NATIONAL QUALIFICATIONS CURRICULUM
SUPPORT
Course:
Mathematics
Advice and Guidance for Staff
Level: Higher
March 2016
This advice and guidance has been produced to support the profession with
the delivery of courses which are either new or which have aspects of
significant change within the new national qualifications framework.
The advice and guidance provides suggestions on approaches to learning and
teaching. Staff are encouraged to draw on the materials for their own part of
their continuing professional development in introducing new national
qualifications in ways that match the needs of learners.
Staff should also refer to the course and unit specifications and support notes
which have been issued by the Scottish Qualifications Authority.
http://www.sqa.org.uk/sqa/47910.html
Acknowledgement
© Crown copyright 2016. You may re-use this information (excluding logos) free of
charge in any format or medium, under the terms of the Open Government Licence.
To view this licence, visit http://www.nationalarchives.gov.uk/doc/open-governmentlicence/ or e-mail: psi@nationalarchives.gsi.gov.uk.
Where we have identified any third party copyright information you will need to obtain
permission from the copyright holders concerned.
Any enquiries regarding this document/publication should be sent to us at
enquiries@educationscotland.gov.uk.
This document is also available from our website at www.educationscotland.gov.uk.
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MATHEMATICS (HIGHER)
© Crown copyright 2016
ADVICE AND GUIDANCE FOR PRACTITIONERS
Advice and guidance for practitioners
Mathematics is important in everyday life, allowing us to make sense of the
world around us and 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
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 learners’ skills in using mathematical language and exploring
advanced mathematical ideas.
MATHEMATICS (HIGHER)
© Crown copyright 2016
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ADVICE AND GUIDANCE FOR PRACTITIONERS
Area of mathematics
Applying geometric skills to
vectors
Learning and teaching approaches
Learners will already have been introduced to twoand three-dimensional vectors at National 5. They
should be familiar with adding and subtracting, and
using directed line segments and components. They
should also be able to calculate the magnitude of a
vector. Revise above and introduce position vectors.
Applying is the ability to use existing information to
solve a problem in a different context, and to plan,
organise and complete a task.
Learners could be encouraged to think about how
they are going to tackle problems, decide which skills
to use and then carry out the calculations in order to
complete the task. To determine a learner’s level of
understanding, learners could be encouraged to
show and explain their thinking. Staff are encouraged
to promote learning and understanding through
interactive activities using a variety of real-life
contexts.
It is essential that learners are provided with
opportunities to link their learning across different
contexts.
Exemplification

Learners’ skills should be developed so that they can:

determining the resultant of vector pathways in
three dimensions

work with collinearity

determining the co-ordinates of an internal
division point of a line

use the scalar product

use unit vectors i, j, k as a basis.

TES also provides a range of activities for two- and
three-dimensional vectors.

National Centre for Excellence in the Teaching of
Mathematics (NCETM):
https://www.ncetm.org.uk/resources/47049 Requires login

It’s all in the detail: a detailed account of the use of
vectors in computer-aided design:
https://plus.maths.org/content/its-all-detail
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MATHEMATICS (HIGHER)
© Crown copyright 2016
ADVICE AND GUIDANCE FOR PRACTITIONERS
Using recurrence relations to
increase understanding of
mathematical modelling
Recurrence relations are a great topic for showing
the importance of mathematics in real life, for
example modelling the amount of CO2 in the
atmosphere, population increases and decreases, or
concentrations of drugs in a patient. This can link in
with current events, for example decreasing bee
populations or climate change.
Analysing and evaluating is the ability to identify and
weigh up the features of a situation or issue and use
your judgement of them in coming to a conclusion. It
includes reviewing and considering any potential
solutions.
Staff are encouraged to promote learning and
understanding through interactive activities using a
variety of real-life contexts.


Learners’ skills should be developed so that they can:

determine a recurrence relation from given
information

use a recurrence relation to calculate a required
term

find and interpret the limit of a sequence, where it
exists.
TES also identifies some practice in this area of
mathematics:
https://www.tes.com/teaching-resource/higher-mathsactive-lesson-ideas-6171425

Further reading can be found here:
Recurrent chaos:
http://wild.maths.org/recurrent-chaos
How to add up quickly: a detailed account of the use
of recurrence relations:
https://plus.maths.org/content/how-add-quickly
MATHEMATICS (HIGHER)
© Crown copyright 2016
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ADVICE AND GUIDANCE FOR PRACTITIONERS
Using logarithmic and
exponential functions
Opportunities for staff and learners to explore,
research and investigate data and its representation.
Higher-order thinking can be developed through
high-level questioning.
Learning and teaching of logarithms and
exponentials provides opportunities for
interdisciplinary contexts to be used. There are many
applications in science, for instance decibel scale for
sound, Richter scale for earthquake magnitude,
acidity and pH.

Learners’ skills should be developed so that they can:

identify and sketch related functions

manipulate algebraic expressions using the laws
of logarithms and exponentials
 solve logarithmic and exponential equations.

TES also identifies some practice in this area of
mathematics:
https://www.tes.com/teaching-resource/higher-mathsactive-lesson-ideas-6171425

Further video exemplification can be found here:
https://cdn-media.twigworld.com/lp/maths/TWG00853_Lesson_Plan.pdf
https://cdn-media.twigworld.com/lp/maths/TWG00933_Lesson_Plan.pdf

Further reading can be found here:
Have we caught your interest? A detailed account of
the use of logarithms:
https://plus.maths.org/content/have-we-caught-yourinterest
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MATHEMATICS (HIGHER)
© Crown copyright 2016
ADVICE AND GUIDANCE FOR PRACTITIONERS
Integrating polynomial and
simple trigonometric
functions
Integration is often introduced as the reverse
 Learners’ skills should be developed so that they can:
process to differentiation, and has wide applications,
 integrate an algebraic function which is, or can
for example in finding areas under curves and
be, simplified to an expression of powers of x
volumes of solids.
 integrate functions of the form
Anti-differentiation is one way to introduce

f(x) = (x + q)n, n ≠ –1
integration. Learners should understand that each
process is the inverse of the other, and that this will

f(x) = (px + q)n, n ≠ –1
help them to check their answers for accuracy.

f(x) = pcosx and f(x) = psinx
Learners should be aware of the importance of the

f(x) = pcos(qx + r) and f(x) = psin(qx + r)
constant of integration when limits are not given or
 solve differential equations using integration
cannot be found. They should also appreciate that a
 use integration to calculate definite integrals:
constant can be taken outside the integral, and that
in some cases this may ease the process of

calculate definite integrals of polynomial
integration.
functions with integer limits
Where appropriate or possible learners should

calculate definite integrals of functions
experience practical applications and contexts, which
with limits which are radians, surds or
may also link to other curricular areas.
fractions.

Further video exemplification can be found here:
https://www.twigonglow.com/film/calculus-newton1756/ - Glow login required
MATHEMATICS (HIGHER)
© Crown copyright 2016
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USEFUL WEBSITES
Useful websites
BBC Skillswise
http://www.bbc.co.uk/skillswise
Khan Academy
www.khanacademy.org/
Twig
www.twigonglow.com
Plus Maths
www.plus.maths.org
TES Resources
www.tes.com
Wild Maths
www.wild.maths.org
National Centre of Excellence in Mathematics
www.ncetm.org.uk
HSN
www.hsn.uk.net
Scholar
www.scholar.hw.ac.uk
SQA
www.sqa.org.uk/sqa/47910.html
DESMOS
https://blogs.glowscotland.org.uk/glowblogs/desmosresources/
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MATHEMATICS (HIGHER)
© Crown copyright 2016