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Energy House → Focus on Mathematics
Solar Mathematics Learning Journey
Introduction
The scientific
community and society as a whole are becoming increasing aware of the impact of pollution on the world
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around us. Dependence on finite reserves of fossil fuels as our main source of energy poses difficult questions for future
generations. The twin factors of environmental impact and dwindling resources have been drivers of change in recent
years and many exciting new energy sources are being developed. Changes in climate along with media attention have
raised the profile of 'alternative energy', moving it from the realms of counter-culture into the mainstream.
The Glasgow House project makes use of solar thermal panels and in this learning journey learners use mathematics
and numeracy to explore the optimum size and positioning of solar roof panels for a house to gain optimum efficiency.
Retro-fitting energy saving devices can be expensive and less effective than fitting them to purpose in a new build.
Learners may wonder about solar panels which adjust to the direction of the Sun. The builders at the Glasgow House
say such technology is prohibitively expensive but learners should be aware that this may change in the future.
This context for learning would provide rich opportunities for planning for interdisciplinary learning with departments such
as technologies, sciences and geography. 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 of learning which could be gathered 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 to apply relevant skills.
Mathematics experiences and
outcomes
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 have explored the relationships that exist between
the sides, or sides and angles, in right-angled
triangles and can select and use an appropriate
strategy to solve related problems, interpreting my
answer for the context. MTH 4-16a
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 creating a
system for heating a home could be incorporated
into planning for interdisciplinary learning relating to
a scenario where a local authority want to consider
using solar panels on their new-build houses for
families.
Possible link
Technologies TCH 4-12b
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Energy House → Focus on Mathematics
Solar Mathematics Learning Journey
Experiences and
outcomes
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.
Learning intentions
Success criteria
Possible evidence
Use mathematical research
techniques to solve a problem
I can plan what to research, which
data might need to be gathered to
solve an engineering problem
Posters showing the groups’ planning
and annotations of their reflections
Gain insights into how modelling is
used in mathematics
I can apply some of the skills of
modelling in mathematics, such as
simplifying to create a model, using
my model, evaluating my results and
refining the model
A portfolio could be created in which
the learners could keep the results of
their mathematical investigations,
including data, evaluations and
reflections on learning
MNU 4-20a
I have explored the relationships that
exist between the sides, or sides and
angles, in right-angled triangles and
can select and use an appropriate
strategy to solve related problems,
interpreting my answer for the
context.
Understand and use shape
properties in this modelling process
Results of investigations
I can use geometry in modelling to
explore an engineering problem
Use data to make informed decisions
and judgements
I can organise, present and analyse
data in tabular and graphical form
I can use computer software as a tool
for the presentation of data
Data displayed in tabular and
graphical form and learners
discussions of what the data shows
Structure a report to present results
and make recommendations based
upon these
I can create a report presenting the
results of my investigations and
made recommendations based upon
these
I can discuss the role of mathematics
in engineering
Written report outlining the
investigations carried out and
summarising what they show
MTH 4-16a
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Energy House → Focus on Mathematics
Solar Mathematics Learning Journey
Learning experiences: Engage
Possible tasks/challenges
Possible evidence
Introduction
Show the Glasgow House film and ask the
learners to discuss where solar is being used to
transfer energy in the house. Discuss prior science
knowledge they may have relating to this problem.
o Poster showing the groups’ planning
o Post-it notes with their reflections on skills used
in this project
Engage 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 and numeracy skills and knowledge
could help to inform and reflect upon the
importance of mathematics and numeracy to the
solving of engineering problems.
Stimulus
o Look at the Glasgow House film on the STEM
Central website and note where solar energy is
being utilised
o Pictures of photovoltaic cells being used in
different parts of the world, for example
California
o Pictures of solar panels being used on the roofs
of buildings
o Discussion of the differences between solar
photovoltaic panels and solar thermal panels
Learning intention
Use mathematical research techniques to solve a
problem.
Groups could be given pictures of solar panels and
sun rooms being used in building design and
asked to plan what kind of data could be gathered
using mathematics and numeracy knowledge and
skills that would inform the designing of housing to
best utilise solar energy. They could then be told
that the Glasgow House architects have asked
them to create a report on the best position and
size for the solar thermal panels that they are
using on the roof of the house.
Each group could now decide what the main areas
of investigation would need to be and what kind of
data could be gathered in order to create this
report. Groups could present their planning to the
whole class and areas of investigation could be
agreed upon. Different groups could work on
different areas or the class could work together on
the different inquiries each group identifies.
Teacher’s notes are provided in supplementary
resources to give some ideas about the kinds of
areas the learners might explore.
Reflecting on learning
Learners could be asked to reflect on their learning
using questions like the ones below:
o What are the kinds of skills that will be used in
this project?
o Which skills and knowledge from other areas
might help when designing the optimum system
for using solar thermal panels in the house?
o Engineering problems such as this require the
application of knowledge and skills from
different curriculum areas; what might these be?
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Energy House → Focus on Mathematics
Solar Mathematics Learning Journey
Learning experiences: Explore
Possible tasks/challenges
Possible evidence
Introduction
Having developed their understanding of the kinds
of things that could be researched to inform the
positioning of the panels, learners could now be
involved in a number of investigations.
Learners could keep a portfolio of the graphs and
data they gathered and their evaluation of these to
help with the preparation of a final report, display
or presentation.
These could include:
Reflecting on learning
Explore activities enable learners to investigate the
problems that have been identified and come to a
better understanding of knowledge and skills
relating to these.
Stimulus
Teacher’s and learner’s notes, relating to all of the
queries listed under possible challenges, are
provided in supporting resources on the STEM
Central website.
Learning intentions
o Gain insights into how modelling is used in
mathematics.
o Understand and use shape properties in this
modelling process.
o Use data to make informed decisions and
judgements.
o Determining the angle you would recommend
for pitch of the roof to optimise output from the
solar panels over the year.
o Investigating the relationship between a solar
panels effective size and its position.
o Exploring the relationship between the amount
of daylight and altitude.
o The pattern of energy input over the year for
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different pitches.
These queries would take several sessions to
explore.
Learners can reflect on what they thought in
relation to the questions before and after they did
more research. How and why did our thinking
change? Which mathematical skills and knowledge
did we make use of?
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Energy House → Focus on Mathematics
Solar Mathematics Learning Journey
Learning experiences:
Explain/elaborate
Introduction
Elaborate activities will enable learners to
synthesise new knowledge and apply it to the
solution 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.
After investigating the queries needed to give
advice on the best pitch, angle and position for the
solar panels learners will then organise their
findings into some form of report and give
recommendations based on these.
Learning intention
Structure a report to present results and make
recommendations based upon these.
Possible tasks/challenges
Possible evidence
Learners are now asked to draw upon the results
of the investigations they have been doing, the
data and evaluations they have gathered to create
a report.
Written report outlining the investigations carried
out and summarising what they show
This report could be created using a range of
media, for example, a Glow wiki or blog, a
PowerPoint presentation, a formal report, a
display.
Success criteria could be agreed with the learners
to help them think about such aspects as:
o The accuracy and detail of their investigations
and evaluations
o How successfully these are communicated to
the intended audience
Responsibility to all
These learning experiences would provide a
strong opportunity to address an aspect of
responsibility of all such as:
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
Reflecting on learning
This task involves groups of learners working
together to solve a problem, complete a task,
and/or create a product. It is based on the idea
that learning is a naturally social act in which the
participants talk amongst themselves. It is through
this talk and hands-on activities that learning
occurs.