SPRING 2013 SYLLABUS
ECO 405/590: SUSTAINABLE ENERGY ECONOMICS AND POLICY
Instructor: Sharon (Wagner) Klein
School of Economics
305C Winslow Hall
(207) 581-3174
Office Hours: Tues/Wed 2-3pm or by appointment
Prerequisites
ECO 120 and ECO 121, or ECO 410, or equivalent; or permission
Required Texts
Everett, B., Boyle, G., Peake, S., Ramage, J., 2012, Energy Systems and Sustainability,
Second Edition, Oxford University Press, ISBN: 978-0-19-959374-3.
Boyle, G., 2012, Renewable Energy: Power for a Sustainable Future, Third Edition, Oxford
University Press, ISBN: 978-0-19-954533-9.
To purchase combo pack at reduced price, ISBN: 9780199307449
You are also required to register for TopHat Monocle (see instructions on Blackboard:
“Student Quick Start Guide”)
Course Description
This course presents the economic, environmental, and social implications of energy supply,
distribution, and use in the context of transitioning toward a sustainable energy future. A
variety of energy types are examined including fossil fuels, nuclear power, and a range of
renewable energy technologies including solar, wind, biomass, hydro, and geothermal power.
The effects of energy use on greenhouse gas (GHG) emissions and climate change, on air
and water quality, and on human health are considered along with policies to mitigate these
effects such as carbon prices, emissions targets, efficiency requirements and investments,
and renewable portfolio standards. The effects of import dependence and development of
indigenous renewable energy resources on energy security and regional economic growth
and development are assessed. Alternative future energy paths are developed that are
consistent with environmental stewardship, energy security, and sustainable economic growth
and development.
Course Learning Objective:
Pending UPCC approval, it is expected that this course will meet the University of Maine’s
general education requirement for the areas of Population and the Environment, and
Quantitative Literacyi. The main objective of this course is to expand your understanding of
and reasoning skills related to energy choices, issues, and policies in the context of the varied
social, economic and environmental implications of energy production, distribution and use.
Course Learning Outcomes
1
Upon successful completion of this course, students will be able to:
1. Distinguish between concepts of power and energy and convert between power and
energy units across a wide range of energy resources, technologies and uses.
2. Analyze data from the U.S. Energy Information Administration, International Energy
Agency, and other resources in order to describe the total amount of energy used in
the U.S. and world economies over time, the trends in energy intensity, the trends in
energy prices, and the trends in traditional and alternative energy (TAE) shares
3. Identify the key TAE resources and technologies and describe their development costs,
production structure, market characteristics, and special issues
4. Compare the social costs and benefits of TAE production, distribution and use with
respect to climate change, other environmental impacts, and human health and wellbeing, and explain the basic methods used to arrive at these social cost estimates
5. Explain what “energy security” means, how it relates (or not) to import dependence,
how it can be measured, and how TAE resources and technologies rank in terms of
energy security impacts
6. Explain what a sustainable energy-environment-economy path is, what makes it
sustainable, why there must be transition to it, and what the key features of the
transition are expected to look like (including timing)
7. Compare centralized and distributed energy approaches and explain how each might
be included in a sustainable energy path
8. Use multi-criteria decision analysis to compare energy options and develop
sustainable energy portfolios
9. Describe the key policies that will facilitate the transition and explain the economics of
how the policies will introduce incentives that will support the transition
10. Describe and explain the effects of TAE resources and technologies on economic
growth and economic development including transition effects and those associated
with moving the economy along the sustainable path
11. Identify the key economic development consequences of the development of local
indigenous alternative energy resources
12. Summarize current visions for transitioning to sustainable paths in the U.S., Europe,
the world, and locally
13. Synthesize a vision for transitioning to a sustainable energy future
Grading
Grades will be based on performance on the following assessments:
In-class assignments (lowest 2 grades dropped)
Online quizzes (lowest 2 grades dropped)
Exams (best 2 out of 3)
Final project
25%
25%
30%
20%
100%
All students are expected to attend class each day and be prepared with a calculator, paper
and something to write with. Each day in class, there will be at least one in-class
assignment, consisting of individual or group quantitative analysis, discussions, debates,
individual writing assignments, and games. Quantitative analysis will be graded based on
2
whether the individual or group has obtained the correct answer and used the appropriate
procedure to arrive at the correct answer. Discussions, debates, and individual writing
assignments will be graded using the rubrics presented below. Games will be graded in a
similar fashion to a quiz – the grade will depend on getting the correct answer, providing the
correct explanation, etc. At least one in-class assignment each day (except for possibly guest
lecture days) will require the use of a classroom response program called TopHat Monocle
(see instructions on Blackboard for how to register – the URL for this course in THM is
https://www.tophatmonocle.com/e/582886). The two lowest grades from the set of graded inclass assignments will be dropped. In-class assignments will constitute 25% of the final
grade.
