math analysis Exp & Log Functions webquest

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Embark on a
WEBQUEST:
You Be The Leader!
1
Embark on a WEBQUEST:
You Be The Leader!
THE INTRODUCTION.
Consider these facts and questions:
1. On August 9, 2005, the United States Fish & Wildlife Service determined that the
Northern Sea Otter was a “threatened” species under the Endangered Species Act. The
sea otter is recognized as a “keystone species,” because its life and livelihood are
essential to the integrity and stability of its marine environment.
http://ecos.fws.gov/speciesProfile/SpeciesReport.do?spcode=A0HK
How many years will elapse before the sea otter is endangered, or
extinct? What steps may be taken to preserve the sea otter, and
other threatened species, and enhance opportunities for population
growth?
2. On March 11, 2011, an earthquake and tsunami caused severe damage to several nuclear
reactors in northeastern Japan. http://www.guardian.co.uk/world/2011/may/24/japannuclear-plant-more-meltdowns. On the one hand, nuclear energy, and specifically
electricity generated by nuclear reactors (such as the power plant in nearby Surry County,
Virginia), may be the answer to the ever-increasing energy needs of today’s global
economies. On the other hand, radioactive materials, the fuel sources for nuclear power
generation, pose significant risks to humans and our environment. When radioactive
materials are depleted, the waste products remain hazardous, and the disposal of
radioactive waste is costly. Radioactive materials decay at determinable “half-lives,” so
they may remain in our environment for many years in the future. For example, the halflife of radioactive iodine, a byproduct of many nuclear reactors, is a mere 60 days. But
the half-life of uranium II is 250,000 years.
http://www.mcclatchydc.com/2011/03/17/110645/us-nuclear-plants-store-morespent.html
How can we predict the time periods during which these radioactive
materials will remain dangerous? How do we plan for the safe
disposal of such materials? What will be the costs?
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3. Immigration has a major effect on the size, distribution, and composition of the U.S.
population, and its role has increased because national birth and death rates are relatively
low. Immigration contributed at least a third to the total population increase between
1990 and 2010, as the number of foreign-born U.S. residents rose from almost 20 million
to over 40 million. The number of foreign-born persons (the first generation) living in the
United States is projected to continue to rise increase throughout the 21st century.
http://www.census.gov/prod/2011pubs/acsbr10-16.pdf
What are the effects of global and United States
population growths? How do we predict global
population growth, and the conditions caused by
such growth? How do migration and immigration
trends and policies impact societies, such as the
United States? Is there a need to limit population
growth around the world?
4. “The largest recorded earthquake in the United States struck
Prince William Sound, Alaska on Good Friday, March 28,
1964. It is estimated that there are 500,000 detectable
earthquakes in the world each year. 100,000 of those can be
felt, and 100 of them cause damage.”
http://earthquake.usgs.gov/learning/facts.php
The magnitudes of earthquakes are measured by seismologists
on the Richter scale, and the data are analyzed both to predict
levels of risk from earthquakes and to recommend courses of
action to limit the loss of human life and property. How does the
Richter scale work? What does it tell us? How can earthquake
measurements be utilized to make the world a safer place?
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5. “In the absence of environmental constraints, a population of organisms reproducing at
their full potential would rapidly cover the surface of the earth. However, it is clear that
most biological populations do not grow in an uncontrolled, explosive way. Instead,
limitations in resources set a limit above which continued population growth does not
occur. Resources that might be limiting include sunlight, space, nutrients, pollinators,
shelter from weather or predators, or other factors. The availability of such resources will
determine the carrying capacity, the maximum population size that resources can
sustain. The abundance of other species that function as predators, parasites, or
competitors also may limit population growth.”
http://dbs.umt.edu/courses/biol103/labs/Christian/12a_populationgrowth.htm
What are the implications of unfettered, or perhaps
environmentally hazardous, population growth (for example,
life-threatening bacteria)? What models are useful to predict
benefits and dangers? What steps may be implemented to
address these challenges?
