by Reginald McClain & Kai Ernest
Introduction / Task / Sources / Process / Evaluation / Conclusion
Have you ever wondered what the most silent destructive force on Earth is? It is not a hurricane, earthquake, or even a tornado; it is the slothful inferno of molten rock called a volcano. Volcanoes are mountains or hills formed by the accumulation of materials through one or more openings in the Earth's surface. Within the past 10,000 years, over 1,500 volcanoes have been activated and roughly 539 of them erupted one or more times above sea level. On average, 50 to 60 above sea-level volcanoes worldwide, are active in any given year. Drastically, a volcano's eruption can happen in populated and unpopulated regions, and can be a significant threat to people, property, and agriculture. These dangerous eruptions are the focus of today's activity.
Geologist have predicted that a volcano will erupt on September 21, 2004 at 11:00 a.m. The citizens of Corinth failed to comply with the predictions of the geologist because the volcano at the top of the Philippines has been inactive for several decades. It is the responsibility of the students to assist the citizens of Corinth in determining the time its takes for the lava to reach the boundaries of the valley.
NCTM Principles and Standards for Mathematics Standard 4, Measurement, Grades 6-8: Instructional programs from prekindergarten through grade 12 should enable all students to
-Understand measurable attributes of objects and the unit, systems, and process of measurement
understand relationship among units and convert from one unit to another within the same system
-Apply appropriate techniques, tools, and formulas to determine measurement
solve simple problems involving rates and derived measurements for such attributes as velocity and density
Greenspun, P. (1985-2002). Photo net. Retrieved November 9, 2004, from http://www.photo.net/photo/pcd4229/mirage-volcano-7
Howard, J. M. (2004). Rockhounding arkansas. Retrieved November 9, 2004, from http://rockhoundingar.com/pebblepups/volcano.html
Kingston, G. Extradinary news for fifteen year old. Retrieved November 9, 2004, from http://users.netconnect.com.au/~georgek/EXTRAORDINARY%20NEWS%20FOR%20FIFTEEN%20YEAR%20OLDS/4%20Velocity%20Of%20The%20Sun.htm#_top
Rocks and minerals. Retrieved November 9, 2004, from http://www.rocks-and-minerals.com/more-about-rocks/rocks-that-erupt.htm
State Farm. (2002). Volcano safety tip. Retrieved November 9,2004, from http://www.statefarm.com/consumer/vhouse/articles/volcano.htm
In this activity, we will solve a series of questions that pertain to volcanic eruptions. We will calculate the time its takes for the lava to reach the village, the speed at which the lava would flow, and the distance at which lava would travel. Use the expressions below to solve the following scenarios dealing with the volcanic eruptions.
A. Geologists data show that the Philippine volcano is approximately 3,456 ft from the village. Furthermore, they estimated that the lava flows at a velocity of 15 ft/min. Given this information, how much time would the local citizens have to evacuate the village.
Use the velocity formula in ft/sec to answer question (A) (scroll to formula under the fourth diagram).
B. Suppose the distance from the village to the Philippines is 3,700 ft and it took 25 minutes for the lava to reach the village perimeter. What is the speed at which the lava would flow down the mountain to the village? (Use the above formula to solve this equation.)
C. Now that you know how to calculate time and speed, we can also use the same formula to find the distance, if we know the velocity and time, or rate. Use the same formula to calculate distance, given that the velocity of the lava is 38 ft/min and the time is 10 minutes.
D. Writing Assignment:
There are two options given to you below; choose only one option and write a two to three paragraph detailed essay.
Suppose you are a citizen of Corinth Valley, and reflect on the destruction of the Philippine volcano. How did this eruption affect your life? Explain this event in detail.
How do you think the citizens reacted to the eruption of Philippine volcano? Using your prior knowledge on volcanoes, what suggestions would you give to the citizens of the valley and state the importance of each suggestion.
E. Hands-on Experiment
To better understand how volcanoes erupt, you will construct your own volcano model. All materials will be provided in order to complete this experiment. Follow all directions properly.
A. t= d / v = 3456ft/ 15ft/min= 230.4 min or 4 hrs and 24 minutes
B. v= d /t = 3700ft/ 25min= 148 ft/min or 2 hrs and 47 minutes
C. d= (v)(t)= (38 ft/min)(10minutes)= 380 ft/min2
D. Answers may vary.
E. View students' final model to make sure all directions have been followed.
In this activity, the students used mathematics to solve real-world situations. Through using the velocity formula, students were able to calculate the distance between the village and the mountain, the velocity, and the time of the lava flow. In other applications, students were able to use their artistic skills to construct a volcano (eruption); furthermore, they were able to express their own individual writing style on volcanic eruptions. We hope this lesson was enjoyable, as well as educational.