Math is central to many processes in economics, physics, the sciences, and engineering. The complex issues of global warming and climate change are natural and currently-relevant for algebra, arithmetic, calculus, geometry, trigonometry, and statistics, and many problems lend themselves to more than one approach. For example, when measuring greenhouse gas emissions [GHG], we often need to convert units from one system to another; depending on your students’ ability level, they can do this using multiplication by conversion factors, ratios, or algebraic equations.

Which of the following sample questions could you use in your classroom to help initiate or add depth to discussions about global warming, climate change, and your school’s GHG emissions?

- How can we calculate the volume of ice in the Greenland & Antarctic ice sheets?
- What volume of water will be released if those ice sheets melt?
- Can we calculate how much that will affect sea level?

- Concentrations of GHG in the atmosphere are often expressed in parts per million (ppm) — currently over 400 ppm. How else could we express the same information?
- Why do some measurements use English units such as pounds or feet, while others use
**metric system**units such as kilograms (kg) or kilometers (km) or megawatt (MW)?- 20°
**Celsius**(68°**Fahrenheit**) is often recommended as a thermostat setting for heating systems—how do we convert 20°C to the equivalent on the Fahrenheit scale? - Set up an equation to find the temperature(s) at which °C = °F.

- 20°
- In a classroom or office, how much electrical power do the lights use per year? (Assume each T8 4-foot fluorescent tube draws 36 Watts and is on 8 hours/day for 250 days/year.)
- Do we need all the lights? (Can we turn off lights near the windows on bright days or reduce the number of hours the lights are on?)
- How much can we reduce emissions and costs if we can shorten the time by 1 hour every day and turn off half the lights on 3 days out of 5?

- How can we calculate the impact on GHG emissions from our use of energy for heat, lighting, and transportation?
- If we spend money to generate ongoing savings, how can we calculate how long it takes to recover the investment?
- Suppose it costs $500 to rewire the lights to make it easier to switch off some of them. How long will it take to recover this cost through reduced electric bills?

- If you replace an incandescent lamp with an LED lamp, how long will it take for the savings in electricity to repay the cost of the new lamp? (Assume the LED bulb costs $10, uses 85% less electricity, and electricity costs 10¢ / kWh.)
- How does this compare to replacing it with a compact fluorescent (CFL) that costs $2 and uses 70% less electricity than
**incandescent**?

- How do we calculate ‘return on investment’ and ‘payback period’? What is the mathematical relationship between them?

When we think of measurement, we often think of quantitative measurements expressed as numbers (cardinal measurements). What other very important types of measurement are used? (qualitative, nominal, ordinal, interval, and ratio)

In many cases, **estimates** and **approximations** provide a more useful answer than a precise measurement. For example, someone’s average speed on a bicycle 15–20 kilometers per hour [10–12 mph], but his or her actual speed is affected by hills, traffic, and other factors. Unless we know all those conditions, we can’t calculate exactly how long it will take to ride 20 km—but we can easily estimate a time between 1 and 1 ½ hours.

### Big Ideas

- Math can help students understand many processes in economics, physics, the sciences, and engineering, including those relevant for understanding global warming, climate change, and sustainability.
- The various branches of math can be applied to model relationships, define the relationships between variables, or measure individual variables.

### Additional Resources for Mathematics

- Current state of the polar ice caps [nsidc.org/arcticseaicenews]
- Education Resources on the Metric System (SI). National Institute of Standards & Technology website. [www.nist.gov/pml/weights-and-measures/education-resources-metric-system-si]
- Emission Factors for GHG Inventories [PDF], Environmental Protection Agency [EPA]

[www.epa.gov/sites/production/files/2015-11/documents/emission-factors_nov_2015.pdf] - Every Day With Metric. National Institute of Standards & Technology website. [www.nist.gov/pml/weights-and-measures/metric-si/everyday-metric]
- Global Warming’s Terrifying New Math, by Bill McKibben.
*Rolling Stone*, July 2012. [www.rollingstone.com/politics/news/global-warmings-terrifying-new-math-20120719] - Global Warming’s Terrifying New Chemistry, by Bill McKibben.
*The Nation*, April 2016. [www.thenation.com/article/global-warming-terrifying-new-chemistry] - ‘The Green New Deal and Our Schools’. Rethinking Schools, Summer 2019.
- Ice Sheets and Sea Level Rise [PDF]. NASA, 1999. (Curriculum document, good source for calculation methods, but volume of ice sheets may not be up to date.) [pumas.nasa.gov/files/02_10_97_1.pdf]
- Math Is Fun – Metric System of Measurement – Math is Fun website.

[www.mathsisfun.com/measure/metric-system.html] - [Metric System] SI Teacher Kits for Educators. National Institute of Standards & Technology website. [www.nist.gov/pml/weights-and-measures/si-teacher-kits-available-educators]
- The Metric System, the U.S.A., and Scientific Literacy. Public Library of Science website. [blogs.plos.org/scied/2013/01/28/the-metric-system-united-states-of-america-and-scientific-literacy/]
- Planetary boundaries (great visual, TED talk) Stockholm Resilience Center. [www.stockholmresilience.org/research/planetary-boundaries.html]
- Rainforest destruction Rainforest Concern website.

[www.rainforestconcern.org/rainforest_facts/why_are_they_being_destroyed] - Exploring Climate Change,
**Space Math**at NASA website. National Aeronautical and Space Administration [NASA]. [spacemath.gsfc.nasa.gov/Warming.html] - ‘Solar Power Comes to Math Class‘. Rethinking Schools, Summer 2019.
- Sustainability Math website. Tom Pfaff – ‘a resource for teachers interested in sustainability curriculum for their mathematics courses’. [www.sustainabilitymath.org]

Additional resources on the Metric System, including free classroom resources.

Also see Resources That Apply to Many Subject Areas and Teacher-Recommended Readings for Students.