BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Title of Course: MAT 216 Mathematics for Elementary Education II
Semester: Fall 2012
Credits: 4
Class hours: 4
Instructor: Dr. J.L. Gastón
Office: N536
Office Hours: M,W 1-2 pm; Sat. 8-9 am;
Sat. 1:30-2:30 pm
Tel: 212-220-1342
E-mail: jgaston@bmcc.cuny.edu
Students: Always type MAT 216 on the subject line
of your e-mail. Dr. Gastón will respond as quickly
as possible, Monday-Saturday, when she is not
teaching.
Course Description
This course covers mathematics recommended by the NCTM for prospective elementary school teachers, including
geometry and spatial sense, measurement, statistics and probability. MAT 216 focuses on a learner-oriented
approach to teaching mathematics. Emphasis is placed on mathematical concepts and skills, as well as techniques of
inquiry and critical thinking. The course includes a survey of elementary mathematical concepts with appropriate
materials to assist teachers in the classroom setting. MAT 216 meets the mathematics requirement for students who
plan to teach on the elementary school level.
Prerequisites
• The student must have passed or been exempt from MAT 214, and all remedial reading, writing and ESL
requirements.
• For this hybrid course, students must have an active e-mail address in the BMCC system, a valid CUNY Bb
(Blackboard) account and password, know how to navigate the current version of Blackboard, and understand
how to access and utilize related online course information. For additional details, contact the BMCC ELearning Center (S501A), elearning@bmcc.cuny.edu, 212-220-1243. A minimum 2.0 GPA is required to
register for an e-learning course. A freshman or first semester transfer student may only take one e-Learning
course.
Overview of Course Format
This hybrid course will include online and offline discussions and research based upon assignments, quizzes and
tests. Students are required to attend 5 face-to-face sessions during which course requirements, assignments and
related questions will be discussed, and during which tests and the final examination will be administered. There
will be no make-ups or extensions on assignments, tests or the final examination. You are required to attend face-toface sessions in N502, 1-5 pm, on the following Saturdays: 8/25/12, 9/15/12, 10/20/12, 12/8/12 and 12/15/12.
Required Texts
• Mathematical Ideas (11th or 12th Edition), Miller, Heeren, Hornsby and Morrow; HarperCollins Publishers,
New York.
• Mathematics, A Good Beginning (Sixth Edition),Troutman and Lichtenberg; Brooks/Cole, California, 2003.
For additional textbook information, see the TEXTBOOKS file in your Bb MAT 216 COURSE INFORMATION
folder.
Weblinks for Mathematics Reference, Review and Practice
Success in Math: http://mathcs.slu.edu/undergrad-math/success-in-mathematics
Sample chapter tests and final exam: http://mathcenter.usf.edu/courses/finite/finite_tests.html
HS Algebra Review: http://www.regentsprep.org/Regents/math/ALGEBRA/math-algebra.htm
HS Geometry Review: http://regentsprep.org/Regents/math/geometry/math-GEOMETRY.htm
HS Intermediate Algebra & Trig Review: http://regentsprep.org/Regents/math/algtrig/math-algtrig.htm
Teacher Videos-Number and Operations: http://www.learner.org/resources/series171.html
Teacher Videos-Patterns, Functions, Algebra: http://www.learner.org/resources/series140.html
Teacher Videos-Patterns, Functions, Algebra: http://www.learner.org/resources/series66.html
Math K-4 Pedagogy Videos: http://learner.org/resources/series32.html
National Library of Virtual Manipulatives: http://nlvm.usu.edu
Youtube Math Videoclips: http://k12wiki.wikispaces.com/Effective+Math+Videos
Gastón MAT 216.p1
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
MAT 216 Student Learning Outcomes
In order to learn the mathematics covered in this course, you must make connections to build upon a mathematical foundation from grades k-12.
When a topic is very difficult for you to understand, it means that your foundation is weak. You need to go back to one or more k-12 levels to
learn or review the basic concepts that will enable you to establish a better foundation, then make the appropriate connections to build upon it.
No one can do this for you. You are responsible for your own learning. Dr. Gastón will help you with this process but she cannot do it for you.
