# Teaching Notes

In this Section

Mathematics are designed for upper level high school or college student (multiplying and unit conversion), although younger students should also be capable of the general concepts if the spreadsheet for calculations is more fully prepared for them.

## Learning Goals

After completing this unit, users will be able to:

• Create equations in a spreadsheet and manipulate data to calculate greenhouse gas emissions.
• Compare and analyze options to select a mode of travel that minimizes GHG emissions.
• Understand the consequence of long-distance travel and the differences among modes of travel on greenhouse gas emissions.
• Gain familiarity with the lexicon of greenhouse gas inventory vocabulary.

## Rationale

The combustion of fossil fuels for transportation purposes is a major contributor to our National and global greenhouse gas emissions.  In the United States, greenhouse gas (GHG) emissions from the transportation sector are approximately one-third of the nation’s total and represent the fastest-growing major source of greenhouse gases. Transportation emissions are related to the amount of carbon in the fuel and how much fuel is used. Between 1990 and 2003 greenhouse gas emissions from passenger vehicles increased by 19 percent due to the increased sales of light-duty vehicles (SUVs, minivans, etc.) and a 34% increase in the number of miles Americans travel every year.

## Key Concepts and Vocabulary

Global warming potential (GWP) is a relative measure of how much heat a greenhouse gas traps in the atmosphere relative to the amount of heat trapped by a similar mass of carbon dioxide.  More formally, the GWP of a greenhouse gas is defined as the ratio of the time-integrated radiative forcing from the instantaneous release of 1 kilogram (kg) of a trace substance relative to that of 1 kg of a reference gas (Intergovernmental Panel on Climate Change (IPCC) 2001). A GWP is calculated over a specific time interval, commonly 20, 100 or 500 years and is expressed as a factor of carbon dioxide (whose GWP is standardized to 1).  The GWP is determined from its lifetime in the atmosphere and the intensity of its radiative forcing at specific wavelengths.

For a given mixture and amount of greenhouse gases, the carbon dioxide equivalency describes the amount of CO2 (parts per million by volume, ppmv) that would have the same global warming potential (GWP) over a specified timescale (e.g., 100 years). The carbon dioxide equivalency for a gas (kg CO2 eq./y) is obtained by multiplying the mass of the greenhouse gas emitted (for example, kg CH4/y) by its GWP
(24 kg CO2 eq./kg CH4).

Greenhouse gas inventory is an accounting of all of the sources and sinks of greenhouse gases over a specified system boundary and time period (typically one year).  A GHG inventory can be determined for a country, an industry, a school district or an individual household.  In 1992, the United States signed and ratified the United Nations Framework Convention on Climate Change (UNFCCC), which included a commitment to conduct an annual greenhouse gas inventory.  The U.S. EPA published the inventory for the country on an annual basis. Carbon footprint calculators are an example of tools to help a household or school district to conduct their own greenhouse gas inventory.

An emission factor is the average emission rate of a given pollutant from a given source or activity; for example grams of carbon dioxide released per megajoule of energy produced. Emission factors for many different types of pollutants are reported by federal agencies and the IPCC.  Some examples of the activities for which emission factors are available include fuel combustion, animal husbandry, industrial production, and travel.

Fuel economy is a measure of the efficiency of automobile travel in terms of miles driven per gallon (MPG) of gasoline consumed.  The U.S. tracks the total average fuel economy of vehicles operated and sold in the U.S.  In 2008, the average fuel economy of passenger cars was 22.6 miles per gallon. Standards are set to define the corporate average fuel economy (CAFE), which is an average of all of the vehicles sold by an individual manufacturer. The 2011 CAFÉ standard for passenger cars is 27.5 MPG.

Concepts:

• An inventory of greenhouse gas emissions requires an understanding of human activities and the amount of greenhouse gases produced from each of these various activities.
• A GHG inventory can be used to identify specific human activities that are better or worse in terms of their impact on global warming and other changes in the climate.
• A GHG inventory for transportation modes requires that the miles driven, fuel consumption per mile, and GHG emissions associated with the fuel consumption be quantified.
• A significant amount of GHGs are emitted during long-distance air travel.

## Background Information

The key calculations the students require are:

• For each type of travel and each GHG:

Emission = activity X emission factor

where the “activity” is defined as gallons of gasoline consumed for passenger vehicles and passenger miles travelled for all other transport modes. The emission factors are included in Table 1 (see also details on the MS Excel Spreadsheet).

