiments and tests. There is use throughout the financial services sector, such as in economics, accountancy and actuarial work. April 2015, version 1.1 6

**Course structure and conditions of award **

**Course structure **

This Course will develop, deepen and extend the mathematical skills necessary at this level and beyond.

Learners will acquire and apply operational skills necessary for exploring more complex mathematical ideas. In addition, learners will develop mathematical reasoning skills and will gain experience in logical thinking and methods of proof.

The Advanced Higher Mathematics Course has three Units, totalling 24 SCQF credit points, with an additional eight SCQF credit points to allow the use of an extended range of learning and teaching approaches, consolidation of learning, integration, and preparation for external assessment.

Units are statements of standards for assessment and not programmes of learning and teaching. They can be delivered in a number of ways.

**Mathematics: Methods in Algebra and Calculus (Advanced Higher) **

The general aim of the Unit is to develop advanced knowledge and skills in algebra and calculus that can be used in practical and abstract situations to manage information in mathematical form. The Outcomes cover partial fractions, standard procedures for both differential calculus and integral calculus, as well as methods for solving both first order and second order differential equations. The importance of logical thinking and proof is emphasised throughout.

**Mathematics: Applications of Algebra and Calculus (Advanced Higher) **

The general aim of the Unit is to develop advanced knowledge and skills that involve the application of algebra and calculus to real-life and mathematical situations, including applications of geometry. Learners will acquire skills in interpreting and analysing problem situations where these skills can be used. The Outcomes cover the binomial theorem, the algebra of complex numbers, properties of functions, rates of change and volumes of revolution. Aspects of sequences and series are introduced, including summations, proved by induction.

**Mathematics: Geometry, Proof and Systems of Equations (Advanced Higher) **

The general aim of the Unit is to develop advanced knowledge and skills that involve geometry, number and algebra, and to examine the close relationship between them. Learners will develop skills in logical thinking. The Outcomes cover matrices, vectors, solving systems of equations, the geometry of complex numbers, as well as processes of rigorous proof.

**Conditions of award **

To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment. The required Units are shown in the Course outline section. Course assessment will provide the basis for grading attainment in the Course award.

**What you offer in terms of vocational experiences and qualifications****What the progressions are from here****What skills are developed and what potential next steps are in terms of career/further education etc**

# Staff

#### Mr B. Campbell

#### Ms L. Philp

#### Miss J. Yorkshades

#### Mrs L. McKenzie

#### Mr I. Hardie

#### Mr G. Prior

#### Mr S. Gowans

#### Mr T. Fox

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