MATHEMATICS ACTIVITIES

Greenhouse Gases


Objectives-Mathematics

1. Students will design and construct three-dimensional models illustrating the heat-trapping abilities of the major greenhouse gases.

2. Students will be able to interpret data related to electrical appliances to determine the amount of CO2 emission given off in the production of the electricity needed to operate the appliances.

3. Students will be able to identify ways in which their personal use of energy contributes to carbon dioxide emissions.

4. Students will be able to use mathematics to help them convince people of the importance of tree-planting to help combat high CO2 levels in our atmosphere.

Module Overview - Mathematics

The mathematics portion of this unit revolves around the greenhouse gases. Students are introduced to the different heat-trapping abilities of the major greenhouse gases. The students are challenged to build three-dimensional models illustrating this differing heat-trapping ability. In Activity 2, students keep an Energy Diary which includes a record of all the activities they engaged in, over a one-day period, requiring the use of electricity. They are then able to analyze this data to determine their total contribution to the CO2 in Earth's atmosphere as a result of their use of electricity for that day. In the final activity, students discover the CO2-absorbing ability of trees. Mathematics is used as a tool to help the students convince others to go out and plant a tree.

Suggested Teaching Strategies

As students complete the science portion of this unit, they gain experience in testing for the presence of carbon dioxide. They learn the major sources of excess carbon dioxide in our atmosphere as well. At this point, students may develop (or may already have developed) the attitude that greenhouse gases are not related to them...they have to do with big cities and factories. The mathematics activities are designed to show students that this is not the case. Each person contributes to the high CO2 levels in Earth's atmosphere, especially where high amounts of electricity are used and lots of driving is involved.

Begin the unit by asking students what they know about global climate change and greenhouse gases. They will likely have lots of ideas to share, especially if they are working on the science section of this unit. There are about 30 different gases considered to be greenhouse gases. Each of these traps excess heat within the Earth's atmosphere. The main culprits of global warming are thought to be carbon dioxide (CO2), chlorofluocarbons (CFC's), nitrous oxide (N2O), and methane (CH4). Each of these four gases is present in the atmosphere in differing amounts. To make matters even more complicated, each gas traps a different amount of heat and each gas stays active in the atmosphere for a different number of years. Both the amounts and the heat-trapping ability of the gases are taken into account in developing graphs like the one shown below.

This graph shows that CO2 certainly may play a large role in global climate change. But you cannot tell anything about the amounts of CO2 in our atmosphere, its heat-trapping ability, or how long it stays in the atmopshere from this graph. In the first activity, students will be given some of this information and will develop models to illustrate the relative heat-trapping ability of each of the four major greenhouse gases. Share this information with students by asking them which gas is present in the largest amount, according to the pie graph. They will, of course, say CO2. However, this is not the case. It will be difficult for students to see that the graph does not mean "amounts of each gas," it means "amount of damage or warming" caused by each gas. Activity 1 will help clear up some of this confusion by having students illustrate the different heat-trapping abilities of each type of gas.


Heat Traps

Teacher Notes

Objective:
Students will design and construct models illustrating the heat-trapping abilities of the major greenhouse gases.

Materials:
graph paper
scissors
calculators
tape
markers
scratch paper

Background:
History tells us that the Earth has been much warmer than it is now, has had more CO2 in the atmosphere, and that no humans were around to cause these changes. The amount of CO2 not only changes from year to year, but from place to place and season to season.

Carbon dioxide is thought to be responsible for about 55 to 60% of the global warming trend. Increased CO2 from fossil fuel burning along with reduced CO2 removal from deforestation have resulted in an increase in CO2 levels in the atmosphere from about 314 parts per million in 1958 to about 348 in 1988.

Chlorofluorocarbons (CFC's) are thought to be responsible for about 25% of the global warming trend. CFC's are used in air conditioners and refrigerators, in the production of plastic foams, in various industrial processes, and in aerosol propellants. Use of CFC's in aerosal cans has been banned in the United States since 1978. Many other countries have banned the use of CFC's as well.

Methane (CH4) is thought to be responsible for about 12% of the global warming trend. It is produced by decomposing matter and in the digestive tracts of cattle, sheep, termites, and other organisms. Some methane escapes from industrial and other man-made sources.

Nitrous oxide (N2O) is responsible for about 6% of the global warming trend. It is produced by the breakdown of nitrogen fertilizers, livestock wastes, and by burning of various fuels. Together, these gases are believed by some scientists to account for over 90% of the global warming trend.