• For passenger vehicles – the fuel required is calculated as:

Gasoline consumed = vehicle miles travelled / fuel economy of the vehicle

The fuel economy used can be the current U.S. average (22.6 MPG for passenger cars) or a known fuel economy for a particular vehicle (http://www.fueleconomy.gov/ )

• To determine the total greenhouse gas emission, the totals for each leg of the travel are summed for each greenhouse gas and then the greenhouse gases are aggregated using their global warming potentials (Table 2):

Total GHG emissions = CO2 Emissions + CH4 Emissions X GWPCH4 + N2O Emissions X GWPN2O

The units of the total GHG emissions will be kg CO2 equivalents for the trip.

Table 1: Greenhouse gas emission factors for travel

 Passenger Vehicle CO2 Emission Factor (kg CO2/ gallon gasoline combusted) CH4 Emission Factor (g CH4/ gallon gasoline combusted) N2O Emission Factor (g N2O/ gallon gasoline combusted) Car or Light-duty Truck 8.81 0.75 0.77 Rail/Bus System CO2 Emission Factor   (kg CO2/passenger -mile) CH4 Emission Factor  (g CH4/passenger -mile) N2O Emission Factor  (g N2O/passenger -mile) Intercity Rail  (e.g., Amtrak) 0.185 0.002 0.001 Commuter Rail 0.172 0.002 0.001 Transit Rail (e.g., Trams and Subways) 0.163 0.004 0.002 Bus 0.107 0.0006 0.0005 Airline Travel  Distance CO2 Emission Factor   (kg CO2/passenger -mile) CH4 Emission Factor  (g CH4/passenger -mile) N2O Emission Factor  (g N2O/passenger -mile) Long Haul (_> 700 miles) 0.185 0.0104 0.0085 Medium Haul (_> 300 and < 700 miles) 0.229 0.0104 0.0085 Short Haul (< 300 miles) 0.277 0.0104 0.0085 Distance Not Known 0.271 0.0104 0.0085

Table 2: Global Warming Potentials for primary greenhouse gases emitted during transportation

 Species Units Global Warming Potential (Time Horizon) 20 years 100 years Carbon dioxide kg CO2 eq./ kg CO2 1 1 Methane kg CO2 eq./ kg CH4 56 21 Nitrous oxide kg CO2 eq./ kg N2O 280 310

Other Resources

Values for global warming potentials http://unfccc.int/ghg_data/items/3825.php

U.S. Greenhouse Gas Inventory: http://www.epa.gov/climatechange/emissions/usinventoryreport.html

Global GHG inventories: http://cait.wri.org (registration required)

U.S. EPA Personal Household Carbon Emissions Calculator: http://www.epa.gov/climatechange/emissions/ind_calculator.html

Fuel economy of automobiles http://www.fueleconomy.gov/

Corporate Average Fuel Economy - http://www.nhtsa.gov/fuel-economy

Emission factors for travel - http://www.epa.gov/climateleaders/documents/resources/commute_travel_product.pdf

## Instructional Strategies

General Approach

Prior to the calculation and evaluation aspects of this activity, students should have had an introduction to greenhouse gas inventories, including the concept and use of global warming potentials and emission factors.

This activity is best done with computer access, one or two students per computer.  The students should have ready access to internet resources to estimate the miles travelled to their destination and MS Excel to estimate their total GHG emissions.

The students should follow the instructions and questions in the MS Excel spreadsheet to document their findings and explore how changes in their travel plans (mode of travel or destination) will impact the total greenhouse gas emissions.

Students can each add tags to a Google Earth file to show their mode of transport and GHG emissions to their destination.  This is most illustrative if all tags get added to the same file for comparison purposes.

Optional approaches:

• You may want assign different types of travel (regional, national, international) to different sets of students to help to ensure that a wide range of results are obtained for comparison and evaluation.
• The calculation and conceptual complexity can be reduced if only CO2 emissions are calculated.  The global warming potentials and CO2 equivalency concepts can then be ignored and the activity focus more on miles and choices of transportation modes.
• The Google Earth component can be deleted with only the loss of some geography concepts.

Implementation

Anticipatory Set Ask students about their travels – either actual or ideas of where to go and how to get there.  List all of the steps in a trip that would result in GHG emissions. Pose the questions – “Have you ever thought about making travel plans in a way to reduce GHG emissions?”  “What do you think you could do when planning a vacation to reduce GHG emissions?”

Procedure The use of the MS Excel spreadsheet should be modeled with a short example with a common local trip.  Project spreadsheet image and show students how to enter data and review the calculations required to determine the total GHG emissions. Students can then complete the activity. (Note – the teacher can choose to pre-populate the calculation cells with equations in the case where the interpretation from this exercise is more valuable than building MS Excel skills. A tutorial is available with basic MS Excel functions and equations).