Students are required to complete an online quiz for each set of assigned readings. The
quiz will be listed in the Assignments folder on Blackboard and will be due 1 hour prior to the
start of each class. Each quiz will cover the readings listed on the Course Outline for the
respective class date. Late quizzes will not be accepted. The lowest 2 quiz grades for the
semester will be dropped. Online quizzes will constitute 25% of the final grade.
There will be four in-class multiple-choice exams during the semester. The lowest exam
grade will be dropped, and each of the three highest exam grades will count as 10% toward
the final grade. You will be expected to have a calculator (NOT a cell phone, computer, iPad,
etc) for exams. If you do not have a calculator for exams, you will have to do your
calculations by hand and will receive the same amount of time as everyone else.
Each student will be required to complete a final project, which will consist of the following:
1) a project proposal, 2) a final presentation during the scheduled final exam period, and 3) a
2-page justification report (graduate students enrolled in ECO 590 should check the additional
grading requirements below). More information on the final project will be forthcoming. The
final project will be 20% of the final grade.
In-class assignments and exams, online quizzes, and the final project will cover reading
materials, class lectures and discussions/activities. Late assignments will not be accepted
given the policy of dropping the 2 lowest in-class assignments, 2 lowest online quizzes, and
the lowest exam grade.
Please refer to the Course Outline for expected due dates of most assignments – these due
dates are subject to change if necessary. Any changes to the course outline during the
semester will be announced in class and posted in the Announcements section of
Blackboard.
Final grades will be based on the weighted percentage of points earned. Final grades will be
assigned as follows:
A (93 to 100 percent); A- (90-92.9); B+ (87-89.9); B (82-86.9); B- (80-81.9); C+ (77-79.9); C
(72-76.9); C- (70-71.9); D+ (67-69.9); D (62-66.9); D- (60-69.9); F (59.9 or less).
Classroom policies, late assignments, incompletes
3
Please display your name card on your desk during each class so your classmates and I can
learn your name. Please bring a calculator, paper, and something to write with to every class.
You will be expected to have a calculator (NOT a cell phone, computer, iPad, etc) for exams.
If you do not have a calculator for exams, you will have to do your calculations by hand and
will receive the same amount of time as everyone else. Please turn all cell phones to silent
and only use electronic devices for taking class notes and/or responding to questions via Top
Hat Monocle. Headphones are not allowed in class. Late assignments will not be accepted
given the policy on dropping the lowest exam grade, the 2 lowest in-class assignments, and
the 2 lowest online quizzes. A grade of “Incomplete” will not be given except in welldocumented and extraordinary circumstances.
Extra Help
The School of Economics has a Student Laboratory & Advising Center in Stevens Hall Room
305. You can come to get extra help at this lab including: exam preparation, prepare/discuss
discussion points. This lab is also a great place to meet for group study sessions/
presentation preparation. Office hours are also a great time to get extra help.
Course Communication through Blackboard
We will be using the on-line course website program called Blackboard. This website will
contain all course materials – including readings, discussions, announcements and grades.
www.courses.maine.edu. Please use blackboard for all email communications with the
instructors. It is very important that you make sure you can access our course on
Blackboard!
Email Policy
I welcome contact via email with course-related questions and do not want to discourage anyone from
doing so; however, I hope that you will first attempt to use your resources (e.g., your syllabus,
handouts, your peers, office hours, etc.) to address your questions before sending an email. I expect
emails from students (and vice versa) to be composed professionally with complete sentences and
proper English writing style with no spelling mistakes or cryptic abbreviations (i.e, an email is not a text
message), a CLEAR subject line and a clear, concise question. Please use blackboard for all email
correspondence so I know which course you are in since I teach more than course.
If you forget to use blackboard, please include in the subject line: the course number or name,
the days of week the course meets, and the time during the day the course meets as I each teach
more than one course. For example: ECO 405 Tu-Th 930.
