Mathematics

Aims of the Mathematics Department

  • To develop the 4 capacities of the Curriculum for Excellence. Successful learners, confident individuals, effective contributors and responsible citizens.
  • To contribute to the broad general education in S1-3 through delivery of appropriate Literacy and Health and Wellbeing experiences and outcomes which are the responsibility of all teachers.
  • To build on the prior knowledge gained in primary schools to extend each pupil’s mathematical information
  • To stimulate interest, enthusiasm, enjoyment and fun in the study of mathematics.
  • To improve the problem-solving skills of our pupils.
  • To identify and correct mathematical weakness.
  • To prepare our pupils to successfully meet the mathematical challenges of the wider curriculum and real life.
  • To prepare our pupils for the demands of national qualifications.


Staff

  • Mrs L Millar
  • Mr D Grieve
  • Mrs J Gurun
  • Mr M Freeman
  • Mrs M Johnston

 


Accommodation

The department consists of seven working classrooms with a designated computer suite in the department base. 

Each classroom is equipped with an Interactive Whiteboard used in conjunction with regular black/whiteboards.

There are designated display areas in each classroom as well as the Maths Department open area.

Mathematics Courses

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 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.

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 be involved in the following types of tasks:- 

  • Investigative or project-based.
  • Collaborative and independent.
  • Working with real life materials.
  • Problem solving and critical thinking.
  • Explaining thinking and presenting strategies and solutions.
  • Questioning and discussion.
  • Making links across the curriculum to encourage transferable skills.
  • Using technology where appropriate to extend experience and confidence.

In S1-3 the Mathematics Department delivers courses which contribute to the broad general education in line with the principals of the Curriculum for Excellence.

In S4-6 the Mathematics Department deliver a suite of courses designed to prepare pupils for presentation at National 3 Lifeskills Mathematics, National 4/5 Lifeskills Mathematics, National 4, National 5, Higher and Advanced Higher Mathematics as appropriate to their proven ability.

Pupil Profiles.
Each pupil will build up a portfolio of work as they progress through the department. This will consist of unit assessments, course work tasks, self evaluations and pupil and teachers targets.

 

Lifeskills Mathematics          

National 3

Background

Mathematics is rich and stimulating. It engages and fascinates learners of all ages, interests and abilities. This course builds on the experiences and outcomes of mathematics and numeracy delivered through the Broad General Education to equip pupils with the mathematical skills required for life, learning and work.

They will develop important skills, attitudes and attributes, including:

  • logical thinking
  • problem solving skills
  • the ability to think in general terms
  • appropriate use of technology
  • communication

They will also have the opportunity to acquire and develop the attributes and capabilities of the four capacities, including:

  • perseverance and resilience.
  • confidence and enterprise through success in mathematical activities.
  • becoming  a responsible citizen by using the results of calculations to make informed decisions. 
  • contributing effectively by communicating mathematic ideas in an appropriate way.

This course enables learners to acquire mathematical and numerical skills and apply them in a variety of real-life situations. In addition, learners will develop thinking skills and will gain experience in making informed decisions.

Aims

The aims of the course are to enable pupils to:-

  • interpret real-life situations involving mathematics.
  • investigate the use of basic mathematical ideas and number processes in real-life contexts.
  • select and apply basic mathematical and numeracy skills in real-life contexts.
  • interpret and use the results of calculations, measurements and data to make informed decisions.
  • communicate mathematical information in an appropriate way.

Processes

Pupils will be involved in the following types of tasks:-

  • Investigative or project-based.
  • Collaborative, individual and group.
  • Working with real-life materials such as invoices, bills and adverts.
  • Practical activities.
  • Making links across the curriculum to encourage transferable skills.
  • E-learning where appropriate to extend experience and confidence.

Clientele

This course is for pupils who want to develop their mathematical and numerical skills. Pupils will have experienced learning across the Mathematics Experiences and Outcomes at level 2 and 3 in S3. A strong performance in the National 3 Lifeskills course should provide a good background for employment and/or training and may allow pupils to progress to a National 4 qualification in Mathematics in S5.