Closure The activity should be closed with a comparison of student findings in terms of where they travelled, how they travelled, and the resulting GHG emissions.  The following general conclusions should be apparent by the end of this group discussion and comparison of their findings:

• Long distance travel, especially by airplane, can add substantially to an individual’s average annual greenhouse gas emissions.
• For moderate distances, fewer GHGs are emitted from passenger cars than airplanes, especially if several travelers (e.g., a family) participate.

## Learning Contexts

This investigation could be done in combination with a social studies unit if students are studying geography or history.  “Vacation destinations” could also be related to business travel.

There are several concepts that can be integrated with a mathematics classroom: unit conversions, using units to help develop logic of calculations and determine which operations needed, and percentage change calculations.

## Standards

National Science Education Standards Grade 9-12 (http://pals.sri.com/pals/standards/nses9-12text.html)

Science as Inquiry (12ASI)

12ASI1.3 Use technology and mathematics to improve investigations and communications. A variety of technologies, such as hand tools, measuring instruments, and calculators, should be an integral component of scientific investigations. The use of computers for the collection, analysis, and display of data is also a part of this standard. Mathematics plays an essential role in all aspects of an inquiry. For example, measurement is used for posing questions, formulas are used for developing explanations, and charts and graphs are used for communicating results.

12ASI2.4 Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations and communicating results

Science and Technology (12EST)

12EST1.1 Identify a problem or design an opportunity. Students should be able to identify new problems or needs and to change and improve current technological designs.

12EST1.2 Propose designs and choose between alternative solutions. Students should demonstrate thoughtful planning for a piece of technology or technique. Students should be introduced to the roles of models and simulations in these processes.

12EST1.4 Evaluate the solution and its consequences. Students should test any solution against the needs and criteria it was designed to meet. At this stage, new criteria not originally considered may be reviewed.

12EST1.5 Communicate the problem, process, and solution. Students should present their results to students, teachers, and others in a variety of ways, such as orally, in writing, and in other forms - including models, diagrams, and demonstrations.

Science in Personal and Social Perspectives (12FSPSP)

12FSPSP3.1 Human populations use resources in the environment in order to maintain and improve their existence. Natural resources have been and will continue to be used to maintain human populations.

12FSPSP4.2 Materials from human societies affect both physical and chemical cycles of the earth.

12FSPSP4.3 Many factors influence environmental quality. Factors that students might investigate include population growth, resource use, population distribution, overconsumption, the capacity of technology to solve problems, poverty, the role of economic, political, and religious views, and different ways humans view the earth.

12FSPSP6.1 Science and technology are essential social enterprises, but alone they can only indicate what can happen, not what should happen. The latter involves human decisions about the use of knowledge.

Mathematics Standards (9-12) (http://www.nctm.org/standards/content.aspx?id=4294967312 )

Number and Operations - Compute fluently and make reasonable estimates:

• develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
• judge the reasonableness of numerical computations and their results.

Algebra - Use mathematical models to represent and understand quantitative relationships

• identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
• draw reasonable conclusions about a situation being modeled

Measurements - Understand measurable attributes of objects and the units, systems, and processes of measurement

• understand relationships among units and convert from one unit to another within the same system (6-8);
• make decisions about units and scales that are appropriate for problem situations involving measurement
• use unit analysis to check measurement computations.

Process Standards

• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
• Recognize and use connections among mathematical ideas
• Recognize and apply mathematics in contexts outside of mathematics
• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems
• Use representations to model and interpret physical, social, and mathematical phenomena

National Geography Standards
(http://www.nationalgeographic.com/xpeditions/standards/matrix.html )

• How to Use Maps and Other Geographic Representations, Tools, and Technologies to Acquire, Process, and Report Information from a Spatial Perspective.
• How to Analyze the Spatial Organization of People, Places, and Environments on Earth’s Surface
• The Physical and Human Characteristics of Places
• The Characteristics and Spatial Distribution of Ecosystems on Earth’s Surface

## Assessment

Completed worksheets with discussion questions should be submitted by each student to be graded.

## Other Resources

MS Excel Workbook

MS Excel worksheet used for itinerary and calculations: vacation-GHGs.xlsx

Travel information sources

Fuel economy of automobiles: http://www.fueleconomy.gov/

Flying distances:  www.webflyer.com/travel/mileage_calculator/

Driving distances:  www.mapquest.com