1
Renewables → Focus on Mathematics
Calculating the wind Learning Journey
Introduction
The call
v for the use of renewable energy sources to replace fossil fuels is seldom far from the headlines. Scotland is
already engaged in using renewable energy in the forms of wind, wave and tidal power. The introductory video
celebrates the work of young Scottish engineers in this rapidly advancing field. The topic of renewable energy
provides rich opportunities for learning in science, technologies and geography in the light of cutting engineering
activity that is happening in Scotland now.
This learning journey with a mathematics focus is aimed at fourth level. Lessons give learners experiences and
opportunities to develop their understanding of applying appropriate skills and mathematical knowledge to solving
problems relating to an engineering context.
An overview planning sheet is shown on the next page which gives a plan for learning and teaching starting from the
experiences and outcomes. Learning intentions, success criteria and possible evidence which could be gathered to
assess learning are shown. The pages that follow the overview give examples of learning experiences which would
address the learning intentions. They illustrate opportunities for learners to develop knowledge and understanding and
opportunities to apply relevant skills.
Mathematics experiences and
outcomes
Having investigated the relationships between the
radius, diameter, circumference and area of a
circle, I can apply my knowledge to solve related
problems. MTH 4-16b
Having explored how real-life situations can be
modelled by number patterns, I can establish a
number sequence to represent a physical or
pictorial pattern, determine a general formula to
describe the sequence, then use it to make
evaluations and solve related problems. MTH 413a
Responsibility of all areas which
could be addressed in this learning
journey:
By considering the type of text I am creating, I can
independently select ideas and relevant
information for different purposes, and organise
essential information or ideas and any supporting
detail in a logical order. I can use suitable
vocabulary to communicate effectively with my
audience. LIT 4-26a
Interdisciplinary learning planning
opportunities
An engineering challenge related to technologies
which harness renewable forms of energy could
be incorporated into planning for interdisciplinary
learning between departments relating to a
scenario where islanders want to move away from
using fossil fuels.
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Renewables → Focus on Mathematics
Calculating the wind Learning Journey
Experiences and outcomes
Learning intentions
Success criteria
Possible evidence
Having investigated the relationships
between the radius, diameter,
circumference and area of a circle, I can
apply my knowledge to solve related
problems. MTH 4-16b
Apply mathematical concepts to
practical models and problems
I can investigate how wind speed, air
density and length of rotor can affect
the power efficiency of a turbine
Observation of the quality of ongoing
peer discussions
Having explored how real-life situations
can be modelled by number patterns, I can
establish a number sequence to represent
a physical or pictorial pattern, determine a
general formula to describe the sequence,
then use it to make evaluations and solve
related problems. MTH 4-13a
Verbal feedback from
learners/groups
Determine the power produced
I can use identified formulae to
calculate energy and power
accurately
Calculations completed effectively –
using appropriate formulae
Identify some factors which affect the
power efficiency of a wind turbine
I can use a practical example to
estimate wind speed
Observation of the learners carrying
out the practical task
Report on the best location and
design for the turbine
I can evaluate whole number powers
of any appropriate number
Oral presentation to peers / written
report identifying ideal
conditions/locations for a wind
turbine – including wind speed, air
density, weather conditions, etc
Prior knowledge
Having explored the notation and
vocabulary associated with whole number
powers and the advantages of writing
numbers in this form, I can evaluate
powers of whole numbers mentally or
using technology. MTH 3-06a
I can show how quantities that are related
can be increased or decreased
proportionally and apply this to solve
problems in everyday contexts.
MTH 3-06a
I can solve practical problems by applying
my knowledge of measure, choosing the
appropriate units and degree of accuracy
for the task and using a formula to
calculate area or volume when require.
MNU 3-08a
I can evaluate my findings and report
on them giving advice based on
these
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Renewables → Focus on Mathematics
Calculating the wind Learning Journey
Learning experiences
Possible tasks
Resources
Introduction
Show a film clip of wind turbines. In groups
learners will be asked to consider which factors
have to be considered when engineers design a
wind turbine. Ideas the learners may come up with
could include the:
Working with a STEM ambassador or someone
else working in the area of Scottish renewable
energy would help to bring the learning alive.