Methane decays more rapidly in the atmosphere than does CO2. A single CO2 molecule may remain in the atmosphere for 250 years. It takes about 10 years for a molecule of methane to break down in the atmosphere. One CFC molecule may remain in the atmosphere for 75 years. A nitrous oxide molecule may remain in the atmosphere for 175 years. Even when these figures are taken into account, carbon dioxide is still considered to be the largest contributor to the greenhouse effect.

Suggested Teaching Strategies:
The purpose of this activity is to illustrate the relative heat-trapping ability of each of the major greenhouse gases. This exercise will help students to better grasp the process of making models to scale.

Begin the activity by asking students to name the major greenhouse gases. If students have already completed the science portion of this module, they will likely know these gases. If they are unable to name the four major greenhouse gases, list them on the chalkboard. Behind each name, write the chemical formula. Ask students to imagine that these gases act like blankets, holding heat in the Earth's atmosphere. Each "gas blanket" has a different ability to trap heat. Their job, in this activity, is to help us better picture the amounts of heat each gas blanket can trap.

Students are likely to have difficulty comparing the heat trapping ability of each gas to a standard. In this case, the standard should be CO2 since all other gases are compared to CO2. Provide several examples to show students how this concept works. For example, ask students what they know about the average lifetime of a dog. Most kids will know that dogs live an average of about 14 years. By using a standard, we sometimes say things like, "that is equal to 72 years in dog years.'" Do not use the greenhouse gases to illustrate how camparisons to standards work. The challenge will be for them to figure this out for themselves.

Challenge students to find the most efficient way to make their models. For example, it would be very difficult and time-consuming to tape together 20 separate cubes to illustrate the heat-trapping ability of methane. However, students can easily cut out a sheet of graph paper that is 4 cubes tall, but goes the length of the paper. By simply creasing the paper in the right places and folding the creases, students can make 10 cubes that are connected in one piece.

Because this activity has the potential to use a great deal of graph paper, students have been informed on the student direction page, that they may have only three complete sheets of graph paper, but an unlimited (within reason) supply of scratch paper. This will necessitate that students come up with a way of figuring out what to do. They will likely think of making a template using their graph paper or simply measuring with a metric ruler. Resist the temptation of giving them hints to solve this dilemma. They will benefit more from the opportunity to problem solve!

Encourage students to plan their models. Once the CO2 cube has been constructed, students should calculate the number of sheets of paper needed to illustrate the heat-trapping ability of CFC's.

Sample Answers to Summing Up:
1. Because CFC's have the ability to trap a great deal of heat, it is important that the level of CFC's in our environment be kept as low as possible.

2. Student answers will vary, depending on the size of the CO2 cube used as their standard.

Home/Community Connections:

Extensions:

Heat Traps

Student Page

Problem:
How can you build models to show how much heat is trapped by different types of greenhouse gases?

Materials:
3 sheets of graph paper
scissors
tape
markers
calculator
scratch paper

Let's Investigate:
What does eating fast food have to do with sunburns and skin cancer? Every time you pick up a hamburger in a plastic foam container, you are increasing your chances of impacting global warming, getting a severe sunburn and, possibly, skin cancer. As the plastic packaging slowly breaks down, the plastic gives off chlorofluorocarbons (CFC's). CFC's are chemicals that trap excess heat in the Earth's atmosphere. One CFC molecule is capable of trapping 10,000 times more heat than one molecule of carbon dioxide. CFC's cause further damage by attacking the ozone layer. Each chlorine atom in a CFC molecule can attack and destroy 100,000 ozone molecules. Our fast-food society is just one thing that is upsetting the atmospheric balance that has protected the Earth for millions of years.

What about the other greenhouse gases? Do they all trap the same amount of heat? Definitely not. Below is a table showing the relative amount of heat trapped by the different greenhouse gases, compared to carbon dioxide's heat trapping ability.

Greenhouse Gas -- Heat Trapping Ability Compared to CO2
Carbon Dioxide(CO2) -- 1
Methane(CH4) -- 20 -30
Nitrous Oxide(N2O) -- 180
Chlorofluorocarbons(CFCs) -- 10,000

Your job in this investigation, is to build cubes that will show the different heat-trapping abilities of the major greenhouse gases. All the greenhouse gases listed in the table above are compared to the heat trapping ability of carbon dioxide. This means you can represent CO2 by one square cube. If a particular gas, GAS X, is known to trap three times the amount of heat as CO2, you would build a model for GAS X that is the size of three CO2 cubes.

