Lesson Plan: Teaching Introductory Calculus (Differentiation) using Atmospheric CO2 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.

1.Introduce the topic through a reading and exercises	•  Introduce the topic of differentiation. •  Explain derivatives of polynomials with the help of the reading and exercises, “Derivatives of Polynomials”, from World Web Math, Massachusetts Institute of Technology at • http://web.mit.edu/wwmath/calculus/differentiation/polynomials.html
2. Play a micro-lecture (video)	• Next, play this micro-lecture (approx. 10 min), “Differentiating polynomials”, to help students further understand polynomial differentiation through examples and exercises. • The micro-lecture “Differentiating Polynomials”, from Khan Academy, is available at https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-poly-diff/v/derivative-properties-and-polynomial-derivatives.
3. Conduct a classroom/ laboratory activity	• Then, help your students apply the learned concepts through a hands-on classroom/laboratory activity, “Mauna Loa Yearly Average CO2”, by Thomas J. Pfaff at Sustainability Math. This activity uses atmospheric CO2 data from the Mauna Loa site for the period 1950 to 2017. • This activity will help students to •  observe the trend in increasing atmospheric CO2 levels •  infer the approximate year when atmospheric CO2 levels could cause global temperatures to increase by 2°C (leading to serious climate change-related problems) • determine the desired trends in atmospheric CO2 levels that could help in avoiding or mitigating such climate change-related consequences http://sustainabilitymath.org/calculus-materials/ • Download the material in the project, “Mauna Loa Yearly Average CO2”, under Calculus I – Differentiation Related Projects. • Conduct the exercises 1-6 to predict atmospheric CO2 levels in the future. (Optional: exercises 7 and 8). •  Discuss the possible impact of these trends on global temperature and climate.

 

Use the tools and the concepts learned so far to discuss and determine answers to the following questions:

• • Plot a graph and find the polynomial equation to model the average yearly atmospheric CO₂ levels from 1950 to 2017 (using data records provided).
• •  Compare and analyze the rate of change of atmospheric CO2 levels by applying Polynomial Differentiation.
• •  Based on observed trends, what will the atmospheric CO₂ level be in 2100?

The tools in this lesson plan will enable students to:

• • calculate the derivatives of polynomials
• • interpret and compare the slope of a curve at different points
• • compare and analyze the rate of change of atmospheric CO₂ levels by applying polynomial differentiation
• • predict future atmospheric CO₂ levels based on current levels, and discuss the corresponding effect on climate

Further questions that have been listed as associated with the main activity :

This activity will help students to

• • observe the trend in increasing atmospheric CO₂ levels
• • infer the approximate year when atmospheric CO₂ levels could cause global temperatures to increase by 2°C (leading to serious climate change-related problems)
• • determine the desired trends in atmospheric CO₂ levels that could help in avoiding or mitigating such climate change-related consequences

If you or your students would like to explore the topic further, following additional resource will be useful.

Visualization

An interactive visualization, “Interactive Graph showing Differentiation of a Polynomial Function” from Interactive Mathematics: https://www.intmath.com/differentiation/derivative-graphs.php

If you or your students would like to explore the topic further, these additional resources will be useful.

Reading, “Derivatives of Polynomials”	World Web Math, Massachusetts Institute of Technology
Micro-lecture (video), “Differentiating polynomials”	Khan Academy
Classroom/Laboratory Activity , “Mauna Loa Yearly Average CO2”	Thomas J. Pfaff, Sustainability Math
Additional Resource	Interactive Mathematics
Images	Earth System Research Laboratory Global Monitoring Division Wikipedia

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