Topics
● Arithmetic and
Algebraic Connections
● Graphs, Functions
and Systems of
Equations
Learning Mathematical Pedagogy
MAT 216 students will be able to:
Understand unifying ideas (such as
abstract representation, classification,
and function used to link arithmetic and
algebra) that help teachers achieve
clarity and depth in both their
understanding and teaching of
mathematics.
Learning Mathematical Content
MAT 216 students will be able to:
1. Use terminology of coordinate
geometry
2. Use distance and midpoint formulas
3. Graph and find the equation of a
circle given its center and radius (or
diameter)
4. Find center and radius (or diameter)
of circle given its equation
5. Find (x,y) pairs that satisfy an
equation
6. Graph lines
7. Find x and y intercepts
8. Find the slope of a line given two
points
9. Graph a line given point and slope
10. Use graphs and equations to
identify lines that are parallel,
perpendicular, or neither
11. Find the equation of the line given
point/slope
12. Find the equation of the line given
two points
13. Find the equation of the line given
slope/intercept
14. Find slope/intercept given the
equation of the line
15. Write the equation of parallel or
perpendicular lines
16. Find an equation relating two
unknowns
17. Identify and evaluate functions
18. Find domain and range
19. Use the vertical line test
20. Use f(x) notation
21. Graph linear, quadratic and
exponential functions
22. Find the vertex of a parabola
23. Solve linear systems by
substitution
24. Solve linear systems by addition
25. Solve systems in three or more
variables
26. Solve applications related to
equation and function concepts
Gastón MAT 216.p2
Assessment of Learning
MAT 216 students will
exhibit competency (by a
grade of C=73 or better) on:
written assignments,
quizzes,
Test #1, and the
final examination.
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Geometry
MAT 216 students will be able to:
1. Identify, classify, and define
geometric figures.
2. Construct appropriate models for
geometric figures.
3. Define and construct examples and
counterexamples for each of the
following: Congruence, Rotation,
Symmetry, Similarity, Rotational
symmetry, Translation, Reflection,
Reflection symmetry.
4. Identify physical situations that
reflect specific geometric concepts.
5. Locates points on a rectangular
coordinate system.
6. Make scale drawings for simple line
drawings.
7. Use a point p and a scale factor to
produce an enlargement or reproduction
of a figure.
8. Identify and explain geometric
concepts that children should develop in
kindergarten through eighth grade,
using age levels, Piaget’s stages of
development, and Van Hiele’s levels of
development.
9. Create and implement learning
activities that enable children to
construct geometric concepts.
10. Diagnose the performance of
children with respect to geometric
concepts.
11. Understand the importance of
measurement and provide practical
applications of measurement concepts.
12. Identify attributes of measurement.
13. Use informal, U. S. customary, and
metric units of measurement
appropriately.
14. Illustrate metric units of
measurement with physical referents.
15. Provide relationships between U.S.
customary and metric units for informal
comparison purposes.
16. Describe the levels of children’s
development of measurement ideas.
17. Associate the levels of concept
development with approximate ages of
children.
18. Identify appropriate readiness
activities for teaching measurement
concepts.
19. Plan instructional strategies that will
enable children to construct concepts
related to measuring length, area, and
volume, weight, angles, time and
temperature (also reading clocks and
thermometers).
20. Assess and diagnose children’s
abilities through analysis of their
measurement experiences.
21. Develop problem-solving activities
involving measurement concepts that
are appropriate for children at different
grade and ability levels.