Using the graph paper provided by your teacher, prepare cube-shaped models that show the amount of heat trapped by each of the different greenhouse gases, compared to carbon dioxide. You do have one extra challenge, you may have only three sheets of graph paper for your models. You may, however, use scratch paper for your models. Begin by building your CO2 cube. Once that is done, determine the number of sheets of paper needed to show the heat-trapping ability of a CFC molecule. If it requires too much paper, scale down your CO2 cube.

Once your models have been completed, add some color to the models. Make certain that each model is clearly labeled. Devise some interesting way to display your models.

Summing Up:
1. Based on the amount of heat trapped by the different greenhouse gases, which gas would you conclude is most important to keep at low levels in our atmosphere? Explain your choice.

2. How many sheets of graph paper would be needed to show how much heat is trapped by a gas that traps 25,000 times as much heat as does CO2?


Dear Diary.....

Teacher Notes

Objective:
Students will be able to identify ways in which their personal use of energy contributes to carbon dioxide emissions.

Materials:
calculators
table to figure CO2 emissions (Appendix B)

Background:
Carbon dioxide is considered to be the largest contributor to the greenhouse gases. How much coal does it take to turn on each light bulb in your home? And, how much of the carbon dioxide in our atmosphere can we blame on that one light bulb at your house? More than half of the electricity produced in this country comes from utility plants powered by coal. Coal burning is our largest source of carbon dioxide, the major greenhouse gas.

To figure out how electricity use contributes to the greenhouse effect that many scientists believe is already warming our planet, it helps to understand how energy use is calculated. Electric companies bill for the number of kilowatts. One kilowatt is equal to 1,000 watts. If a 100 watt light bulb is left on for 10 hours, one kilowatt hour (KWH) of electricity is used. Suppose a 100-watt bulb, serving as an outside night light, is left on for eight hours a night, 365 days a year. This bulb consumes 292 KWH of electricity a year ((365 x 8 x 100)/1,000 = 292 KWH). By knowing the watt rating of a particular appliance and the amount of time the appliance is used for, it is possible to estimate the amount of carbon dioxide emitted in the process of producing the electricity needed to "power" the appliance. Of course this assumes that all of the electricity in your area is produced by coal-burning power plants. The calculation also necessitates averaging the CO2 emissions based on the different grades of coal that are burned throughout the United States. Obviously, students will be getting an estimate, rather than an exact answer.

Suggested Teaching Strategies:
In this activity, students become familiar with one of the major sources of carbon dioxide: the production of electricity. They identify ways in which they might decrease their contribution to the carbon dioxide in our atmosphere by decreasing their use of electricity.

This activity helps to show students their possible impact on global warming. Most people believe that air pollution is a problem caused by factories and cars. This makes them feel they can do nothing to help alleviate air pollution problems. However, this is not the case. The largest contributor to excess carbon dioxide in the atmosphere is from the burning of fossil fuels. We burn fossil fuels directly in our cars. But our largest contribution to excess carbon dioxide in the atmosphere is from our use of electricity. The electricity we use here in Iowa is generated primarily by burning coal. Every time we use electricity, we are contributing to the greenhouse gases.

The directions for this activity are most easily delivered to students orally. Because of this, no student page is provided for this activity. Begin the activity by presenting students with this challenge:
Your Energy Diary Challenge: How much CO2 do you put into the environment each day by your use of electricity?

Students can calculate the approximate amount of carbon dioxide added to the atmosphere each time they use electricity in their home. All they need to know is the watt rating of the appliance and the amount of time they use the electricity. Students may need assistance in calculating the amounts of CO2 emissions in cases where they use an appliance for only a portion of an hour. You may want to provide several examples of how students can determine the total CO2 emissions, for example, when an appliance is used for only 5 minutes.

As students are keeping their energy diary for one day, they may list using some appliances that are not listed in the table. This can still be figured into their daily electricity use. Ask them to read the watt rating off the appliance. Use the table in Apendix B to illustrate how the conversion to pounds of CO2 can be accomplished. The example (see the sample diary data table) of the electric range can be used to show students how to convert watt numbers to pounds of CO2.

Summing Up Questions:
1. Which four items on your list consumed the most electricity?

2. Which four items consumed the least electricity?

3. If you had to choose 3 items to "go without" for 2 weeks in order to help reduce CO2 emissions, which items would you choose? Explain why you choose each item. How much CO2 did you save over the 2 week period? (Show how you determined this.)

Home/Community Connections:

Extensions:


Slowing the Greenhouse Effect

Teacher Notes

Objective:
Students will determine how trees can help slow the greenhouse effect.

