Derivatives Lesson: Evaluating NYC Climate Trends
Lesson Plan
2 hours 10 minutesGrades11, 12, APMathematics
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Written by Sol Giesso
About this lesson
In this lesson, students apply calculus concepts, including derivatives, to analyze climate change trends using real-world data, then collaborate to synthesize their findings into a report that informs and inspires climate action.
Inquire: Students explore the Intergovernmental Panel on Climate Change and consider how modeling is used for understanding climate change.
Investigate: Students calculate and interpret derivatives of CO₂ emissions plus one extra dataset (Arctic sea-ice cover extent, NYC average annual temperature, or NYC relative sea-level rise).
Inspire: In groups, students synthesize their findings from across datasets into an IPCC-style report to persuade policymakers to take climate action.
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Suggestions
- This lesson is designed to be completed over two days and can be extended further. If students complete the independent worksheets as homework, complete the Inquire and Investigate sections in one day and reserve the Inspire section for the next day. If you prefer to have students work on the worksheets in class, begin the second day with independent work and then transition to the Inspire section.
- This lesson can be taught as an application of derivatives to help students understand their meaning in context. Because the functions are relatively simple (exponential, quadratic, and linear), it can be completed before learning many of the derivation rules (product rule, quotient rule, etc.).
- This lesson is a companion lesson to the Integrals Lesson: Analyzing NYC Climate Goals. Together, the two lessons help students see how derivatives and integrals provide complementary perspectives to understand climate change and climate action.
- Teachers can have students build their own regressions in Desmos using the data, prompting them to think about why to choose certain regression models over others.
- Global CO₂ emissions model (data from Our World in Data)
- Global sea-ice extent model (data from NOAA)
- NYC annual average temperature model (data from NOAA)
- NYC relative sea-level rise model (data from NOAA).
- Teachers may also choose to use additional datasets to incorporate into the lesson. Student groups could pick three datasets of interest to them and base their report on their analysis of them.
- If in a different context than New York City, teachers can replace the third and fourth datasets with local equivalents.
- If students are interested, this graphic novel about the IPCC explains more about its history and role.
- This lesson empowers students to use mathematical analysis as a tool for advocacy, demonstrating how quantitative reasoning can illuminate climate impacts and inform real policy decisions.
- This lesson highlights local connections to New York City and an authentic, career-based assessment.
Prerequisites
- Students should have a basic understanding of functions (linear, exponential, quadratic), including how to interpret graphs, domain/range, and rates of change.
- Students should have an introductory understanding of derivatives of linear, exponential, and quadratic functions.
- Teachers should review the IPCC's role and skim its latest reports in advance.
- Teachers should set up all four Desmos models and ensure students have access to them in advance.
- Teachers should consider local climate impacts and how they affect NYC communities differently.
- Teachers should be aware that some students may experience climate grief, anxiety, or despair. Frame the lesson around solutions and agency rather than doom.
Differentiation
- To extend the final activity, ask students to create a multimedia presentation that uses data visualizations to explain climate trends to community members.
- Alternatively, students could role-play as IPCC scientists presenting to a mock city council or climate commission, where they must defend their mathematical analysis and recommendation.
- To scaffold this activity, add optional sentence stems for the report and reduce worksheet complexity by having students focus on fewer data points (e.g., calculate f'(x) at only 3 time intervals instead of 5).
- To ensure all students can participate and support one another, strategically group students based on their strengths and weaknesses. Teachers can also provide group roles (data analyst, communicator, community advocate, etc.).
- To deepen understanding of modeling, challenge students to build their own regression models on Desmos using raw data, then explain why they chose certain models (exponential vs. quadratic vs. linear) and compare their models to the provided ones.
- To extend beyond derivatives, ask students to estimate the total accumulation of CO₂ emissions by finding the area under the curve using integrals.
From the scientist review
This lesson tasks students with using their calculus skills to understand the rate of change of climate data. All text and figures are clear, with data sourced from trusted institutions such as IPCC and NOAA. Through the writing of a technical report, calculus is connected to advocacy as students use their analysis to persuade policymakers that climate action needs to happen now. This lesson is grounded in current climate data and is recommended for teaching.
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About the teacher writer
Sol Giesso
Content Writer
Sol Giesso, Ed.M., is SubjectToClimate's Content Writer and a middle school math teacher in Boston. She holds an M.S. in Community Climate Adaptation from Worcester Polytechnic Institute and an Ed.M. in Teaching and Teacher Leadership from the Harvard Graduate School of Education, and previously worked at the Smithsonian Environmental Research Center leading hands-on outdoor education field trips for K–12 students. Fun fact: she loves to draw, scuba dive, and turn any recipe into a vegetarian one.