I reserve the right not to respond to emails that don’t meet these qualifications!
During the weekdays, please expect at least a 36-hour turnaround time for answering emails and on
weekends, the time will be 60 hours. I have a busy work schedule, and I try to have a personal life as
well.
** PLEASE only use the Blackboard mail system when emailing!
Students with disabilities
4
If you have a disability for which you may be requesting an accommodation, please contact
Ann Smith, Coordinator of Services for Students with Disabilities (121 East Annex Building,
581- 2319), as early as possible in the term.
Academic honesty (plagiarism, etc.)
Academic honesty is very important. It is dishonest to cheat on exams, to copy term papers,
to submit papers written by another person, to fake experimental results, or to copy or reword
parts of books or articles into your own papers without appropriately citing the source.
Students committing or aiding in any of these violations may be given failing grades for an
assignment or for an entire course, at the discretion of the instructor. In addition to any
academic action taken by an instructor, these violations are also subject to action under the
University of Maine Student Conduct Code. The maximum possible sanction under the
student conduct code is dismissal from the University.
ECO 590 Students
ECO 590 students will be receiving credit for a graduate level course. Therefore, more will be
expected of them in terms of workload and quality of work. The following changes to the
information listed above apply to all ECO 590 students:
1) ECO 590 students must complete all of the “optional” readings listed on the Course
Outline in addition to all of the “required” readings.
2) Exams for ECO 590 students may be different from exams for ECO 405 students in
any or all of the following ways:
a. Additional questions based on readings that are optional for ECO 405 students.
b. More difficult questions.
c. Different types of questions (i.e., other than multiple choice)
3) ECO 590 students will complete a longer and more in-depth final project.
4) The grading distribution for ECO 590 students will be as follows:
In-class assignments (lowest 1 grade dropped)
20%
Online quizzes (lowest 1 grade dropped)
20%
Exams (best 2 out of 3)
30%
Final project
30%
100%
5
Evaluation Rubrics (how you will be graded)
Written Response Rubric
Teacher Name: Dr. Wagner
Student Name: ____________________ ____________________
(Last name)
(First name)
2 points
CATEGORY
Relevance
Accuracy
Use of course materials
Importance
Completeness
Readability
1 points
0 points
The response partially
answers the question
posed.
The answer is partially
The answer is correct.
correct.
Some of the argument(s)
The argument(s) is/are
supported with reference is/are supported with
to class readings and/or reference to class
readings and/or lectures.
lectures.
The response discusses The response discusses
some important aspects
the most important
of the topic.
aspects of the topic.
The ideas conveyed in the Some of the ideas
conveyed in the response
response are complete
and satisfy the word or are complete and/or the
response is either too
page requirements.
short or too long.
The response does not
answer the question
posed.
The answer is not correct
at all.
There is no mention of
class readings and/or
lecture materials.
I can read most of the
I am able to read the
response and understand response and understand
most of the writing
the writing.
(anything I cannot
understand will not
receive points in other
categories).
The response is
completely illegible or
doesn't make any sense
at all (anything I cannot
understand will not
receive points in other
categories).
The response answers
the question posed.
Date Created: December 10, 2012
Total Points
Earned (in
each cell,
enter a
value from
0-4):
2
2
2
The response does not
discuss any important
aspects of the topic.
No complete ideas are
conveyed and/or the
response is extremely too
short or too long.
TOTAL POINTS
EARNED:
GRADE:
Max
poissible
points
2
2
2
0
12
0%
100%
6
Debate Evaluation
Teacher Name: Dr. Wagner
Student Name: ____________________ ____________________
(First name)
(Last name)
CATEGORY
Information
Use of Facts/Statistics
Organization
Rebuttal
Understanding of Topic
Respect for Other Team
Presentation Style
4 points
3 points
All information presented Most information
in the debate was clear, presented in the debate
accurate and thorough. was clear, accurate and
thorough.
Every major point was
well supported with
several relevant facts,
statistics and/or
examples.
Every major point was
adequately supported
with relevant facts,
statistics and/or
examples.
All arguments were
clearly tied to an idea
(premise) and organized
in a tight, logical fashion.
Most arguments were
clearly tied to an idea
(premise) and organized
in a tight, logical fashion.
All counter-arguments
were accurate, relevant
and strong.
Most counter-arguments
were accurate, relevant,
and strong.
