NATIONAL QUALIFICATIONS CURRICULUM SUPPORT
Mathematics
Advice and Guidance for
Staff
[NATIONAL 4]
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 (NQ) 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/34714.html
Acknowledgement
© Crown copyright 2014. 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-government-licence/ 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 (NAT 4, MATHEMATICS)
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Contents
Introduction
4
Resources
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INTRODUCTION
Introduction
Applying statistical skills to representing data and interpreting situations
involving probability to solve real-life problems
Mathematics is important in everyday life, allowing us to make sense of the
world around us and to manage our lives.
This advice and guidance suggests an approach to the learning and teaching of
probability, scattergraphs and line of best fit within the context of Mathematics
National 4.
The learning and teaching approaches incorpora te opportunities for
collaborative and independent learning using a range of real -life situations. This
will enable learners to draw conclusions, assess risk and gain the ability to
respond to mathematical situations that could arise in everyday life. Learners
will be able to use mathematical reasoning skills to make and explain their
decisions within a given relevant context. The knowledge, skills and
understanding within third level experiences and outcomes, as detailed below,
provide a firm foundation for further learning within SCQF level 4.
I can work collaboratively making appropriate use of technology to
source information presented in a range of ways, interpret what it
conveys and discuss whether I believe the information to be robust,
vague or misleading. MNU 3-20a
I can display data in a clear way using a suitable scale, by choosing
appropriately from an extended range of tables, charts, diagrams and
graphs, making effective use of technology. MTH 3-21a
I can find the probability of a simple eve nt happening and explain why
the consequences of the event, as well as its probability, should be
considered when making choices. MNU 3-22a
New national courses have been designed to draw on and build on Curriculum
for Excellence experiences and outcomes as appropriate. SCQF level 4 and
fourth level experiences and outcomes are broadly equivalent in terms of level
of demand, although qualifications at SCQF level 4 will be more specific to
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INTRODUCTION
allow for more specialist study of subjects. The following fourth le vel
experiences and outcomes may have been experienced by learners:
I can evaluate and interpret raw and graphical data using a variety of
methods, comment on relationships I observe within the data and
communicate my findings to others. MNU 4-20a
I can select appropriately, from a wide range of tables, charts, diagrams
and graphs when displaying discrete, continuous or grouped data, clearly
communicating the significant features of the data . MNU 4-21a
By applying my understanding of probability, I can d etermine how many
times I expect an event to occur, and use this information to make
predictions, risk assessment, informed choices and decisions . MNU 422a
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INTRODUCTION
Area of
mathematics
Constructing a
scattergraph:
 Given a set of
data
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Learning and teaching approaches
Exemplification
 Learners should be given the opportunity to
collect their own data for constructing
scattergraphs. Contexts should reflect the age and
stage of the learner, for example using charity
fundraising data to plot money raised against the
distance participants ran or swam in a sponsored
event. Alternatively, links with social subjects and
travel and tourism can be made by considering, for
example, the price changes of a convenience item
along an environmental gradient near a major
tourist attraction. The hypothesis tested is that
prices should decrease with distance from the key
area surrounding the major tourist attraction.
Straightforward examples can be adapted to be age
specific.
 Learners should be able to use graphs to answer
related questions. Staff should reflect on how they
will incorporate some ‘thinking questions’ into
their teaching. Sequences of questions can
gradually increase the level of challenge, for
example ‘What is wrong with the statement…?’ ,
‘How would you describe…?’, ‘What is the same
and what is different about these…?’
 Peer- and self-assessment are encouraged.
Straightforward examples of contexts for
constructing a scattergraph can be found using the
following links:
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http://www.tes.co.uk/teaching-resource/Line-ofBest-Fit-6017667/
http://www.cimt.plymouth.ac.uk/projects/mepres/bo
ok7/bk7i3/bk7_3i1.htm
INTRODUCTION
Drawing and
applying a line of
best fit:
 The line should
have roughly
the same
number of data
points on either
side.
 Use the line of
best fit to
estimate one
variable given
the other.
Making and
explaining
decisions based
on interpretation
of data from
straightforward
graphical forms:
 Make decisions
based on
observations of
patterns and
trends in data.
 Staff are encouraged to use a wide range of
learning and teaching approaches to enhance the
understanding of learners. Real-life contexts, for
example health statistics against environmental
(http://www.metoffice.gov.uk/climate/uk/stationda
ta/), social or economic factors, can enhance
learning.
 Staff are encouraged to promote learning and
understanding through interactive activities using
a variety of real-life contexts. Using data that is fit
for purpose will support learners’ understanding of
this graphical form. For example, discuss graphs
of data related to global warming, such as historic
mean global temperature and CO 2 level in the
atmosphere.