Engaging activities help to immerse learners in a
particular context or problem and get them
thinking, talking and exploring.
In this session, learners are introduced to the
problem and identify some of the main issues that
mathematics skills and knowledge could help to
inform and will reflect upon the importance of
mathematics and numeracy to the solving of
engineering problems.
o
o
o
o
wind exposure of the site
size of the blades
size of the overall turbine
number of generators required on a site to
guarantee a certain output on a windy day
Learning intentions
Groups could then be told about some of the
relationships involved in calculating energy
transferred from wind to electrical energy via the
turbine, for example, the power generated is
related to the area swept by the arm of the
windmill and the speed of the wind.
o Apply mathematical concepts to practical
models and problems.
o Identify some factors which affect the power
efficiency of a wind turbine.
Teacher notes and examples of problems that
could be presented to learners are provided in
supplementary resources.
Stimulus
o Look at a stimulus film on wind turbines
o Pictures of wind turbines in different locations
Groups could now work on problems relating to
this relationship.
Finally they could discuss why this kind of
information would be important to the engineers
and how best this information could be displayed.
Possible evidence
Oral recordings of the learners discussing the
results of their calculations and why this
information would be useful to inform engineers
and different ways in which it could be presented
for the audience.
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Renewables → Focus on Mathematics
Calculating the wind Learning Journey
Learning experiences
Possible tasks/challenges
Resources
Introduction
Having developed their understanding of the
mathematical relationships involved in energy
transfers created by wind turbines learners could
now explore how these relate to energy usage.
See teacher’s and learner’s notes, which can be
found in supporting resources
Explore activities allow learners to investigate the
problems that have been identified and come to a
better understanding of the knowledge and skills
relating to these.
Stimulus
Teacher’s notes and learner notes relating to all of
the queries listed under possible challenges are
provided in the supplementary materials folder.
Learning intention
Determine the power produced.
Possible evidence
Queries could include:
o relating power produced to wind speed
o graphing relationships between energy and
power
o relating power produced and wind speed to
electrical energy used by various appliances in
their homes (examples are provided in the
teacher’s and learner’s notes)
o listing the top devices used in their houses and
v
finding
the wattage needed to power them and
relating this to a wind turbine with a particular
sweep
These queries would take several sessions to
explore. Another activity could be to apply
formulae relating to wind turbines. Examples of
these are provided in the teacher’s and learner’s
notes found in supplementary resources.
o The learners’ data when solving their problem
and their oral explanations of their thinking
o Learners could keep a portfolio of the graphs
and data they gather and their evaluation of
these to help with the preparation of a final
report, display or presentation
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Renewables → Focus on Mathematics
Calculating the wind Learning Journey
Learning experiences
Possible tasks/challenge
Resources
Introduction
Learners are now asked to draw upon the results
of the investigations they have been doing and the
data and evaluations they have gathered to add to
the exhibition for the islanders.
A STEM ambassador could be invited in to provide
an authentic audience for the learners. They could
explain some of the ways they use maths in their
work and could give feedback to the learners on
the exhibited information.
Elaborate activities allow learners to synthesise
new knowledge and apply it to the solving of
problems. Giving learners opportunities to explain
their investigations helps them to use formal terms
and language and explain the skills and processes
they have been using.
Stimulus
Teacher’s notes and learner’s notes relating to all
of the queries listed under possible challenges are
provided in the supplementary materials folder.
Learning intention
Report on the best location and design for the
turbine.
Their findings could be presented in a range of
ways but should include information about:
o What their findings show that could help to
inform the best design for wind turbines on the
island
o How their findings relate to everyday electrical
appliances the islanders may use
These findings should be presented in a way
clearly understandable to their audience and
should be illustrated by graphical information and
tables.
Possible evidence
Written report of findings – which could also
include graphical information and tables for
illustration of key points
Reflecting on learning
Learning could also be shared with parents
through the exhibition and opportunities given for
them to give feedback to the learners.
A session could be organised to allow learners to
evaluate their learning journey and identify
successes, areas for improvement and next steps.