Outcomes 

Pupils will be able to:- 

  • Manage money in basic real-life contexts.
  • Manage data in real-life contexts.
  • Use shape and space in basic real-life contexts.
  • Use measures in basic real-life contexts.
  • Use numerical skills to solve simple real-life problems involving money/time/measurement.
  • Interpret graphical data and situations involving probability to solve simple real-life problems.

Units of Work

Manage Money and Data

  • Income and expenditure.
  • Budgeting and saving.
  • Best value.
  • Organise, display and interpret data.

Shape, Space and Measure

  • Perimeter and area of regular 2D shapes and volume of a cuboid.
  • Measurement: Length, weight, volume, temperature and time.
  • Give and follow directions and work with scale.
  • Patterns.

Numeracy

  • Numerical notation and units.
  • Select and carry out calculations.
  • Record measurements.
  • Interpret calculations and make decisions based on results.
  • Interpret data and make decisions based on interpretation.
  • Make decisions based on probability.

Assessment

These units are internally assessed against the requirements shown in unit specifications.

They will be assessed as pass/fail within centres.

SQA will provide rigorous external quality assurance, including external verification, to ensure assessment judgments are consistent and meet national standards.

 

National 4 /National 5 Lifeskills

The National 4 / National 5 Lifeskills Mathematics Course enables learners to apply mathematical ideas and strategies to managing finance, statistics, geometry and measurement in real-life contexts.

The mathematical skills within this Course are underpinned by numeracy and are designed to develop learners’ skills in mathematical reasoning relevant to learning, life and work. This is likely to run as a Bi-level class with pupils being directed towards the correct level according to their progress in the reasoning skills developed.

The Courses aim to:

  • motivate and challenge learners by enabling them to select and apply mathematical skills to tackle a range of real-life problems or situations
  • develop the ability to interpret/analyse real-life problems or situations involving often complex mathematics
  • develop the ability to use a range of mathematical skills to analyse, interpret and present a range of information
  • develop confidence in the subject and a positive attitude towards the use of mathematics in real-life situations
  • develop the ability to select, apply, combine and adapt mathematical operational skills to new and unfamiliar situations in life and work to an appropriate degree of accuracy
  • use mathematical reasoning skills to generalise, assess risk, build arguments,  draw logical conclusions and explain decisions
  • communicate mathematical information in an appropriate way
  • develop the ability to think creatively and in more abstract ways

Information about typical learners who might do the Course

National 4 Lifeskills would be suitable for learners who have attained the National 3 Lifeskills Mathematics Course or who have passed National 4 Maths and are looking for an alternative Mathematics Course to help develop reasoning skills. National 5 Lifeskills would be suitable for learners who have attained National 4 Maths or National 4 Lifeskills. It would be particularly suitable for learners who can respond to a level of challenge, and who can apply what they have learned in new and unfamiliar situations.

Unit Assessments

Lifeskills Mathematics: Geometry and Measures (National 4 & 5)

Learners will be required to provide evidence of using reasoning and geometric skills linked to real-life contexts by drawing on the following:

  • Scale Drawings and bearings.
  • Tolerance
  • Area and Volume
  • Precedence tables
  • Time management
  • Gradient
  • Pythagoras

The general aim of this Unit is to develop skills that focus on the use of mathematical ideas and valid strategies that can be applied to geometry and measurement in real-life contexts which may be new to the learner. This includes skills in analysing and using geometry and measures to determine and justify solutions to real-life problems.

Lifeskills Mathematics :Managing Finance and Statistics (National 4 & 5)

Learners will be required to provide evidence of using reasoning and financial skills / statistical linked to real-life contexts by drawing on the following:

  • Financial Maths – budgeting, income, best deal, savings, borrowing, currency
  • Statistics - represent and interpret data

The general aim of this Unit is to develop skills that focus on the use of mathematical ideas and strategies that can be applied to managing finance and statistics in real-life contexts. This includes using skills in budgeting as well as skills in organising and presenting data, to explain solutions and/or draw conclusions Learners will use their solutions to make and justify decisions.