 Opportunities exist for staff and learners to
explore, research and investigate data and its
representation. Higher-order thinking can be
developed through high-level questioning and
Staff may use activities that link to other areas of
learning within mathematics. For example,
investigating the connection between finger and
arm proportions will lead to learners discovering
the golden ratio and there are possible extensions to
its real-life applications such the design of the
Parthenon, the ‘perfect’ body and the works of da
Vinci. Learners should be encouraged to understand
the importance of their findings.
http://www.goldennumber.net/body.htm is a
website that gives an opportunity for further
research by individuals or for extension activities.
See the ‘Finger and arm proportions’ PowerPoint.
Maths case studies will promote deeper
understanding and reasoning skills. Examples of
contexts for learning can be found at
http://www.bowlandmaths.org.uk/index.html.
Staff may use a matching activity to promote
understanding and interpretation of correlation.
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INTRODUCTION
 Make decisions
based on
calculations
involving data.
 Make decisions
based on
reading scales
in
straightforward
graphical
forms.
 Offer reasons
for decisions
made based on
interpretation
of data.
Making and
explaining
decisions based
on probability
 Recognise
patterns and
trends and use
these to state
the probability
of an event
happening.
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creating open-ended questions. Who may want to
know about the correlation between these
quantities, and why? Discuss high positive or
negative correlation, indicating the connection
between the variables. Discuss correlation,
interpolation and extrapolation, and the real
possibilities of errors in interpreting graphs.
Learners should be encouraged to use correct
mathematical terminology within their response.
 Staff have the opportunity to adopt a range of
resources, particularly ICT and other media.
 A range of activities using a variety of resources
will enable learners to acquire an understanding of
probability and risk. Resources should include
activities that are interactive and provide
opportunities for collaborative learning, for
example working collaboratively to arrange in
order on a probability scale the possibilities of an
event occurring, as detailed on probability card s.
 Use activities promoting an awareness of, and
creating opportunities for discussion on, factors
that affect the likelihood of an event occurring.
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See the ‘Misleading graphs leading to misleading
probabilities’ and ‘Stock market game’ Word
documents.
Learners could obtain a prediction for weather for
the coming week and compare it with actual
INTRODUCTION
 Make
predictions and
use these
predictions to
make
decisions.
 Promote discussion through use of scenarios to
enable learners to deepen their understanding of
how to make and explain decisions based on
probabilities. Staff can encourage learners to
understand risk within the financial sector by
linking activities to aspects of financial education ,
eg examining electricity and gas tariffs.
Alternatively, staff may encourage learners to
explore aspects of health and wellbeing, eg the
probability of sustaining attendance at a local gym
or examining health issues linked to smoking.
 Enhance learners’ understanding through
experiments and contingency tables. Using real life contexts can illustrate how making predictions
is based on probability data, eg weather
predictions based on the previous year’s weather.
 It is important to promote an awareness of how
data, information and statistics are portrayed in
the media and use this to make informed decisions
and justify those decisions. Learners could use
probability as a measure of chance and
uncertainty. This could include reference to the
likelihood of events happening in familiar
contexts, such as selecting a holiday destination
from seasonal tables of average rainfall, sunshine
and temperatures.
weather. They could discuss how accurate such
forecasts are likely to be.
http://theweatheroutlook.com/forecast/uk/Glasgow.
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RESOURCES
Resources
http://www.tes.co.uk/teaching-resource/Provoking-discussion-about-correlation6087038/
Staff notes plus an interactive Excel activity using the ‘hide and reveal'
technique to explore the interpretation of scattergraphs with respect to
correlation, including an option for line of best fit, and to encourage learners to
write explanations of the relationships shown. It encourages learners to develop
the quality of their written explanations.
http://www.tes.co.uk/teaching-resource/Estimating-from-Scatter-GraphsTreasure-Hunt-6124066/
Treasure hunt activity on estimating from scattergraphs using the line of best
fit.
http://www.bbc.co.uk/schools/ks3bitesize/maths/handling_data/representing_dat
a/revise9.shtml
Straightforward revision on drawing scattergraphs, line of best fit, correlation
and interpolation. For learners to use and test themselves.
http://www.scotlandscensus.gov.uk
Census from 27 March 2011.
http://www.socialbakers.com/facebook-statistics/
Daily updated Facebook statistics from over 200 different countries. Clicking
on a country gives Facebook statistics together with demography and a graph in
time.
http://data.gov.uk/dataset/annual_abstract_of_statistics
The national abstract of statistics published annually .
http://www.nationwide.co.uk/hpi/datadownload/data_download.htm
UK house prices data.
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RESOURCES
http://www.statistics.gov.uk/hub/index.html
UK National Statistics.
http://www.scotland.gov.uk/Topics/Statistics
Scottish Government statistics.
http://www.ons.gov.uk
Office for National Statistics.
http://world.bymap.org/
World by Map presents several world statistics and charts by tables, maps and
diagrams.
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