1356_MATH171_01
Mathematics for Elementary School Teachers II
Geometry, Measurement, Chance and Data
Spring 2009
Room SAM 301 Mon. & Weds.
4:30—7:00 pm Professor: Andrea
Levy, Ed.D. Office: SAM214 Mailstop: 2SAM110 Office Phone:
206-587-4082 Email: alevy@sccd.ctc.edu Website: http://seattlecentral.edu/faculty/alevy Office Drop-in
Hours: M & W 3:30-4:20pm or by appointment Text and Course Materials
Sowder, J., Sowder, L., Nickerson, S., Reconceptualizing
Mathematics (Preliminary Edition): Part
#3 Reasoning about Shapes and Measurement and Part #4 Reasoning about Chance and Data, W.H. Freeman & Co.,
NY (Available at the SCCC bookstore) Teach Like Your Hair's on Fire :
The Methods and Madness Inside Room 56
by Rafe Esquith ISBN-13: 978-0-14-311286-0Required Materials:
Textbook Parts 3 & 4, book by Esquith,
scientific calculator, metric and standard ruler, pencil, notebook paper,
graph paper, compass, ruler, protractor, scissors, transparent
tape. From the
Text: Make the kit from the nets found in the first chapter (store in shoe
box). Use the square dot paper and the isometric dot paper in your materials
as masters and make several copies of each. Optional Materials: Set of
100 interlocking snap cubes, student membership to NCTM Supplementary
Readings/Website Access: OSPI: Essential Academic Learning Requirements
(EALRs) http://www.k12.wa.us/CurriculumInstruct/default.aspx
NCTM: Principles and Standards for Science and
Mathematics http://www.nctm.org/standards/ Teaching Children
Mathematics Magazine (optional) http://my.nctm.org/eresources/journal_home.asp?journal_id=4 This course delves deeply into the mathematics elementary teachers are responsible for teaching at the K-8 levels. The mathematics examined in this course covers polyhedra, polygons, symmetry, tessellations, size changes, curves and curved surfaces, transformations, length, angles, area and surface area, volume, measure formulas, reasoning, chance, probability and data analysis. You will gain knowledge of the underlying concepts
related to
exploring geometric and measurement concepts that you already know from a new
perspective, exploring some concepts that are new to you, and developing your
visualization skills. The course is
designed to improve your basic content knowledge, model methods of teaching
mathematics to K-8 students, engage you in activities that increase
confidence and enthusiasm for the subject area, and familiarize you with
local and national standards for teaching mathematics. Teaching is a melding of various
skills. Effective teaching requires an ability to represent and formulate a
subject to make it comprehensible to others. This means understanding what
makes the learning of a concept easy or difficult, which requires an ability
to synthesize knowledge about content with students’ interests, needs, and
cultural influences. One major goal of this
course is that pre-service and current elementary school teachers develop a
deep understanding of the geometric and measurement concepts. A second major
goal is to help students develop a deep sensitivity to sense-making, with an
emphasis on explanation and justification.
The key ideas presented in this course are as follows, although not
necessarily in this order: 3-D and 2-D Shapes - Construct polyhedra and develop workable vocabulary for describing
and distinguishing 3-D shapes. - Explore geometric solids
and their properties. - Explore and review
polygons with an emphasis on the relationship between sides and angles. - Planar symmetry developed
using tessellations. - Issues of similarity with
emphasis on multiplicative relationships (ratio/proportionality). - Multiplicative comparisons
of surface area and volume (squaring and cubing). - Planar curves with an
emphasis on mastering circle vocabulary. - Curved surfaces with a
cross-cultural (cross-disciplinary) element. - Transformation geometry
with emphasis on rigid motion/isometry. Measurement - Key ideas of measurement
with a focus on understanding standard units and the metric system. - Cross-cultural aspects of
measurement systems. - Explore how approximation
relates to measurement. - Area, perimeter, length,
and surface area are explored and calculated - Explore volume to
understand it conceptually. - The history of Pythagorean
Theorem, introducing a Chinese proof, and recognizing Pythagorean triples - Measuring temperature:
Fahrenheit, Celsius, Kelvin - Measuring volume: tbsp,
tsp, cups, pints, gallons, etc. - Development of area
formulas: relationship to area of a rectangle - Development of volume
formulas: layering and relation to area of a rectangular prism - Conservation of volume Data
Analysis and Probability - Reasoning About
Chance - Chance Events - Methods of Assigning
Probabilities -
Simulating
Probabilistic Situations - Tree Diagrams and
Lists for Multistep Experiments - Probability of One Event
OR Another Event - Probability of One
Event AND Another Event - Conditional
Probability - Sampling: The Why
and the How - Simulating Random
Sampling - Types of Data - Conducting a Survey - Representing
Categorical Data with Bar and Circle Graphs - Representing and
Interpreting Measurement Data - Examining the
“Spread-outness” of Data - Measures of Central
Tendency and Spread - Examining
Distributions - Issues for Learning:
Understanding the Mean - Comparing Data Sets -
Lines
of Best Fit and Correlation - Having Confidence in