6. The financial well-being of individuals, families, businesses, and even nations, turns on
the return received from the investment of money, tangible assets and other resources.
Predicting those returns, and being able to plan for any increases and decreases, enables
us all to think about college, home ownership, increased wages and salaries, business
ownership, or retirement.
http://www.moneychimp.com/articles/finworks/fmfutval.htm
http://www.vanguard.com/bogle_site/sp20050210.htm
How are the return on investments (i.e., savings accounts,
stocks, bonds, mutual funds, real estate) calculated? How may
we analyze rates of return data to plan for our futures, or that of
our family, community, state, or nation? What are the
implications of varying rates of return to our well-being?
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In this WebQuest, you will explore in depth one of these topics (or another topic of your
own choosing – with my approval in advance - requiring the application of exponential and/or
logarithmic functions). You will research and investigate your topic on the Internet, determine
the issues, learn how mathematics, specifically exponential and logarithmic functions, helps
describe and resolve the issues, make predictions about what will happen in the future, and
provide recommendations to effectively address the issues.
5
Embark on a WEBQUEST:
You Be The Leader!
THE TASK.
You have been selected to represent Virginia at a conference in Washington, D.C. in July,
2013. You will be one of 51 high school students, one from each state and the District of
Columbia, making presentations to the leaders of Congress on solutions to the pressing global,
economic, and environmental issues confronting your generation. Your goal is to persuade these
national leaders to draft and adopt legislation which confirms your findings and implements your
recommendations.
Your presentation must be accurate, comprehensive, and persuasive. Your factual
assertions must be supported by statistical data and the application of sound mathematics. Your
presentation must reflect both an in-depth analysis of the issues and a reasonable evaluation of
the options for action. Finally, your policy recommendation(s) must be, in your judgment, the
best course of action, based upon your research, analysis, and evaluation.
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Embark on a WEBQUEST:
You Be The Leader!
THE PROCESS.
To accomplish this task, and to prepare an accurate and persuasive presentation, you will
undertake these activities:
1. Select one (1) of the global, economic, or environmental fields of study described in
the Introduction section. For example:
a. Identify a species of wildlife (flora or fauna) threatened with extinction, or at
substantial risk of harm in its environment (find a newly-threatened species absolutely NO projects on Northern Sea otters will be accepted!);
b. Explore the current status of nuclear power generation in the United States (or
the world), and the problems of disposing of nuclear waste;
c. Select a country with a relatively rapidly growing human population, and
explore the social and economic issues associated with such growth;
d. Collect a list of some the great earthquakes in history, learn how to measure
their magnitudes, and identify the risks we live with and the lessons we have
learned;
e. Identify some types of bacteria or other organisms which grow rapidly,
threatening their environment and other species; or
f. Investigate the realm of finance, investment returns, and economic growth:
what are the issues; how do we sustain economic growth; why is investment,
and the accumulation of interest, so important?
NOTE: You may select another topic or phenomenon in which you are
interested, provided it is explained or analyzed through exponential or logarithmic
relationships. If you want to identify such topics, I suggest you explore Chapter 3
in our textbook: each section’s problem sets contains some real world topics
relevant to our study of these types of functions (i.e., the loudness of sound; music
scales; light intensity in astronomy; etc.).
2. Provide Ms Lighthart the topic you have selected on the attached form ON OR
BEFORE FRIDAY, DECEMBER 7 , 2012.
3. Develop a plan and conduct research on your topic on the web. I suggest these steps:
a. Review Chapter 3 in our textbook and examine the examples of these real
world issues described in the problems for each section.
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b. Visit the suggested websites listed in the Resources section of this WebQuest.
