As a high school or undergraduate Mathematics teacher, you can use this set of computer-based tools to help you in teaching topics such as Differentiation, Derivatives of Polynomials, and Tangent Line Problems in Introductory Calculus.

This lesson plan allows students to perform polynomial differentiation and solve tangent line problems using climate data such as atmospheric CO2 concentrations data since 1950.
Thus, the use of this lesson plan allows you to integrate the teaching of a climate science topic with a core topic in Mathematics.

Image: Mouna Loa Observatory, Island of Hawaii

Questions

Use this lesson plan to help your students find answers to:

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

Differentiation

About Lesson Plan

Grade Level High School, Undergraduate
Discipline Mathematics
Topic(s) in Discipline • Introductory Calculus
• Differentiation
• Derivatives of Polynomials
• Tangent Line Problem
Climate Topic Climate and the Atmosphere, The Greenhouse Effect
Location Global
Languages English
Access Online , Offline
Approximate Time Required 120-130 min

Contents

Reading (30 – 45 min) A reading that introduces the topics of differentiation
and derivatives of polynomials. The resource also includes exercises.
http://web.mit.edu/wwmath/calculus/differentiation/polynomials.html
Micro-lecture (video) (~10 min) A micro-lecture (video) that explains polynomial differentiation
with examples and practice questions.
It also includes a tutorial on tangents of polynomials.
https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-poly-diff/v/derivative-properties-and-polynomial-derivatives
Classroom/ Laboratory activity (~60 min) A classroom/laboratory activity to learn and apply polynomial differentiation and solve tangent line problems for global average CO2 data from 1950 to 2017.
http://sustainabilitymath.org/calculus-materials/
Step-by-Step User Guide
Questions/Assignments
Learning Outcomes
Additional Resources
Credits

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
2. Play a micro-lecture (video)
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
All the teaching tools and images  in our collated list are owned by the corresponding creators/authors/organizations as  listed on their websites. Please view the individual copyright and ownership details for each tool by following the individual links provided. We have selected and analyzed the tools that align with the overall objective of our project and have provided the corresponding links. We do not claim ownership of or responsibility/liability for any of the listed tools.