a Sample Statistic - Confidence Intervals You are expected to attend all class
sessions, arrive in class on-time and be prepared for the daily lesson. Being
prepared means that homework assignments are complete, and you have all the necessary
supplies for full participation in the daily coursework. You will: 1. Work individually
and collaboratively in small and large groups to accomplish the course goals
and objectives 2. Actively engage in
mathematical manipulation and representation through the course activities. 3. Articulate your
understanding of mathematical concepts and procedures through involvement in
course activities and reflective observations in a mathematics journal. 4. Critique your own
and others procedures and thinking about math for the purpose of deepening
your understanding of how people come to learn and understand mathematics.
Self evaluation and peer evaluation will be integrated throughout the course.
In-Class:
Partnership/Small Group/Whole Class Activities
Activities
and discussions are conducted in small groups. The group members report their
findings to class with emphasis on the important concepts, connecting
unconventional procedures with standard algorithms. You will be actively
involved during the class time, either working on mathematics problems,
presenting your solution processes, evaluating peer presentations, or
reflecting on your understanding of the mathematics. Communication is an
important aspect of this class, therefore you are responsible for providing
evidence that you understand the material presented. One way to do this is by
fully participating in partnership, small group, and whole class activities.
The partnership and small group formats provide support to: (a) ease math
anxiety, (b) learn to work collaboratively, (c) develop problem solving and
critical thinking skills, and (d) clearly communicate solution processes to
convince others that the answer is correct. Also, you are expected to
summarize and communicate your group’s findings to the whole class. You will work in
the small groups to do class work and take tests; therefore it is important
that you contribute your thinking, questions, and insights to make this a
collective process. As a productive
group member it is your responsibility to listen carefully, provide positive
feedback, ask clarifying questions rather than depend upon assumptions, and
share your thinking, concerns, and critique of solution processes with one
another. Homework
The
daily assignments deepen your understanding of the mathematical concepts you
learned in previous classes by explicitly connecting the standard algorithm
with the underlying mathematical concept.
Homework is listed in the Course Calendar on the day it is due.
Please do all homework assignments on regular notebook paper (no
spiral bound or scrap pieces of paper), or if you are word processing your
work, then use regular printer paper. Try to keep the homework as neat as
possible. No late work will be
accepted; therefore, if you know you will be absent, email your work before
the day it is due. Completing and handing in homework on time is essential as
it prepares you to be a full participant in the class activities. Tests,
Midterm Essay, and Project
Much of the learning
in this class is done through group work, therefore group tests are used to assess your understanding. This does NOT
mean that you get a group grade. Test problems are complex and require an
explanation of the reasoning used to solve the problem. The testing format
provides an opportunity to discuss the solution process with group members
prior to writing solutions in your own words. A correct answer to a problem
is sufficient for a passing grade (which is a 75% or a 2.0); however, if you
wish to earn a higher grade, you must clearly communicate your thinking and
demonstrate your solution process. The group work is designed to hone your
communication skills (this is a course objective). The individual write-up is
how you provide evidence of your understanding for a formal assessment grade.
This process will be explained in more depth and your questions will be
answered prior to the first formal test. No make-up tests will be given, however, you can
replace a test grade with the grade you get on the final exam. The mid term essay
is worth 100 pts. I strongly recommend you read the entire book, Teach Like Your Hair's on Fire: The Methods and Madness Inside
Room 56 by Rafe Esquith. However only chapters five, six, and twelve
”Add it Up”, “We won’t get fooled again” , and “Think for Yourself”
are required for this essay. This is a two to three page essay. The first
paragraph you should provide a brief synopsis of chapters 5, 6, & 12
(explain the premise of the chapters in your own words—do not analyze, merely
describe.) The rest of the essay, please discuss how Rafe
uses interdisciplinary methods to teach math, problem solving, and test
practice. How does Rafe’s training for standardized
tests compare with your understanding of how it is usually done? How does Rafe’s
problem solving methods and the problems he gives his students compare with
what we have studied in MATH170 & 171? Explain how what you have read
will affect your teaching. The essay should be double spaced, 12pt Times
Roman font. Please submit a hard copy for grading (or as an email Word
attachment).
