As a high school or undergraduate Mathematics teacher, you can use this set of computer-based tools to help you in teaching introductory differential calculus and specifically about polynomial and logistic differentiation and the use of the Quotient (or Product) Rule.
The derivative at different points of a differentiable function (Image: Wikipedia)
This lesson plan will allow you to teach polynomial and logistic differentiation using a hands-on computer-based classroom activity that includes wind energy production data of several countries from 1980 to 2016. In the context of global warming due to carbon emissions from fossil fuel, harnessing a clean renewable source of energy like wind power is increasing across the globe and can provide a potential solution to reducing our greenhouse gas emissions.
This activity includes a set of inquiry-based questions that will enable your students to apply their understanding of polynomial and logistic differentiation and apply the Quotient (or Product) Rule to describe the rates of increase of wind energy production over time in countries such as China, Spain, USA, and the World.
Use this lesson plan to help your students find answers to:
- What are differentiating functions?
- Describe polynomial and logistic differentiation using examples.
- How has the rate of global wind energy production changed since 1980?
- How do the rates of wind energy production in select countries (from the given datasets) differ from that of the World?
- Define a function for the rate of increase of the World’s wind energy production to meet its entire energy requirement.
About Lesson Plan
|Grade Level||High school, Undergraduate|
|Topic(s) in Discipline||Polynomial and Logistic Differentiation
Quotient or Product Rule
|Climate Topic||Energy, Economics and Climate Change
Climate Mitigation and Adaptation
Climate Variability Record
|A teaching module to explain differentiating functions, polynomial and logistic differentiation, differentiation rules and the use of the Quotient or Product Rule.|
|Classroom/ Laboratory activity
|A classroom activity to apply understanding of polynomial and logistic differentiation using datasets of various countries’ wind energy production over time (1980-2016).|
|A set of interactive visualizations using similar datasets to better understand the distribution of and changes in wind energy production across the globe in recent times.
These can be accessed at:
Here is a step-by-step guide to using this lesson plan in the classroom/laboratory. We have suggested these steps as a possible plan of action. You may customize the lesson plan according to your preferences and requirements.
Step 1: Topic introduction and discussion
- Use the teaching module, ‘Differentiation Rules’ by OpenStax, Rice University, to teach differentiating functions, differentiation rules, and polynomial or logistic differentiation.
- Navigate to the sub-sections within the module to explain the types of differentiating functions and the application of the Quotient or Power Rule.
- Use the in-built practice exercises and quizzes to evaluate your students’ understanding of the topics.
Step2 : Extend understanding
- Use the classroom activity, ‘Wind Energy by Selected Countries and World’ from Sustainability Math by Thomas J. Pfaff, Professor of Mathematics, Ithaca College, USA, to enable your students to apply their understanding of polynomial or logistic differentiation using datasets from the International Energy Agency (IEA).
- This classroom activity includes datasets of several countries’ wind energy production (including the World’s cumulative data) from 1980 to 2016. This data is provided in an Excel spreadsheet.
- The classroom activity also includes a Word document that contains directions on how to use different mathematical methods on the data provided.
- It further includes questions that you may wish to use in your classroom to explain differentiating functions to initiate a discussion on the rate of increase in global wind energy production in several countries such as China, Spain, and USA in recent times.
- Direct your students to download the Excel file (with datasets) and the Word document (with directions to use the datasets and a set of questions to analyze the datasets).
- The documents also include datasets of several other countries that may be used for this activity.
- Proceed with the classroom activity and encourage your students to answer the questions by applying their understanding of differentiating functions and the Quotient (or Power) Rule.
- This activity also includes links to readings to help explain to your students the basics of wind energy production and its environmental impacts.
Step 3: Discuss further
Use the visualizations, ‘Wind Power Plants by Capacity (MW)’ by World Resources Institute (WRI) and ‘Wind energy generation, 2018’ by Our World in Data to discuss about the current capacity and distribution, and increase in capacity of global wind energy production for the years 1965-2018. Finally, discuss how the increase in the World’s wind energy production could help reduce carbon emissions and mitigate global warming.