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.

Introduction

Your current lesson plan can be augmented with the following resources :

  1. A video tutorial introducing Riemann Sums and calculation of area under a curve.
  2. Reading and worksheet on how to calculate the area under a curve using Riemann Sums.
  3. A computer based laboratory exercise where students learn concepts in introductory calculus such as area under curves, and Riemann Sums using CO2 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.

About 
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
Contents

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 CO2 emissions data. Students use CO2 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 CO2 Emissions

http://sustainabilitymath.org/calculus-materials/

Credits/Copyrights
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 CO2 Emissions by Thomas J Pfaff Sustainability Math: Calculus I Integration Related Projects

http://sustainabilitymath.org/calculus-materials/

Disclaimer: All the pedagogical 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 or images.