Mathematics

Purpose

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. 

The course aims to 

• motivate and challenge learners by enabling them to select and apply straightforward mathematical skills in a variety of mathematical and real-life situations 

• develop confidence in the subject and a positive attitude towards further study in mathematics 

• enable the use of numerical data and abstract terms and develop the idea of generalisation 

• 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 straightforward mathematical ideas 

• develop skills relevant to learning, life and work in an engaging and enjoyable way

Recommended Entry

Pupils should have covered all CFE Outcomes & Experiences at Level 3 and at least some at Level 4

Course Details

This course consists of 3 units of work and a number of assessments which are to be completed internally.

Mathematics: Expressions and Formulae  

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. The Outcomes cover aspects of algebra, geometry, statistics and reasoning. 

Mathematics: Relationships 

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. The Outcomes cover aspects of algebra, geometry, trigonometry, statistics and reasoning. 

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 

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.

Numeracy (National 5)

All learners taking National 4 Maths will be given the opportunity to achieve the Level 5 Numeracy qualification towards the end of S4.

Progression

Students may progress to National 5 but for some pupils this will be a large step up from National 4 so should only be undertaken after discussion with their Maths teacher 

National 5 Mathematics in a Nutshell

Purpose

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. 

The course aims to 

• motivate and challenge learners by enabling them to select and apply straightforward mathematical skills in a variety of mathematical and real-life situations 

• develop confidence in the subject and a positive attitude towards further study in mathematics 

• enable the use of numerical data and abstract terms and develop the idea of generalisation 

• 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 straightforward mathematical ideas 

• develop skills relevant to learning, life and work in an engaging and enjoyable way 

• 
  

Recommended Entry

While entry is at the discretion of the school, students should have overtaken all CFE experiences and Outcomes at Level 4 or have achieved a pass at National 4 Maths.

Course Details

The course consists of 3 units of work and a final exam. Each unit has an internal assessment which is non-mandatory and can be completed on a stand-alone basis. Completion of the 3 internal assessments also allows pupils to achieve National 5 Numeracy.

Mathematics: Expressions and Formulae 

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 

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 

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. This unit contains maths in a social context, logic diagrams, applying formulae and a statistical assignment.

Progression

Students may progress to Higher Mathematics.  However, this will require a high degree of independent study as a timetabled class may not be available.  The course may also serve as a general or specific entry requirement to HNC or HND courses or as a general entry requirement for other higher education courses which do not have a specific mathematical content.

S5/6 only option

Higher Mathematics in a Nutshell

Purpose

The aim of this course is to build upon and extend students’ mathematical learning in the areas of algebra, geometry and trigonometry and to introduce students to elementary calculus. 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.

Recommended Entry

While entry is at the discretion of the school, students would normally be expected to have attained a pass at National 5 Maths at grade A or B.

Course Details 

The Higher Mathematics Course has three Units, totalling 18 SCQF credit points, with an additional six 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. The course will draw on aspects from all 3 units delivered in parallel.

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.

Progression

Students may progress to Advanced Higher Mathematics or exit to higher or further education, using the qualification as either a general or specific entry requirement for mathematics, engineering, or science HNC/D or degree courses.

Purpose

The aim of this course is to build upon and extend students’ mathematical learning in the areas of algebra, geometry, trigonometry and calculus.  Mathematics 1 (AH), Mathematics 2 (AH) and Mathematics 3 (AH) are progressive units.

Recommended Entry

Students would normally be expected to have attained an award at Higher, Grade A or B.

Course Details

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.

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.

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 to 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, and rates of change. Aspects of sequences and series are introduced, including summations, proved by induction.

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.

Progression

Students would be well prepared to follow a degree course in Mathematics at University or to do a course such as engineering, which has a substantial mathematical content.