Gold Seal Lesson:
Does The End Justify The Means?

Copernicus Education Gateway

 

Subject:

Mathematics

Grade:

 

 

9-12

 

 

ICLE Standards:

 

 

Data Analysis and Statistics:  Collect, organize, analyze, and interpret data

 

 

Performance Task:

 

 

George's grandfather was a coal miner. Most of his mining experience was in a drift mine. Drift mines are tunnels dug into the mountain to a seam of coal. This type of mining is very dangerous. There is always the danger of a "fall-in." Pockets of natural gas and ventilation are other dangers associated with drift mining. 

By the time George's father was old enough to start to work, strip mining was a new way of extracting coal from the mountains. Heavy equipment would gouge out the side of a mountain to expose a seam of coal. Like drift mining, strip mining had some serious problems. Strip mining was ruining the environment in the area until strict laws were passed to help preserve other natural resources.

The purpose of this activity is to have students gain knowledge and understanding of the environmental, social, and economic effects of mining. Students will develop a position paper on the issues that will include the effects of irresponsible mining and plans for reclamation of a mined area.

Procedure:
1. Students will work in groups of four to form a mining company after locating and reading information on the effects of mining on the environment.

2. Each group will secure one-half piece of a poster board.

3. Draw a circle in one corner of the board 30 centimeters in diameter.

4. Draw another circle in the opposite corner. The petri dish can serve as a template to draw this circle. Label this circle Coal. Draw a third circle, using the petri dish as a template, beside the Coal circle. Label this circle Slate.

5. In the large circle, place a layer of birdseed one-centimeter thick. Do not get any of the birdseed outside the perimeter.

6. In the center of the birdseed, place 50 dried beans. Arrange the beans in five rows of ten beans. Be sure to keep them as close to the center as possible. Cover the beans with sunflower seeds.

7. Pour birdseed over the center of the circle. Allow the birdseed to form a pile (mountain) about ten centimeters high. Again, make sure none of the birdseed gets outside the perimeter.

8. Place the petri dish at the foot of the mountain on a diagonal from the corner where the two smaller circles are located.

9. Fill the petri dish with water, being careful not to overfill.

10. Each team will begin the mining process. A student will use the spoon to dig to the sunflower seed. The sunflower seed represents slate. Slate is a type of rock that usually is found around a seam of coal. The slate has to be removed before the coal can be mined. The slate must be piled in the circle labeled Slate. Each sunflower seed represents 100 tons of slate. Slate has no economic value. The mining process lasts 15 seconds. Fifteen seconds equals one year of operation in this activity. The dried beans represent the coal. Each bean mined equals 10,000 tons of coal. The value of the coal is $35 per ton. The mined beans are to be placed in the circle labeled Coal. Students are to record their progress at the end of each 15-second interval. 

11. This process is repeated until all the "coal" and "slate" has been mined.

12. Any birdseed that is outside the perimeter must be returned to the mountain. This event must also be timed in 15-second intervals. 

13. Any birdseed in the petri dish (lake) must be returned to the mountain. This event must also be timed in 15-second intervals.

14. The slate must be returned to the mountain. Also time this event in 15-second intervals.

15. The mountain must be restored to its original contour. This event must be timed.

16. Figuring that the operating expenses for mining coal runs $1,000 dollars per day, what was your group's profit?

17. Graph the results of your operation. Place years on the horizontal axis and tons of coal mined on the vertical axis. Compare the results of your company with the other companies in the class. 

18. Determine the cost of reclamation. What would your company's profits have been if you were not required to restore the land? Judge whether or not the expense of reclamation was worth the effort. Write a position paper and be prepared to defend it.

19. Create a plan on how to reclaim the land and increase the company's profits.

Materials needed: Poster board Petri dish
Plastic teaspoons Dried beans
Sunflower seeds Birdseed
Stopwatch or other timing device 

 

 

Knowledge / Skills:

 

 

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. M.1

Understand the best procedures for statistical data collection, organization, and display. M.5 

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min). Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. M.33

Participate, sometimes leading, in group meetings by contributing, taking turns speaking, and working toward a common goal. ELA.20

Define a position on a controversial topic and write a persuasive essay or make an oral presentation likely to persuade a specific audience to change an opinion or take a particular action. ELA.27

Understand the human impact on the environment through pollution (air, water, and soil), and ways to improve it through education, research, laws, and conservation. S.10

 

 

Rubric:

 

 

Rate each of the statements below using this scale:

4 POINTS: Excellent: The student worked above minimum requirements of the assignment and demonstrated mastery of the subject, topic, or principle with little or no help or coaching.


3 POINTS: Very good: The student worked above minimum requirements of the assignment and demonstrated mastery of the subject, topic, or principle with some coaching and help.


2 POINTS: Good but needs improvement: The student met only the minimum requirements of the assignment. He or she did not demonstrate mastery of the subject, topic, or principle and needed considerable coaching and help.


1 POINT: Poor: The student did not meet the minimum requirements for the assignment even with considerable coaching and extra help.

The student acquired, allocated and used materials efficiently in completing the activity. 

The student participated as a member of a team and worked well with other members of the group. 

The student communicated ideas to justify his or her position on issues. 

The student worked toward agreements to resolve divergent thinking in the operation of their company. 

The student acquired and evaluated information from participating in this activity as evidenced in his or her required finished products. 

The student effectively used a computer to make graphs and write a position paper. 

The student located, understood, and interpreted written
information concerning mining and the environment. 

The student performed basic computations and chose the appropriate mathematical techniques. 

The student used creative thinking to generate new ideas as evidenced by the increase in efficiency of the company's operation. 

The student recognized problems in the operation of his or her company and devised a plan for solving it. 

The student discovered a rule or principle underlying the relationship between two or more entities as evidenced by understanding the relationship between the environment and economics. 

 

 

 

Keywords:

 

 

STATISTICS
DATA ANALYSIS
DATA COLLECTION
GRAPHS
INFERENCE
MEASUREMENT
COMPUTATION
EXPOSITION
TEAMWORK
MODELS AND CONSTRUCTION

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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