Numeracy (National 4 & National 5)

  • Numerical notation and units.
  • Select and carry out calculations.
  • Measurement.
  • Interpret graphical information and probability.

The general aim of this Unit is to develop learners’ numerical and information handling skills to solve 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.

At this level, real-life problems may have some complex features and be set in contexts which are likely to be unfamiliar to the learner. Learners will also interpret graphical data and use their knowledge and understanding of probability to identify solutions to real-life problems involving money, time and measurement. Learners will use their solutions to make and explain decisions.

All units are internally assessed against the requirements shown in unit specifications.

They will be assessed as pass/fail within centres.

Course Assessment

The Course assessment for National 5 Lifeskills will consist of two question papers.

            Paper 1 – Non calculator – 35 marks- 50 minutes.

            Paper 2 – Calculator – 55 marks – 1 hour 40 minutes.

These question papers will set and marked by the SQA, and conducted in school under exam conditions. The course award will be graded A – D

The Course assessment for National 4 Lifeskills will consist of two question papers.

            Paper 1 – Non calculator – 35 marks- 50 minutes.

            Paper 2 – Calculator – 55 marks – 1 hour 40 minutes.

This test will be set and marked within the school and will be awarded as pass/fail. 

SQA will provide rigorous external quality assurance, including external verification, to ensure assessment judgments are consistent and meet national standards.

Conditions of award

To gain the award of the Course, the learner MUST pass all of the Units as well as the Course assessment

 

National 4 Mathematics

The National 4 Mathematics Course enables learners to select and apply straightforward mathematical skills in a variety of mathematical and real-life situations. Learners interpret, communicate and manage information in mathematical form. Learners will use their solutions to make and explain decisions.

The course aims to:

  • 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 

Information about typical learners who might do the Course

The Course would be suitable for those who have made strong progress in the National 3 Lifeskills Mathematics Course, or have equivalent qualification or experience.

Unit Assessments

Mathematics: Expressions and Formulae (National 4)

Formulae for circumference, area and volume

  • Algebraic expressions.
  • Represent, calculate  and analyse statistical data.
  • Calculate probability

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)

  • Equations.
  • Geometry in 2D shapes.
  • Trigonometry in right-angled triangles.
  • Scattergraphs and line of best fit.

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)

  • Numerical notation and units.
  • Select and carry out calculations.
  • Measurement.
  • Interpret graphical information and probability.

All units cover the skills of reasoning

 

National 5 Mathematics

The Course 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
  • 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

Information about typical learners who might do the Course

This would be a suitable Course for learners who have made strong progress in the National 4 Mathematics Course, who can respond to challenging situations and can apply what they have learned in new and unfamiliar situations.

Unit Assessments

Mathematics: Expressions and Formulae (National 5)

  • Surds and indices.
  • Geometric formulae. - Gradient, arc length, sector area and volume.
  • Algebraic expressions and fractions.

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.                     

Mathematics: Relationships (National 5)

  • Linear equations.
  • Quadratic graphs and equations.
  • Geometry: Pythagoras’ Theorem, similarity, shapes properties.
  • Trigonometry graphs and identities

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.

Mathematics: Applications (National 5)

  • Trigonometry in non-right-angled triangles.
  • Vectors.
  • Fractions and percentages.
  • Analysing data: Standard deviation, Interquartile Range and Line of best fit.

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.

All Units cover skills in reasoning.

All units are internally assessed against the requirements shown in unit specifications.

They will be assessed as pass/fail within centres.

Course Assessment

The Course assessment will consist of two question papers.

            Paper 1 – Non calculator – 40 marks- 1 hour.

            Paper 2 – Calculator – 50 marks – 1 hour 30 minutes.