For each topic, the listing is simply a beginning point: follow links in those
sites as dig deeper into your topic; and use some Internet search engines
(Google.com, Ask.com, etc.) to gather more information. You want to find
accurate data about the issue you are researching, as well as descriptions or
analysis of the ramifications of the data. Keep searching until you are
satisfied you have the data and that you understand it.
c. Keep a list of the websites you will cite in a Table of Resources to support
your presentation to the panel.
d. While the panel members at the conference anticipate that your primary
resources will be websites, you may utilize any other resources in the LHS
Media Center, public libraries, encyclopedias, or other media. One cautionary
note: make sure you are using reliable sources (no Wikipedia, for example).
4. Identify the critical issue(s) to be resolved. The panel of congressional leaders wants
to know why your topic is critical: What specific situations exist? What important
matters must be addressed? What are the potential risks or hazards that require
meaningful action?
5. Investigate the facts on your selected issue(s). Find and study the statistics.
Determine the exponential or logarithmic equations which best express those
statistics.
6. Analyze your data and the equations. Do the
equations accurately express or estimate the
behavior of the phenomena you are studying? How
may the equations be used to make predictions of
future behavior?
7. Evaluate the options available or currently under
study (based on your research) to address your
issue(s). Which option is best? Why? Be prepared
to explain your reasons.
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8. Create a presentation you will take to Washington, D.C. While the conference
leaders anticipate that you will take advantage of PowerPoint and other technology
tools, you may choose any form or combination of forms of media to make your
presentation. As you create this critical component of your presentation, please
remember to include these elements:
a. Tables and plots of your data;
b. Graphs of your equations;
c. Pictures or other visual aids to explain your issue;
d. Narrative report with specific, identified sections as follows: “Issue(s)”:
“Findings”; “Analysis”; “Options”; and “Recommendations”.
e. A Table of Resources, identifying all sources utilized in preparing your
presentation.
9. Conduct a self-assessment of your presentation by completing the attached rubric.
This is the same rubric Ms Lighthart will utilize to assess your presentation and
provide you a TEST CATEGORY grade for this WebQuest.
10. Make your presentation to your class according to the schedule provided by Ms
Lighthart
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Embark on a WEBQUEST:
You Be The Leader!
SUGGESTED RESOURCES.
1. Function Graphing Tools – Online:
a. Online Graphing Calculator:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
b. Seeing Math Online Function Graphers – creates graphs and solves equations
graphically for a variety of algebraic functions. Students may use this site to create
and save graphs of their data and equations.
http://seeingmath.concord.org/sms_interactives.html
2. Human Population Studies – websites for populations data, trends and other
information:
a.
Population Reference Bureau – A wealth of information on global
population issues from a well-respected NGO:
http://www.prb.org/
b.
United States Census Bureau – Official website for U.S. population and
demographics:
http://www.census.gov/
c.
Internet World Stats – a compendium of population, Internet usage, and
other global demographic data:
http://www.internetworldstats.com/
d.
Office of Population Research at Princeton University – population
statistics and related data, research projects, related Internet links:
http://opr.princeton.edu/
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3. Bacteria Growth – websites with data, explanations and other information on
the increase and decrease of bacteria populations. Students will utilize these sites
for research, experimentation, and analysis:
a.
Math Warehouse – visual bacteria growth activity.
http://www.mathwarehouse.com/exponential-growth/exponential-growthactivity.php
b.
MicrobiologyBytes.com – a virtual lab experiment with results to be
plotted.
http://www.microbiologybytes.com/LabWork/bact/bact1.htm
c.
Cells Alive – Interactive examination of bacteria and other cell growth.
http://www.cellsalive.com/ecoli.htm
d.