MAT 216 students will be able to:
1. Identify geometric terms about lines
2. Name and classify angles
3. Find complement or supplement of
angles
4. Use parallel lines cut by a transversal
to find angle relationships
5. Identify types of curves
6. Classify and measure polygons
7. Find exterior angles of a triangle
8. Identify parts of a circle
9. Find the perimeter of a polygon
10. Find the area of a rectangle or a
square
11. Find the area of a parallelogram
12. Find the area of a trapezoid
13. Find the area of a triangle
14. Find the circumference of a circle
15. Find the area of a circle
16. Find the area of a combined figure
17. Determine when triangles are
congruent
18. Determine when triangles are
similar
19. Solve problems with unknown
angles or sides in similar triangles
20. Understand and use the
Pythagorean Theorem
21. Find volume and surface area of
rectangular solids, pyramids, cylinders,
spheres, cones
22. Solve applications of perimeter,
surface area and volume
23. Understand concepts of
transformational geometry
24. Identify transformations of
different types and combinations
25. Solve problems requiring
transformation(s) on one or more
shapes
26. Understand basic non-Euclidean
geometry concepts
27. Solve problems involving genus
and topological equivalence
28. Identify networks
29. Understand basic fractal geometry
and use iterations to determine
attractors
Gastón MAT 216.p3
MAT 216 students will
exhibit competency (by a
grade of C=73 or better) on:
written assignments,
quizzes,
Test #2, and the
final examination.
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Counting Methods,
Probability and
Statistics
MAT 216 students will be able to:
1. Relate children’s experiences to
statistics and probability concepts.
2. Assist children in the selection of
appropriate problems to be analyzed
and assist in the collection of
appropriate data.
3. Assist children in efficiently
organizing their data by choosing
appropriate graphs, charts, and
statistical measures.
4. Help children with accurate
descriptions and valid interpretations of
data.
5. Plan interesting and appropriate
problems and projects for children to
complete.
6. Explain and identify misuses of
statistics and faulty arguments.
MAT 216 students will be able to:
1. Count by systematic listing
2. Construct and use tree diagrams
3. Use the Fundamental Counting
Principle
4. Evaluate factorials
5. Use permutations in counting
problems
6. Use combinations in counting
problems
7. Use Pascal's Triangle to evaluate
combinations
8. Solve counting problems using not
and or
9. Find the probability of an event
10. Find the odds of an event
11. Find the probability of the
complement
12. Find the probability of an event
with not, or, and
13. Find expected value
14. Understand and find binomial
probability
15. Use frequency
distributions/histograms
16. Use frequency polygons
17. Use bar graphs
18. Use circle graphs
19. Use line graphs
20. Find the mean, weighted mean,
median, mode
21. Find the range, standard deviation
22. Use Chebychev's Theorem
23. Analyze and use properties of a
normal curve
24. Use normal approximation to the
binomial
25. Use regression analysis
MAT 216 students will
exhibit competency (by a
grade of C=73 or better) on:
written assignments,
quizzes,
Test #3, and the
final examination.
Academic Adjustments for Students with Disabilities
Students with disabilities who require reasonable accommodations or academic adjustments for this course must
contact the Office of Services for Students with Disabilities and immediately inform Dr. Gastón. BMCC is
committed to providing equal access to all programs and curricula to all students.
About e-Learning
E-Learning courses are not easier than face-to-face courses. In order to earn a passing grade you must be:
 Comfortable using computers
 Willing to read a lot of text online or in your textbook(s)
 Creative in expressing your ideas in writing
 Able to interpret instructions for assignments
 Responsible for keeping up with reading and coursework
 Prepared to turn your assignments in on time
Students are encouraged to go online and register with the e-Learning Center by following the BMCC e-Learning
link in the upper right corner of the BMCC web page. By clicking on "Once you've registered" students will also
find information on activating e-mail. For further information, contact the BMCC E-Learning Center (Room
S-501a, 212-220-1243, elearning@bmcc.cuny.edu)
Gastón MAT 216.p4
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Course Components and Assessment of Learning/Grading
Each weekly assignment will include textbook readings, online PowerPoint lectures with practice problems and
other resources, opportunities to post related questions or responses to the Bb MAT 216 DISCUSSION BOARD,
written work, and an online quiz with a posted deadline. Since it is sometimes difficult to discuss math problems
online, there will be additional opportunities to pose and discuss questions when you come for face-to-face testing
sessions. This is not an easy course; there are 9 textbook chapters and extensive assignments to be covered in 15
weeks. You must discipline and pace yourself in order to complete each weekly assignment, including the quiz.
