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Renewables
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Focus on Mathematics
Calculating the wind Learning Journey
v 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.
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 4-
13a
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
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.
Possible links
Sciences SCN 4-04a
Technologies TCH 4-01b

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 4-13a
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
Apply mathematical concepts to practical models and problems
Determine the power produced
Identify some factors which affect the power efficiency of a wind turbine
Report on the best location and design for the turbine
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Renewables
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Focus on Mathematics
Calculating the wind Learning Journey
I can investigate how wind speed, air density and length of rotor can affect the power efficiency of a turbine
I can use identified formulae to calculate energy and power accurately
I can use a practical example to estimate wind speed
I can evaluate whole number powers of any appropriate number
I can evaluate my findings and report on them giving advice based on these
Observation of the quality of ongoing peer discussions
Verbal feedback from learners/groups
Calculations completed effectively – using appropriate formulae
Observation of the learners carrying out the practical task
Oral presentation to peers / written report identifying ideal conditions/locations for a wind turbine – including wind speed, air density, weather conditions, etc

Introduction
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.
Stimulus o Look at a stimulus film on wind turbines o Pictures of wind turbines in different locations
Learning intentions o Apply mathematical concepts to practical models and problems. o Identify some factors which affect the power efficiency of a wind turbine.
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: o wind exposure of the site o size of the blades o size of the overall turbine o number of generators required on a site to guarantee a certain output on a windy day
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.
Teacher notes and examples of problems that could be presented to learners are provided in supplementary resources.
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.
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Renewables
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Focus on Mathematics
Calculating the wind Learning Journey
Working with a STEM ambassador or someone else working in the area of Scottish renewable energy would help to bring the learning alive.
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.

Introduction
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.
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.
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 v 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.
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Renewables
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Focus on Mathematics
Calculating the wind Learning Journey
See teacher’s and learner’s notes, which can be found in supporting 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

Introduction
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.
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.
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.
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Renewables
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Focus on Mathematics
Calculating the wind Learning Journey
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.
Written report of findings – which could also include graphical information and tables for illustration of key points
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.