Online Textbook of Bacteriology – Online resource to investigate the
phases of bacterial growth.
http://textbookofbacteriology.net/growth.html
4. Radioactive Decay – websites providing data, explanations, and discussions of
issues related to the decay of radioactive materials and the environmental, waste
recovery, and other issues associated with these materials. Students will utilize
these sites for research, experimentation, and analysis:
a. Lawrence Berkeley National Laboratory / Basic Nuclear Science
website for information and resources on nuclear power:
http://www.lbl.gov/abc/Basic.html
b. Science Education Research Center of Carleton College –
Radioactive Decay:
http://serc.carleton.edu/quantskills/methods/quantlit/RadDecay.html
c. U.S. Nuclear Regulatory Commission – Official information
on nuclear power and other energy sources:
http://www.nrc.gov/
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5. Investments and Debt – websites providing data, resources, explanations and
other information on financial interest compounding and the costs of borrowing
money. Students will utilize these sites for research, investigation, and analysis:
a. Get Objects / Interest – Interactive website to learn about financial
interest rates and growth of principal:
http://www.getobjects.com/Components/Finance/TVM/iy.html
b. The Law of Accelerating Returns – financial and investment information:
http://www.kurzweilai.net/articles/art0134.html?printable=1
The Math Forum @ Drexel University – Interest – Interactive learning site
on the mathematical aspects of interest and investments:
http://mathforum.org/library/drmath/sets/high_interest.html
6. Endangered Species – websites for data, trends. Governmental activities and
related information on endangered animal and plant species. Students will
utilize these sites for research, investigation, statistical data, and analysis:
a.
U. S. fish and Wildlife Service – Endangered Species Program –
Official government site dedicated to implantation of all federal
endangered species programs:
http://www.fws.gov/endangered/
b.
The National Wildlife Foundation – NGO clearinghouse of endangered
species information:
http://www.nwf.org/
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7. Earthquakes – websites for data, trends, research. Governmental activities and
related information on earthquake hazards and planning. Students will utilize
these sites for research, investigation, statistical data, and analysis:
a.
U. S. Geological Survey Earthquakes Hazards Program – Official site
for earthquake information, research and analysis:
http://earthquake.usgs.gov/learning/facts.php
b.
Nevada Seismological Laboratory – Clearinghouse for earthquake
statistics, information, and preparedness:
http://www.seismo.unr.edu/
c.
U. S. Federal Emergency Management Agency Earthquake Disaster
site – information, recommendations, and Internet links for earthquake
disasters:
http://www.fema.gov/hazard/earthquake/index.shtm
d.
Society for Research and Initiatives for Sustainable Technologies and
Institutions / Earthquake Disaster Management Information System –
NGO clearinghouse for disaster preparedness:
http://www.sristi.org/dmis/facts
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Embark on a WEBQUEST:
You Be The Leader!
THE CONCLUSION.
As you finalize your presentation, pack your suitcases, and make your final preparations
for your travel to Washington, D.C., reflect on what you have accomplished:
1. You have gained a deeper insight into a pressing global problem;
2. You have determined how exponential or logarithmic functions, and their respective
graphs, appropriately express the behavior of the phenomena you have studied;
3. You have used your knowledge to make reasonable predictions about the future, and
to devise policy recommendations to address these future challenges; and
4. You have created a persuasive presentation of your findings and recommendations.
The leaders of Congress anxiously await your presentation.
While they will enthusiastically receive your report, they
undoubtedly will have many questions. You must be
prepared to be persuasive: be sure you can answer their
inquiries. Why is the phenomenon you have selected so
important? What data supports your position?
How can you assure them that your predictions are
accurate? Before they vote to commit substantial resources
to your issue, they will want you to answer this final
question: how can you be confident your solution will
work?
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Embark on a WEBQUEST:
You Be The Leader!
CLASS PRESENTATION SCHEDULE.
BLOCK ____
Monday, March 5, 2012
Tuesday, March 6, 2012
Wednesday, March 7, 2012
Thursday, March 8, 2012
Friday, March 9, 2012
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Embark on a WEBQUEST:
You Be The Leader!
TOPIC SELECTION FORM.
Complete and Submit this Form to
Ms Lighthart on or before
December 7, 2012.
Name: _________________________
Block: _________
TOPIC SELECTED:
__________________________________________________________________
__________________________________________________________________
PRELIMINARY ISSUE(S) IDENTIFIED:
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
WEBSITES AND OTHER POTENTIAL RESOURCES:
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
PRESENTATION FORMAT IDEAS:
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
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