The team clearly
understood the topic indepth and presented
their information
forcefully and
convincingly.
All statements, body
language, and responses
were respectful and were
in appropriate language.
The team clearly
understood the topic indepth and presented
their information with
ease.
Statements and
responses were
respectful and used
appropriate language,
but occasionally body
language was not
respectful.
Team consistently used Team usually used
gestures, eye contact,
gestures, eye contact,
tone of voice and a level tone of voice and a level
of enthusiasm in a way
of enthusiasm in a way
that kept the attention of that kept the attention of
the audience.
the audience.
2 points
Most information
presented in the debate
was clear and accurate,
but was not usually
thorough.
Every major point was
supported with facts,
statistics and/or
examples, but the
relevance of some was
questionable.
All arguments were
clearly tied to an idea
(premise) but the
organization was
sometimes not clear or
logical.
Most counter-arguments
were accurate and
relevant, but several
were weak.
1 points
0 points
Information had several
inaccuracies OR was
usually not clear.
No information was
presented or
information was
completely inaccurate
Every point was not
supported.
No points were made
or every point was
obviously false
Arguments were not
clearly tied to an idea
(premise).
Total Points
Earned (in
each cell,
enter a
value from
0-4):
Max
poissible
points
4
4
No organization was
present at all
4
Counter-arguments were There was an
not accurate and/or
opportunity and need
relevant
for counter-arguments
but none were made.
The team seemed to
understand the main
points of the topic and
presented those with
ease.
The team did not show an The team showed
adequate understanding complete
of the topic.
misunderstanding of
topic
Most statements and
responses were
respectful and in
appropriate language,
but there were some
sarcastic remarks.
Statements, responses
and/or body language
were consistently not
respectful.
The team showed no
respect at all.
Team sometimes used
gestures, eye contact,
tone of voice and a level
of enthusiasm in a way
that kept the attention of
the audience.
One or more members of
the team had a
presentation style that
did not keep the
attention of the
audience.
The presentation style
of every member of
the team was boring,
rude, and/or
completely
inappropriate
4
4
4
TOTAL POINTS
EARNED:
GRADE:
4
0
28
0%
100%
7
Discussion Evaluation
Teacher Name: Wagner
Student Name: ____________________ ____________________
(First name)
(Last name)
CATEGORY
Knowledge
Speaking
Listening
4 points
3 points
2 points
1 points
Demonstrates strong
knowledge of course
material, including
lectures, readings and
knowledge gained
through previous class
activities. Synthesizes
new information
appropriately and asks
appropriate questions to
clarify knowledge gaps.
Demonstrates
satisfactory knowledge of
course material, including
lectures, readings and/or
knowledge gained
through previous class
activities. Synthesizes
new information
somewhat appropriately
and/or asks appropriate
questions to clarify
knowledge gaps.
Demonstrates minimal
Has clearly not done the
knowledge of course
readings and/or not paid
material, including
attention in
lectures, readings and/or lectures/previous class
knowledge gained
activities. Makes a strong
through previous class
effort to synthesize new
activities. Has some
information with limited
trouble synthesizing new knowledge and/or asks
information appropriately appropriate questions to
and/or asking
clarify knowledge gaps.
appropriate questions to
clarify knowledge gaps.
Actively contributes
throughout the entire
discussion, including:
Contributes to the
discussion at appropriate
times without
interrupting others.
Builds off others' ideas
and/or challenges others'
assumptions and
perspectives in a
respectful manner.
Contributes ideas that
directly relate to the
topic. Raises thoughtful
questions where
appropriate.
Actively listens to other
group members
throughout entire
discussion. Maintains eye
contact with speaker and
demonstrates interest in
what speaker is saying
through non-verbal cues
(nodding, etc) or verbal
responses.
Actively contributes to
most of the discussion,
including most of the
actions described in first
column.
Contributes to some of
the discussion, including
some of the actions
described in first column.
0 points
Total Points
Earned (in
each cell, enter
a value from 04):
Has clearly not done the
readings and/or not paid
attention in
lectures/previous class
activities. Makes weak/no
effort to synthesize new
information and/or asks
inappropriate/no
questions to clarify
knowledge gaps.
Max
poissible
points
4
Minimally contributes to Makes no contribution to
the discussion, including the discussion and/or
at least one of the actions contributions are offdescribed in first column. topic, disruptive and/or
disrespectful.
