Wind tunnel calculations
Using a wind tunnel to test aerodynamic characteristics of objects
A wind turbine is a device that converts the wind’s kinetic energy into electrical power. Groups of large turbines, known as wind farms, are becoming an increasingly important source of intermittent renewable energy and are used by many countries as part of a strategy to reduce their reliance on fossil fuels.
Throughout this engaging activity designed for GCSE students, learners will face intriguing challenges that revolve around wind turbines, where their problem-solving skills will be tested using equations and systematic listing techniques.
By applying mathematical principles and systematic approaches, learners will uncover the secrets behind these sustainable energy marvels and gain a deeper appreciation for their significance in today’s world.
Activity introduction
Allocate the students sufficient time to read the task and contemplate the question presented on the first slide.
It is recommended to utilise a table format for displaying the values learners substitute into the equation, along with the corresponding outcomes, indicating whether they are too large or too small.
Allow the students ample time to analyse the problem on the second slide, and encourage them to share their thoughts and ideas with a partner. Utilising tools like GeoGebra, a graph plotter, can be beneficial in illustrating and verifying their answers for the initial problem. Additionally, employing spreadsheet applications like Excel or the one integrated into GeoGebra can facilitate a trial and improvement approach for problem-solving.
Problem solving
Students will likely employ trial and improvement or a graphical method to tackle the first question. Some may also opt to utilise a spreadsheet for their calculations. To ensure the accuracy of their solutions up to two decimal places, they are encouraged to consider using a number line, which can aid in the verification process.
As for the final problem, students will need to adopt a systematic listing approach or explore other methodologies to ensure that every possible combination of gears has been thoroughly explored and tested.
This activity aims to empower students to approach challenges creatively and thoughtfully by providing various problem-solving techniques and strategies. This process will sharpen their mathematical abilities and cultivate critical thinking skills, enabling them to tackle complex problems with confidence and precision.
Discussion points
Promote active discussion among the students regarding the diverse approaches they have employed and how they can ensure the accuracy of their answers up to two decimal places. If students have not chosen the graphical approach to solve the problem, consider demonstrating it to the class.
Encourage a comparative analysis of the various methods used to address the subsequent problems and enquire about the students’ strategies to ensure they have explored all potential combinations of gears.
Potential GCSE context
This activity will cover using trial and improvement to solve an equation, calculations with fractions, ratios and systematic listing.
Download the activity sheets for free below!
All activity sheets and supporting resources are free to download, and all the documents are fully editable so that you can tailor them to your students and your schools’ needs.
The activity sheet includes teacher notes, guidance, helpful web links, and links (where appropriate) to the national curriculum in the four devolved UK nations; England, Northern Ireland, Scotland and Wales.
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