The Quarter Project is an individual
project; however, you will have opportunities in class to work with others
who have chosen a similar project. This small group will help you with
planning, editing, and revising. The project is explained in detail on the Project
Protocol page. The project reports will be made on the project
template. You will fill in sections of the template throughout the
quarter. The final completed project template is due the day of the final
exam. Grading policy,
criteria and scales
The proposed grade
distribution is: 20% class participation, 20% homework – Math Problems; 40%
tests and final exam, and 20% quarter project. o
Participation: You will receive 10 points for each day
that you attend class. Points are deducted if you arrive late or leave early,
are not able to attend a session, and for disruptive and disrespectful behavior.
o
Homework: Math Problems—10 points. Homework is
due at the start of each class session, and are
listed on the day they are due on the Course Calendar. No
late work will be accepted; however you may submit them early by email or
in class if you know you will be absent. o
Tests are 100 pts. Since tests are designed for working
in groups, it is important that you make every effort to attend, arriving
on-time, and prepared so that you can support one another. The Final Exam is
100 points (the final exam grade can replace lowest test grade.) o
Quarter Project is 100 points. Please see the Project
Protocol page for details. If you feel that the grade distribution
does not adequately reflect your understanding of the mathematics in this
course, then I encourage you to make an appointment to discuss it with me.
This must be done sometime before
the last month of the quarter.
“NC” (No Credit) grades are NOT given under
any circumstances. If you want to withdraw from the course, request a “W”
grade before the published deadline. “I” (Incomplete) grades are only given
in strict conformity with the college catalog. Specifically, a student must be
in “good standing” to request an Incomplete.
For this course, “good standing” will mean, at a minimum, a current
grade of at least 2.0. “I” grades can only be requested in situations and
circumstances that are out of the control of the student…please read the
catalog for details. I reserve all rights about when and if an “Incomplete”
will be issued. It is your responsibility to request and submit the
signatures and paperwork required for “W” and “I” grades by the deadlines
established by the college. Tutorial Assistance
I am available to help clarify or provide
tutorial assistance. However, (since I have approximately 100 students each
quarter) please discuss the problem with your group members first. Make an
appointment to speak with me if your group members are unable to help you. I
am also available to work with the whole group. If you need tutoring assistance on a fairly
regular basis, please visit the math lab in SAM 106, Mon-Thurs 9AM—6PM, Fri
9AM—4PM. Students with Disabilities Statement
Students with documented disabilities, who need
course accommodations, have emergency medical information or require special
arrangements for building evacuation should contact me within the first week
of class. The instructor
reserves the right to reasonably adjust this syllabus if deemed necessary and
will make available written changes for students to add to this document. |
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Submitting
Project
Use the Project Template to submit your reports. The sections of the Template align with the
reports listed here. You will update the template and resubmit by the due
dates. Use proper grammar and spelling. Electronic
copy submission for grading is required. Student work should be scanned submitted
as a separate attachment. I recommend that you use this project as part of
your electronic portfolio. Save the Project Template onto your desktop, then open it using Word. When you have completed the
appropriate sections on the template, save it as a Word document and send it
to me by email. Student work, work sheets, etc. should be scanned and
sent as an attachment also (if you are unable to scan, hard copies should be
submitted.) Project Declaration: First box on template
Identify
the Project Theme, grade level, and Mathematical Concept for your project
Project Overview – 1st section of template
1.
Identify the Project Theme, Grade Level, and
Mathematical Concept for your project. 2.