Posting questions/responses. This hybrid course uses asynchronous and synchronous communication for the
delivery of course material. Asynchronous communication is restricted; you must post and respond to questions
based only on written assignments via the Bb DISCUSSION BOARD. Synchronous communication (i.e.,
Collaboration, Messaging) is also restricted; you will use Bb e-mail or other tools in the COMMUNICATIONS
folder to participate in discussions related only to the written assignments. This activity is designed to
quickly clarify course material so appropriate on-going, on-line participation, teamwork and/or groupwork are
encouraged. You can thus collaborate in groups and contact group members, as well as the instructor, when you
have questions concerning the assignments. You are accountable for completing all assigned weekly reading before
discussing and/or posting related questions or comments. In posting questions or responses, you must cite the
appropriate text, pages and/or additional online or offline references. Although postings and responses do not earn
course credit, they clearly represent opportunities to better understand course material that may appear on quizzes,
tests and the final examination. All students are required to use the rules of Netiquette that promote and guide
respectful online correspondence (See the document in the COURSE INFORMATION folder).
Written work. Written homework is based upon assigned readings from the required textbooks. All weekly written
assignments must be completed with all the work shown. Do written assignments neatly on letter-sized loose leaf
paper with the following heading:
Name
Date
Class/Section
Assignment number
Grammar, spelling, punctuation and sentence structure are just as important as the ideas they convey. You may lose
points for poor grammar, syntax, and structure, as well as partially or completely wrong answers that remain
uncorrected. The content of written answers must indicate a mastery of the mathematics content and pedagogy in
the related textbook chapter(s). Some questions may also involve a research component, so you may need to
explore or examine ideas beyond the textbook(s). Upon completing any written assignment, it is therefore important
to carefully check your work using the answer key provided. (If you can learn to recognize your own errors, you
will develop the ability to assist your future students in identifying their mistakes.) Mark each correct answer with a
√, and each wrong answer with an x. Try to correct your own errors before posting a problem or point for
discussion; show all work for each correction next to the original problem or at the end of your written assignment.
Place completed and corrected assignments in a folder/portfolio. Note that only work that is neat, correct and
complete with an appropriate solution will earn credit. When you come in for a face-to-face test session, you must
bring in your portfolio of written assignments for grading. Portfolio work which is incomplete or unacceptable will
have to be re-done and re-submitted to earn credit. At the end of the course, submit your portfolio so the record of
each of the graded written assignments can be totaled to calculate your cumulative written homework points.
BMCC Policy on Plagiarism and Academic Integrity Statement
Plagiarism is the presentation of someone else’s ideas, words or artistic, scientific, or technical work as one’s own
creation. Using the idea or work of another is permissible only when the original author is identified. Paraphrasing
and summarizing, as well as direct quotations, require citations to the original source. Plagiarism may be intentional
or unintentional. Lack of dishonest intent does not necessarily absolve a student of responsibility for plagiarism.
If you are unsure how and when to provide documentation, you are advised to consult with Dr. Gastón. The library
has guides designed to help students to appropriately identify a cited work. The full policy can be found on
BMCC’s website, www.bmcc.cuny.edu. For further information on integrity and behavior, please consult the college
bulletin (also available online).
Gastón MAT 216.p5
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Quizzes. There will be 15 online quizzes. Each online quiz will be in the Bb MAT 216 ASSIGNMENTS folder.
Quizzes are each worth 100 points. For each quiz, you will have at least one week and at least three attempts to earn
your best score. Each quiz is automatically graded upon completion and submission by the posted deadline; only the
highest score counts. Otherwise, no credit is earned.
Tests. There will be 3 in-class meetings for face-to-face tests before the final examination. Each test is worth 100
points. You will have one class session and only one attempt to earn your best score on each test. Review the
written homework assignments and online quizzes to prepare for each test. Each online test is automatically graded
upon completion and submission. There will be no make ups or extensions. When you come in for the third test,
you must bring in your portfolio of all written homework assignments for cumulative grading.
Final Examination. The comprehensive online final examination is based on all of the assignments, quizzes and
tests given during the course. There will be one in-class meeting for the face-to-face final examination. The final
examination is worth 100 points. You will have only one attempt to earn your best score on the final examination.
There will be no make ups or extensions. Review your portfolio of written homework assignments and online
quizzes and tests to prepare for the final examination.