Materials:
calculators

Background:
Shade trees reduce cooling costs in the summer, but don't block out the sun's warming rays in the winter. They also absorb carbon dioxide and prevent it from going to the atmosphere. The process of absorbing CO2 and releasing oxygen is part of photosynthesis.

Suggested Teaching Strategies:
The 13-48 pound range stated for the amount of CO2 absorbed per trees presents an interesting challenge for students. While you may choose simply to use the average of this range, it would be more beneficial for students to set up their own criteria for how to use the numbers. For example, students may want to measure the circumference of the tree trunk one meter above the ground as their standard. They could take a trip around the school ground to see the variation that exists and then set up a scale by which they assign a number from 13 to 48 to different circumferences. You might challenge students to locate the widest and the smallest tree trunks in town and to bring that measure to school. Students may wish to estimate the height of the trees. For example, if the tree is one story or less in height, they might want to assign a number close to 13 to its CO2 absorbing ability. This makes for interesting discussion the student's part, while requiring them to think about scales. It is important, however, that a class consensus be reached. If each student uses a different scale, it will not be possible to compare and pool results.

As students are deciding on which areas to sample, you may want to list several small parks, the school yard, and other key areas in your community. Ask students to volunteer to survey these areas. This would insure a broad sampling of a variety of areas. It would be best if each student chooses different areas to survey.

Appendix B contains a sample data table for this activity. Discuss with the class the types of data needed, then go over the data table with sample data from two students. Notice how the calculations are included as part of the data table. Review this with students before they begin collecting data.

Once all the data has been collected and the calculations completed, ask each person to display their findings on a class poster or on the chalkboard. This would allow students to determine total CO2 absorption by all the trees surveyed by their classmates. Once a grand total has been achieved, students will really get the flavor that the trees in their town do make a difference on helping reduce greenhouse gases.

This would be a good point to introduce some of the extensions. Getting students involved in a plant-a-tree campaign would benefit both the students and their community.

Sample Answers to Summing Up:
1. Some of the reasons students might list include; trees are different sizes due to their age, different trees have different leaf sizes, and each type of tree processes nutrients at a specific rate.

2. Information would be needed on the average number of pounds of CO2 absorbed by a tree in the rainforest. This might require information on the average tree size in the rainforest. Information would also be needed on the average number of trees in an average acre of rainforest.

Home/Community Connections:
Challenge the class to draw a street plan of the downtown area of your city. On the map, mark the places where trees are currently growing. Draw up a plan designed to increase the number of trees in the downtown area. You may want to make Plan A, Plan B and Plan C, each proposing a larger number of trees for the area. As part of the plan, include information on the CO2 absorbing ability of the proposed trees. Mark the locations of the new trees on your map. Be sure to consider the importance of shade on buildings in deciding where to place the trees. (Shade helps reduce the cooling costs of buildings.)

Extensions:

Slowing the Greenhouse Effect

Student Page

Problem:
How much carbon dioxide is removed from the atmosphere by the trees around your home?

Materials:
calculator

Let's Investigate:
A healthy, growing tree absorbs between 13 and 48 pounds of carbon dioxide per year. At the 13 pound rate, one acre of trees absorbs 2.6 tons of CO2 per year. At this same rate, every ton of new wood removes 1.47 tons of CO2 from the air and releases 1.07 tons of oxygen.

You can see that trees play a very important role in removing CO2 from the atmosphere. To put this on a more personal level, let's look at the effect on CO2 levels of trees in your area.

How much CO2 do you think is absorbed by each of the following:

In order to answer these questions, you think you will need some information. Make a list of the information you will need to answer these questions.

You were told that growing trees absorb between 13 and 48 pounds of carbon dioxide each year. But which number do you use; 13 lb, 48 lb, or neither? As a class, set up a scale that will allow you to use both 13 and 48, as well as numbers between these values. After you have arrived at a group decision, write your scale below.

Identify three different areas from which you will collect tree data. They need not be the same as those listed in the question above. Collect your data as a homework assignment. Use the data table below to record your data. Be sure to label the rows and columns to describe the data you are recording. Also use the spaces in the data table to calculate the amount of CO2 absorbed by the trees at each site. Use the scale your class has set up for determining the amount of CO2 absorbed by each tree. Be sure you label your calculations clearly.

Summing Up:
1. The rate of CO2 absorption by each tree is at between 13 and 48 pounds per year. What are some reasons explaining why this figure is not the same for all trees?

2. Rainforests are being destroyed at a rate of over 50 acres per minute. What information would you need to know to be able to determine the amount of CO2 absorption that is lost each minute as these acres are cleared of trees?


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