Identify
the EALRs
and NCTM Standards that relate to
your project, indicating the primary and supplementary standards. 3. Make a
record/bibliography of literature, websites, and information sources (i.e., elementary
school teachers, after school programs) that relate to your project. 4. Identify and
contact students (younger sibling, niece or nephew, your child, neighbor or
friend’s child, etc.) who might be willing to work with you on this project. 5. Determine the time
frame and location for conducting an activity If
you are doing this project in combination with service-learning credits, then
you will work with your cooperating teacher to establish your project
parameters. http://seattlecentral.edu/faculty/alevy/service_credits.htm
Activity Description – 2nd section of template
1) Choose and describe
an appropriate activity that fits your project parameters and the
ability/interest level of the child/children who will be working with you. a) Explain where you
found the activity (full citation). b) Identify the main
goal of the activity, keep this simple. c) Record any
adjustments you made to the activity to fit your parameters, time
constraints, student interest/abilities, EALRs and/or
NCTM Standards. d) Explain how you
assessed the child’s/children’s ability/interest level before developing the
activity. 2) Prepare the
activity and record the following: a) Supplies needed b) Do the activity
yourself (or with a peer) and record appropriate changes c) Make arrangements
for conducting the activity (time, place, etc.) 3) Write out how you
will explain the activity to the child/children (mini script) 4) Do the activity with
the child/children who have agreed to work with you a) Record the time,
place, who attended, etc. b) Collect student
work, and/or record notes on student outcomes c) Write down what
happened during the activity Activity Analysis –
Last section of template
1)
Explain what you hoped to accomplish with the activity.
Do you feel it was successful? Why, why not? 2)
Explain the specific mathematics expectations you had
for this activity (make sure to site the EALRs and NCTM Standards.) Was this
a good activity for meeting those expectations? Why/why not? 3)
Explain how the children responded to the activity. How
do you know if they enjoyed it? How do
you know whether they recognized that they were learning something
mathematical? 4)
Are there things you would do differently if you were
to use the activity again for this age group?
What changes would you recommend to use this as a whole class
activity? Would you use it for another age group, and if so, how would you
change the activity? 5)
Explain how you could integrate this activity into a
regular elementary school curriculum. 6)
Has this project changed how you think about
mathematics? If yes, explain. If no, how has it reinforced or validated your
beliefs? Project
Assessment
This
project is worth 100 points. Assessment is described using the following
rubric.
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Bring notebook
paper, graph paper, calculator, textbook, compass (tool used to construct a circle),
ruler, protractor, scissors, transparent tape, and a pencil to class daily. Although tests and
math problems are used as evidence of your understanding and to assign a
formal grade, they also provide a means by which I can determine the
mathematical ideas that you and your classmates need to have further
explained or emphasized. For this reason, the Course Calendar is not fixed, but rather is a working
document which may change as we progress through the material. I will inform you
of any changes to the calendar as they arise.
As you read through
the book sections, it is important that you become familiar with the
activities which we will be working on in class together. The math problems and reading response
questions are due the day they are listed. |
Week
1 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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16.1 Shoeboxes Have
Faces and Nets 17.1 Review of Polygon
Vocabulary 17.2 Organizing Shapes 17.3 Triangles and Quadrilaterals 17.4 Issues for Learning |
Purchase Sowder text parts 3 & 4 at SCCC bookstore |
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Service
learning Credits Explained |
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Weds. Apr.8
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16.2 Introduction to Polyhedra 16.3 Representing and
Visualizing Polyhedra 16.6 Issues for Learning |
Use Nets in back of text to build
personal set of Polyhedra: cutout the shapes A-M
(their nets), then fold and tape them together. Make sure the shape letter
(and your name) is visible on the outside of the polyhedron. (Put them into a
shoebox to protect and transport them to class.) 17.1
#6, 10, 12 a-j, 16, 21 17.2
#4 17.3
#4, 5b, 6, 8 17.4 #2, 3 |
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Introduce Projects |
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Week
2 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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Ch. Review |
Bring
in NETS 16.2: #9,
11, 13 16.3
#4, 5, 18 |
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Ch.16 & 17
TEST |
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Weds. Apr.15 |
18.1 Symmetry of Shapes in a Plane 18.2 Symmetry of Polyhedra 18.3 Issues of Learning |
Check out website TesselMania or
Activities
and bring
in your polyhedra – Tessellation
tutorial Free mac tessellation software: http://mac.wareseeker.com/free-tessellation/ |
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Hand-in Project
Declaration |
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Week
3 |
Class Session
Schedule |
Assignment The homework
is listed on the day it is due. |
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19.1 Tessellating the Plane 19.2 Tessellating Space |
18.1 #4, 7, 14, 15 18.2 #2, 3, 9 |
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Weds. Apr.22 |
Ch. Test Review |
19.1 #1, 2 19.2 #2, 4 |
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Ch.18 & 19
TEST |
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Week
4 |
Class Session Schedule |
Assignment The
homework is listed on the day it is due. |
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20.1 Size Changes in Planar Figures 20.2 More about Similar Figures 20.3 Size Changes in Space Figures 20.4 Issues for Learning |
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Weds. Apr.29 |
21.1 Planar Curves 21.2 Curved Surfaces |
Bring in protractor, compass, tracing paper 20.1 #4, 7, 9,10, 21 20.2 #3, 4, 6 20.3 #3, 9, 11, 15, 22 |
Week
5 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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22.1 Some Types of Rigid Motions 22.2 Finding Images for Rigid Motions 22.3 A Closer Look at Rigid Motions 22.4 Composition of Rigid Motions 22.5 Transformations and Earlier Topics |
21.2 #6, 8, 9 22.1 Activity 1 Let’s Be Pick-y |
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Project group work |
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Weds. May 6 |
Ch.