These question papers will set and marked by the SQA, and conducted in school under exam conditions. The course award will be graded A - D

Conditions of award

To gain the award of the Course, the learner MUST pass all of the Units as well as the Course assessment.

 

Higher Mathematics

The Course aims to:

  •  motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of mathematical situations
  •  develop confidence in the subject and a positive attitude towards further study in mathematics and the use of mathematics in employment
  •  deliver in-depth study of mathematical concepts and the ways in which mathematics describes our world
  •  allow learners to interpret, communicate and manage information in mathematical form; skills which are vital to scientific and technological research and development
  •  deepen the learner’s skills in using mathematical language and exploring advanced mathematical ideas

Information about typical learners who might do the Course

This Course is suitable for learners who are secure in their attainment of the National 5 Mathematics Course. We would recommend it to pupils who have gained at least a grade A or grade B.

Learners will develop skills in selecting and applying mathematical techniques in a variety of mathematical situations. These skills will enable progression to further learning and to employment. Learners will experience in-depth study of the ways in which mathematics describes our world, and become skilled in interpreting, analysing, communicating and managing information in mathematical form.

Unit Assessments

Mathematics: Expressions and Functions (Higher)

  • Algebraic skills- Factorise polynomials, simplify using laws of logarithmic and exponents,
  •  identify and sketch functions.
  • Trigonometric skills —Addition formulae, the wave function, identify and sketch functions.
  • Geometric skills — Differentiating an algebraic function including basic trig functions.

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)

  • Algebraic skills - Polynomials, quadratic, logarithmic and exponential equations
  • Trigonometric skills - Trigonometric equations involving trigonometric formulae or identities
  • Calculus skills - Differentiating algebraic functions and basic trig functions
  • Calculus skills - Vectors

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)

  • Algebraic skills- Equation of a straight line. recurrence relations and equation of a circle.
  • Calculus skills —Area between curves and optimisation problems

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.

All units are internally assessed against the requirements shown in unit specifications.

They will be assessed as pass/fail within centres.

Course Assessment

The Course assessment for Mathematics will consist of two question papers.

                Paper 1 – Non calculator – 60 marks- 1 hour 10 minutes.

                Paper 2 – Calculator       – 70 marks – 1 hour 30 minutes.

These question papers will set and marked by the SQA, and conducted in school under exam conditions. The course award will be graded A – D

Conditions of award

To gain the award of the Course, the learner must pass all of the Units as well as the Course assessment.

Advanced Higher Mathematics

As with all mathematics Courses, Advanced Higher Mathematics aims to build upon and extend candidates' mathematical skills, knowledge and understanding in a way that recognises problem solving as an essential skill and enables them to integrate their knowledge of different aspects of the subject.The syllabus is designed to build upon and extend candidates' learning in the areas of algebra, geometry and calculus. The Advanced Higher 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. The Advanced Higher Course is designed to articulate with the knowledge and skills developed in Higher Mathematics.

Information about typical learners who might do the Course

This Course is suitable for learners who have passed Higher Mathematics. We would recommend it to pupils who have gained at least a grade A or grade B.

Unit Assessments

Mathematics 1(Advanced Higher maths)

  • Use algebraic skills.
  • Use the rules of differentiation on the elementary functions xn (n ∈Q), sin x, cos x, ex and ln x and their composites.
  • Integrate using standard results and the substitution method.
  • Use properties of functions.
  • Use matrix methods to solve systems of linear equations.

Mathematics 2(Advanced Higher maths)

  • Use further differentiation techniques.
  • Use further integration techniques.
  • Understand and use complex numbers.
  • Understand and use sequences and series.
  • Use standard methods to prove results in elementary number theory.

Mathematics 3(Advanced Higher maths)

  • Use vectors in three dimensions.
  • Use matrix algebra.
  • Understand and use further aspects of sequences and series.
  • Solve further ordinary differential equations.
  • Use further number theory and direct methods of proof.