Grading
Each student will receive a grade based upon her/his portfolio of the following materials:
[1] Best 8 of 9 completed and corrected written assignments.
[2] All online quizzes. (Average)
[3] All three online tests. (Average)
[4] Final Examination
Total Points
372-400
360-371
348-359
332-347
320-331
308-319
292-307
0-100 points
0-100 points
0-100 points
0-100 points
Course Grade
A
AB+
B
BC+
C
Reminder: C is the lowest grade accepted for transfer to a 4-year college
280-291
268-279
252-267
240-251
Below 240
CD+
D
DF
Any student who does not submit the portfolio of required materials by the due date 12/8/12, 5 pm, will
receive a failing grade for this course.
Gastón MAT 216.p6
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Reminder:
You must have the required textbooks for the course. These are the same texts required for the prerequisite course,
MAT 214. Each of the PowerPoint lectures will be available in the Bb MAT 216 COURSE DOCUMENTS folder.
Each of the online quizzes will be available in the Bb MAT 216 ASSIGNMENTS folder. Your weekly written
assignment should be completed before you take the online weekly quiz. If you need detailed assistance in
completing a written assignment, seek online or offline help in a timely manner before any given deadline. Contact
Dr. Gastón via e-mail (jgaston@bmcc.cuny.edu, always type MAT 216 on the subject line of your e-mail) – or if you
are on campus go directly to the Math Lab (S511). For technical assistance, you may also try the Math Lab (S511,
212-220-1366), the BMCC Help Desk (Room S-165A, 212-220-8379), or the BMCC e-Learning Center (Room
S501a, 212-220-1243). Check the schedule to see when these rooms are open when you are on campus, and check
for schedule changes during holiday periods. Note that each quiz must be submitted by the posted weekly due date to
receive credit. Make sure to give yourself an adequate amount of time to complete the quiz and re-check your work
so you can submit the quiz by the deadline and earn a good score. You will have at least three attempts to earn your
best score on each quiz; only the highest score will count. Each quiz is automatically graded upon completion and
submission by that posted deadline. Otherwise, no credit is earned.
Students who register during late registration are expected to catch up by the end of the second week of the
semester.
WEEKLY CLASS SCHEDULE
Week #
1
Date
8/25/12
2
9/1/12
3
9/8/12
4
9/15/12
5
9/22/12
6
9/29/12
7
10/6/12
Topics
-Face-to-face course introduction
-Arithmetic and Algebraic
Connections
-The Rectangular Coordinate System
-Circles, Lines and Slopes
Assignment
Mathematics, A Good Beginning
Read Chapter 3.
Written Assignment: p. 96-98 #5, 7, 8, 12, 15, 18, 24, 25, 26.
Mathematical Ideas
Read Chapter 8, Sections 8.1 and 8.2.
Review the corresponding PowerPoint presentations and do the work indicated.
Complete and submit the quiz for this assignment by the posted deadline.
-Equations of Lines
Mathematical Ideas
-Linear Functions and Applications
Read Chapter 8, Sections 8.3 and 8.4.
Review the corresponding PowerPoint presentations and do the work indicated.
Complete and submit the quiz for this assignment by the posted deadline.
-Quadratic Functions
Mathematical Ideas
-Exponential Functions
Read Chapter 8, Sections 8.5, 8.6 and 8.7.
-Systems of Equations & Applications Review the corresponding PowerPoint presentations and do the work indicated.
Written Assignment: Chapter 8 Test, all problems.
Complete and submit the quiz for this assignment by the posted deadline.
Test #1 (Face-to-face class meeting, Room 502, 1-5 pm)
Mathematics, A Good Beginning Chapter 3
Mathematical Ideas Chapter 8
Reminder: Bring your portfolio of written assignments with you when you come in to take Test #1.
-Constructing Geometric Ideas
Mathematics, A Good Beginning
-Points, Lines, Planes, Angles
Read Chapter 16.
-Curves, Polygons, and Circles
Written Assignment: p. 440-442 #5, 14.
Mathematical Ideas
Read Chapter 9, Sections 9.1 and 9.2.
Review the corresponding PowerPoint presentations and do the work indicated.
Complete and submit the quiz for this assignment by the posted deadline.