4
Actively listens to other
group members
throughout most of the
discussion. Maintains eye
contact with speaker and
demonstrates interest in
what speaker is saying
through non-verbal cues
(nodding, etc) or verbal
responses.
Actively listens to other
group members
throughout some of the
discussion. Maintains eye
contact with speaker
and/or demonstrates
interest in what speaker
is saying through nonverbal cues (nodding, etc)
or verbal responses.
Occasionally
Makes absolutely no
demonstrates some form effort to listen to other
of minimal listening effort group members.
during part of the
discussion.
TOTAL POINTS
EARNED:
GRADE*:
4
0
12
0%
100%
* Grade is calculated as
2x the number of points
for Knowledge plus 1x the
number of points for
Speaking and Listening;
for a total possible
number of points = 16
8
TENTATIVE COURSE OUTLINE*
Date
15-Jan
17-Jan
22-Jan
24-Jan
29-Jan
31-Jan
Topic
Assigned Readings
Assignments
What is Sustainable Energy?
ESS: Ch. 1
pre-assessment
quiz; in-class
activity
How should we evaluate the
sustainability of energy
alternatives? PART I
ESS: Ch. 13 (p.505-509; p.529-563); DOE
Report to Congress: Energy Demands on
Water Resources (p.13-23); UNEP Global
Environment Outlook GEO4 – Chapter 5
Biodiversity (p.24-56); Optional: IPCC AR4
Summary for Policymakers – see URL on
blackboard
in-class activity
DOE Report to Congress: Energy
Demands on Water Resources (p.25-27);
Reading Quiz 1
(online); in-class
activity
How should we evaluate the
sustainability of energy
alternatives? PART II
How should we evaluate the
sustainability of energy
alternatives? PART III
in-class activity
What is energy and How do we
use it? PART I
RE: Ch.1 (p.1-10); Appendix A; ESS: Ch.
2 & 3 (p. 77-110)
Reading Quiz 2
(online); in-class
activity
Electricity and heat
ESS: Ch. 9 (Box 9.1, Box 9.2; 359-377);
RE: Ch. 10 (Box 10.2 p.485-486; 487498); History of the US Electric Power
Industry 1882-1991;
Reading Quiz 3
(online); in-class
activity
5-Feb
Central (CG) vs. Distributed (DG)
Generation of Electricity & Heat
7-Feb
Introduction to CG energy
economics
ESS: Ch. 12 & Ch. 13 (p.510-529); RE:
Appendix B
12-Feb
Coal CG energy
ESS: Ch. 5; Ch. 6 (p.183-191; 200-210);
Ch. 14 (p.576-583)
14-Feb
Natural Gas & Oil CG energy
ESS: Ch. 7 (p.213-249; p.259-272); Ch. 9
(p.354-359); TBD
19-Feb
Wind energy (CG) & LCOE
[guest lecture: Prof. Gary Hunt]
RE: Ch. 7 (p.297-338; 342-355)
21-Feb
The social cost of energy
[guest lecture: Prof. Gary Hunt]
NAS study - Hidden costs of energy
26-Feb
Shale gas legal issues
[guest lecture: Prof. Jeff
Thaler]
TBD
28-Feb
Renewable energy law & policy
[guest lecture: Prof. Jeff
Thaler]
RE: Ch. 10 (p. 504-506);TBD
Exam 1 (in-class)
Reading Quiz 4
(online); in-class
activity
Reading Quiz 5
(online); in-class
activity
Reading Quiz 6
(online); in-class
activity
Reading Quiz 7
(online); in-class
activity
Reading Quiz 8
(online); in-class
activity
Reading Quiz 9
(online); in-class
activity
Reading Quiz 10
(online); in-class
activity; Final
Project Proposal
due in-class
BREAK
9
19-Mar
Nuclear CG energy
ESS: Ch. 10 & 11
21-Mar
Biomass CG energy
RE: Ch. 4 (p.117-143; 146-153; 155-159;
163-177)
26-Mar
Geothermal CG energy
RE: Ch. 9 (p.409-434; 438-457)
28-Mar
Hydroelectricity (CG)
RE: Ch. 5; TBD
2-Apr
Tidal and Wave CG Energy
RE: Ch. 6; Ch. 8 (all except p.401)
4-Apr
Solar CG energy
RE: Ch. 2 (p.21-22; 24-35; 57-66; 68-69);
Ch. 3 (p.75-96; 101-104); articles TBD (PV
LCOE and my CSP LCOE articles)
9-Apr
Solar DG energy
RE: Ch. 2 (p.22-24; 35-57; 66-68; 70-71);
Ch. 3 (p.96-100; 104-112); TBD
11-Apr
Other Renewable DG options
(biomass, wind, micro-hydro,
geothermal)
16-Apr
How do we compare different
electricity/heating options?
