As a high school or undergraduate Mathematics teacher, you can use this set of computerbased 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 CO_{2} 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.
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 CO_{2} level be in 2100?
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  120130 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 
Microlecture (video) (~10 min)  A microlecture (video) that explains polynomial differentiation with examples and practice questions. It also includes a tutorial on tangents of polynomials. https://www.khanacademy.org/math/apcalculusab/abderivativerules/abpolydiff/v/derivativepropertiesandpolynomialderivatives 
Classroom/ Laboratory activity (~60 min)  A classroom/laboratory activity to learn and apply polynomial differentiation and solve tangent line problems for global average CO_{2} data from 1950 to 2017. http://sustainabilitymath.org/calculusmaterials/ 
Here is a stepbystep 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 microlecture (video) 

3. Conduct a classroom/ laboratory activity 

 • Plot a graph and find the polynomial equation to model the average yearly atmospheric CO_{2} 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 CO_{2} 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 CO_{2} levels by applying polynomial differentiation
 • predict future atmospheric CO_{2} 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 CO_{2} levels
 • infer the approximate year when atmospheric CO_{2} levels could cause global temperatures to increase by 2°C (leading to serious climate changerelated problems)
 • determine the desired trends in atmospheric CO_{2} levels that could help in avoiding or mitigating such climate changerelated 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/derivativegraphs.php 
Reading, “Derivatives of Polynomials”  World Web Math, Massachusetts Institute of Technology 
Microlecture (video), “Differentiating polynomials”  Khan Academy 
Classroom/Laboratory Activity , “Mauna Loa Yearly Average CO2”  Thomas J. Pfaff, Sustainability Math 
Additional Resource  Interactive Mathematics 
Images 
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