As a teacher of high school or undergraduate Mathematics you can use this set of computer-based tools when teaching topics such as Integration, Riemann Sums and Area Under A Curve in introductory Calculus courses.
Your current lesson plan can be augmented with the following resources :
- A video tutorial introducing Riemann Sums and calculation of area under a curve.
- Reading and worksheet on how to calculate the area under a curve using Riemann Sums.
- A computer based laboratory exercise where students learn concepts in introductory calculus such as area under curves, and Riemann Sums using CO_{2} emissions data.
Thus, the use of this toolkit allows you to integrate the teaching of a climate science topic with a core topic in Mathematics.
Discipline | Mathematics |
Grade Level | High School and Undergraduate |
Topic(s) in discipline | Calculus, Integration, Riemann Sums, Area Under Curves. |
Location | |
Access | Online and Offline |
Language(s) | English |
Climate Topic | Energy, Economics, and Climate Change; Climate and the Anthroposphere; Policies, Politics, and Environmental Governance |
Your current lesson plan can be augmented with the following resources:
1. Video Tutorial | This video tutorial from Khan Academy explains Riemann Sums. As part of their module on Integral Calculus, the video tutorial on Riemann Sums explains Riemann approximation, Riemann sums in summation notation, Motion problem with Riemann sum approximation and associated worksheets.
Khan Academy https://www.khanacademy.org/math/integral-calculus/riemann-sums-ic |
2. Reading | Reading and worksheet on how to calculate the area under a curve using Riemann Sums.
Hosted at Math Insight. Developed by Nykamp DQ http://mathinsight.org/calculating_area_under_curve_riemann_sums |
3. Classroom/Laboratory Activity | A computer based laboratory exercise where students learn concepts in introductory calculus such as area under curves, and Riemann Sums using CO_{2} emissions data. Students use CO_{2} emissions data of the US and China from 1980 to 2014 and learn to calculate area under a curve using Riemann Sums. Students also learn to calculate the average rate of change of total emissions and per capita emissions for each country.
Sustainability Math: Calculus I Integration Related Projects US and China CO_{2 }Emissions |
Integral Calculus: Riemann Sums by Khan Academy
https://www.khanacademy.org/math/integral-calculus/riemann-sums-ic |
Nykamp DQ, “Calculating the area under a curve using Riemann sums.” From Math Insight. http://mathinsight.org/calculating_area_under_curve_riemann_sums |
US and China CO_{2 }Emissions by Thomas J Pfaff Sustainability Math: Calculus I Integration Related Projects |