18-Apr
23-Apr
Transportation use and policy
[guest lecture: Prof. Jonathan
Rubin]
Alternative transportation options
RE: Ch. 4 (p.144); Ch. 7 (p.339-342); Ch.
8 (p.401); Ch. 9 (p.434-438); ESS: Ch. 14
(p.598-599; p.601-602)
RE: Ch. 10 (p.467-482) & TBD (possibly:
Fthenakis land & water studies,
Sustainability assessment study, MCDA
studies)
ESS: Ch. 8; Ch. 14 (p.587-597; p.599601); RE: Ch. 4 (p.145-146; 153-155; 159163); Ch. 10 (p.498-503); and TBD
TBD
25-Apr
An International Perspective
[guest lecture: Prof. Gary Hunt]
TBD
30-Apr
What will the energy future look
like?
RE: Ch. 10 (p.506-521); Ch. 14 (p.583587)
2-May
What can you do? AND
DEBATE: What should the role of
fossil fuels be in a sustainable
energy future?
Ch. 10 RE (p. 506-521) & TBD
2-May
FINAL EXAM 8:00-10:00 AM
Reading Quiz 11
(online); in-class
activity
Reading Quiz 12
(online); in-class
activity
Exam 2 (in-class)
Reading Quiz 13
(online); in-class
activity
Reading Quiz 14
(online); in-class
activity
Reading Quiz 15
(online); in-class
activity
Reading Quiz 16
(online); in-class
activity
Reading Quiz 17
(online); in-class
activity
Reading Quiz 18
(online); in-class
activity
Reading Quiz 19
(online); in-class
activity
Exam 3 (in-class)
Reading Quiz 20
(online); in-class
activity
Reading Quiz 21
(online); in-class
activity
Reading Quiz 22
(online); in-class
activity
FINAL
PRESENTATION:
In assigned
classroom (Final
Paper due at start
of exam period)
ESS = Energy Systems and Sustainability
RE = Renewable Energy: Power for a Sustainable Future
TBD = to be determined (check for updated on blackboard)
*This course outline is subject to change as the course progresses – updated versions can be
found on blackboard throughout the semester
10
i
(1) The stated objectives and outcomes address the learning outcome goals for the University of Maine’s general education requirement for
the area of Population and the Environment, which state (in brief):
Courses included in the Population and Environment sub-category help students to understand how humankind interacts with our finite
physical and biological environment by addressing:
(a) The role of both local and global environmental change on the quality of human life;
(b) The pervasive role of human population growth on environmental quality and the quality of life, both in industrial and developing
countries;
(c) The influence of cultural, religious, economic, educational and political factors on population growth and environmental quality; and
(d) Possible solutions to the population/environmental problems, which may include the role of technological advancements, a reexamination of educational and political institutions, enlightened reassessment of traditional religious and economic conceptions, and
rethinking contemporary Western conception of “the good life”
(2) The stated objectives and outcomes address the learning outcome goals for the University of Maine’s general education requirement for
the area of Quantitative Literacy, which state (in brief):
Quantitative literacy is the ability to formulate, evaluate, and communicate conclusions and inferences from quantitative information. Upon
completion of general education study in quantitative literacy, students will understand the role that mathematics and quantitative thinking
plays in solving and communicating information about real world problems and relationships. Students will be able to:
1. Translate problems from everyday spoken and written language to appropriate quantitative questions.
2. Interpret quantitative information from formulas, graphs, tables, schematics, simulations, and visualizations, and draw inferences from that
information.
3. Solve problems using arithmetical, algebraic, geometrical, statistical, or computational methods.
4. Analyze answers to quantitative problems in order to determine reasonableness. Suggest alternative approaches if necessary.
5. Represent quantitative information symbolically, visually, and numerically.
6. Present quantitative results in context using everyday spoken and written language as well as using formulas, graphs, tables, schematics,
simulations, and visualizations.
11