-Measurement and Its Attributes
Mathematics, A Good Beginning
-Perimeter, Area, Circumference
Read Chapter 17.
-Geometry of Triangles
Written Assignment: p. 487-489 #3, 4, 5, 6, 8, 11, 14, 15, 16, 18, 22, 23, 30, 33,
35.
Mathematical Ideas
Read Chapter 9, Sections 9.3 and 9.4.
Review the corresponding PowerPoint presentations and do the work indicated.
Complete and submit the quiz for this assignment by the posted deadline.
-Space, Volume, Surface Area
Mathematical Ideas
-Transformations
Read Chapter 9, Section 9.5 and 9.6.
Review the corresponding PowerPoint presentations and do the work indicated.
Complete and submit the quiz for this assignment by the posted deadline.
Gastón MAT 216.p7
BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
8
10/13/12
9
10/20/12
10-11
10/27/12
11/3/12
12
11/10/12
13-14
11/17/12
11/24/11
15
12/1/12
16
12/8/12
17
12/15/12
-Non-Euclidean Geometry, Topology,
Networks
-Fractal Geometry
Mathematical Ideas
Read Chapter 9, Sections 9.7 and 9.8.
Review the corresponding PowerPoint presentations and do the work indicated.
Written Assignment: Chapter 9 Test, all problems.
Complete and submit the quiz for this assignment by the posted deadline.
Test #2 (Face-to-face class meeting Room 502, 1-5 pm)
Mathematics, A Good Beginning Chapters 16 and 17
Mathematical Ideas Chapter 9
Reminder: Bring your portfolio of written assignments with you when you come in to take Test #2.
-Counting by Systematic Listing
Mathematical Ideas
-Fundamental Counting Principle
Read Chapter 11, Sections 11.1, 11.2, 11.3, 11.4 and 11.5.
-Permutations and Combinations
Review the corresponding PowerPoint presentations and do the work indicated.
-Pascal's Triangle
Written Assignment: Chapter 11 Test, all problems.
-Counting Problems with Not and Or
Complete and submit the quiz for this assignment by the posted deadline.
-Analyzing Data
Mathematics, A Good Beginning
-Probability and Odds, Basic
Read Chapter 18.
Concepts
Written Assignment: p. 516-517 #5, 6, 7, 8.
-Events with Not, Or, And
Mathematical Ideas
-Binomial Probability
Read Chapter 12, Sections 12.1, 12.2, 12.3, and 12.4.
Review the corresponding PowerPoint presentations and do the work indicated.
Written Assignment: Chapter 12 Test, #1-22 only.
Complete and submit the quiz for this assignment by the posted deadline.
-Frequency Distributions
Mathematical Ideas
-Measures of Central Tendency
Read Chapter 13, Sections 13.1, 13.2, 13.3 and 13.4.
-Measures of Dispersion
Review the corresponding PowerPoint presentations and do the work indicated.
-Measures of Position
Complete and submit the quiz for this assignment by the posted deadline.
-Normal Distribution
Mathematical Ideas
-Regression and Correlation
Read Chapter 13, Sections 13.5 and 13.6.
Review the corresponding PowerPoint presentations and do the work indicated.
Written Assignment: Chapter 13 Test, #1-24 only.
Complete and submit the quiz for this assignment by the posted deadline.
Test #3 (Face-to-face class meeting Room 502, 1-5 pm)
Mathematics, A Good Beginning Chapter 18
Mathematical Ideas Chapters 11, 12, and 13
Reminder: Bring your portfolio of written assignments with you when you come in to take Test #3.
Cumulative Portfolio Review
Organize and review all of your written assignments for the cumulative Portfolio Review and for the final examination.
Make sure that you have completed and corrected each written assignment you are submitting for credit. Be sure that
your name, class, and assignment number are indicated at the top of each one.
Final Examination (Face-to-face class meeting Room 502, 1-5 pm)
Mathematics, A Good Beginning Chapters 3, 16, 17 and 18
Mathematical Ideas Chapters 8, 9, 11, 12, and 13
Reminder: Bring your entire portfolio of written assignments with you when you come in to take the final examination.
Gastón MAT 216.p8