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 integration, definite integral, area under a curve, and Riemann sum in Introductory Calculus.
This lesson plan allows students to understand Riemann sum, calculate the area under a curve using Riemann sum, and explore how this value converges to a definite integral. The activity helps students to apply the Riemann sums method for analysis and comparison of data on CO2 emission, which is considered to be a significant contributor to climate change.
Thus, the use of this lesson plan allows you to integrate the teaching of a climate science topic with a core topic in Mathematics.
Use this lesson plan to help your students find answers to:
- 1. For a given function f(x) and n, calculate the left Riemann sum and right Riemann sum.
- 2. For the same f(x) (as above) and double the value of n (from above), calculate and compare the left and right Riemann sums.
- 3. Using Riemann sums, calculate and compare the total CO2 emissions (data records provided in the activity) for the U.S. and China from 1980 to 2015. What are the possible effects of these CO2 emissions on the Earth’s climate?
About Lesson Plan
|Grade Level||High School, Undergraduate|
|Topic(s) in Discipline||• Calculus, Integration
• Definite Integral
• Area under a Curve
• Riemann Sum
|Climate Topic||• Energy, Economics, and Climate Change
• Climate and the Anthroposphere
• Policies, Politics, and Environmental Governance
|Location||USA and China|
|Approximate Time Required||90 – 120 min|
|Reading and Associated Activity
(30 – 60 min)
|A reading that introduces Riemann sum and the types of Riemann sums. It describes the calculation of the area under a curve by using Riemann sum, and explains how this value can converge to the definite integral.
Go to the Reading
|Classroom/ Laboratory activity
|A classroom/laboratory activity to analyze CO2 emissions data for the U.S. and China by using Riemann sums for the calculation of area under the curve.
Go to the Activity
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 by using a reading and an associated activity||
|2. Conduct Classroom/ Laboratory activity (~60 min)||