Lesson Plan: Teaching Integration using World Petroleum Consumption Data

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 

1. 1. Use the teaching module, ‘Integration- Introduction’ by OpenStax, Rice University, to teach about integration and its applications.
   2. Navigate to the sub-sections within the module to explain the relation between a function and its integral.
   3. Use the in-built practice exercises and quizzes to evaluate your students’ understanding of the topics.

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Step2 : Extend understanding

1. Use the classroom activity, ‘World Petroleum Consumption’ from Sustainability Math by Thomas J. Pfaff, Professor of Mathematics, Ithaca College, USA, to enable your students to apply their understanding of integration using a dataset from the US Energy Information Administration (EIA).
2. This classroom activity includes a dataset of the World’s Petroleum Consumption from 1980 to 2016. This data is provided in an Excel spreadsheet.
3. The classroom activity also includes a Word document that contains directions on how to use different mathematical methods on the data provided.
4. It further includes questions that you may wish to use in your classroom to explain integration to initiate a discussion on the global oil consumption in recent times.
5. Direct your students to download the Excel file (with datasets) and the Word document (with directions to use the dataset and a set of questions to analyze the dataset).
6. Proceed with the classroom activity and encourage your students to answer the questions by applying their understanding of integration and setting up and solving equations with integrals.
7. Discuss how this global petroleum consumption is responsible for carbon emissions that have contributed towards post-industrial age global warming.

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Step 3: Discuss further

1. Use the visualizations and associated reading, ‘How long before we run out of fossil fuels’ by Hannah Ritchie, Our World in Data, to discuss the global fossil fuel reserves and the carbon budget for a 2-degree world.
2. Begin by discussing the Hubbert’s Peak Theory that predicts that the United States will run out of its oil reserves in the decades following year 2000.
3. Then use the chart of actual US oil production over time (1910-2016) and discuss why it deviates from the Hubbert’s Peak prediction.
4. Discuss why this is significant in the context of carbon emissions and their effect on global warming. The data for the chart is available to download as a CSV file, if you wish to perform further mathematical problems based on it.
5. Finally, use the other visualizations to discuss the global fossil fuel reserves and the target carbon budget to ensure that global warming is kept within the 2-degree warming scenario (by reducing fossil fuel based carbon emissions), as per the UN’s Paris Agreement.

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Suggested questions/assignments for learning evaluation :

1. How has the world petroleum consumption changed since 1980?
2. What is the relationship between a function and its integral?
3. How does the Hubbert’s peak prediction and actual oil production in the US since 1980 differ?

The tools in this lesson plan will enable students to:

1. learn about integration and the relation between a function and its integral.
2. set up and solve integration equations to describe the trend of global oil consumption since 1980.
3. know the significance of the difference between the Hubbert’s peak prediction and actual US Oil production.
4. discuss the importance of the carbon budget to reduce global warming.

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