Test Review |
22.1 #1, 4, 5 22.2 #4, 13 22.3 #2 22.4 #5, 8 22.5 #5d, 6 |
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Ch.20, 21, & 22
TEST |
Project Overview due |
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Week
6 |
Class Session
Schedule |
Assignment The homework
is listed on the day it is due. |
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23.1 Key Ideas of
Measurement 23.2 Length and Angle
Size. |
Bring in rough draft
of midterm essay |
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Midterm group work |
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Weds. May 13 |
24.1 Area and Surface Area 24.2 Volume 24.3 Issues for Learning: Measurement 24.4 Check Yourself |
23.1 #9a,c,e,g; 1316d,g,I; 24 23.2 #8; 13; 16c,g; 18a; 19; 24a-d; 29 |
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Midterm Essay due today |
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Week
7 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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25.1 Area and Surface Area Formulas 25.2 Volume Formulas 25.3 Check Yourself |
24.1 # 5a-d; 11; 14; 21, 24 24.2 #8; 11; 14; 19a, b, e, h, l |
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Weds. May 20 |
Ch. Test Review |
25.1 #3; 7; 11; 18a, c, e, g;
19, 21a, c; 22 25.2 #9, 11, 13, 18a, 20 |
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Week
8 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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NO SCHOOL – MEMORIAL DAY |
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Weds. May
27 |
27.1 Understanding Chance Events 27.2 Methods of Assigning Probabilities 27.3 Simulating Probabilistic Situations 27.4 Issues for Learning 27.6 Check Yourself |
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Week
9 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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28.1 Tree Diagrams and
Lists for Multi-step Experiments 28.2 Probability of One
Event OR Another Event 28.3 Probability of One
Event AND Another Event 28.4 Conditional
Probability 28.5 Issues for Learning |
27.1 #2, 6 27.2 # 9, 10, 12, 13 b ,d, 14, 19 b, c, 23
27.3 # 5 |
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Weds. June 3 |
29.1 What Are
Statistics? 29.2 Sampling: The Why
and the How 29.3 Simulating Random
Sampling 29.4 Types of Data 29.5 Conducting a Survey
29.6 Issues for Learning |
28.1 # 2, 3, 4 a, b, 7
28.2 #1, 6, 10 28.3 # 6 a, b ,h, 7, 10
28.4 #1, 3, 5, 9, 10
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Week
10 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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30.1 Representing Categorical
Data 30.2 Representing and
Interpreting Measurement Data 30.3 Examining the
Spread of Data 30.4 Measures of Center 30.5 Deviations from
Mean as Measures of Spread 30.6 Examining Distributions 30.7 Issues for Learning: Understanding Mean |
29.2 # 2, 4, 8, 10 29.3 # 1, 3 29.4 # 1 |
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Project group work |
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Weds. June 10 |
Ch Test Review |
30.1 #
1, 2, 7 30.2 #
1, 2, 3 30.3 #
1a, 3a, 7 c, d, 9
30.4 #
1, 3, 5, 13, 15 30.5 # 4, 7 30.6 #3 30.7 #1, 2 |
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Week
11 |
Class Session
Schedule |
Assignment The
homework is listed on the day it is due. |
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Group Project Presentations |
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Course Evaluations |
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Final Exam Review |
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Weds. June 17 |
FINAL EXAM |
Our usual time and place |