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Columbia College
Evening Campus
1001 Rogers Street
Columbia, MO 65216
(800) 231-2391


16 / 34 - Late Spring Session
February - April 2017

Course Syllabus

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Course Syllabus
16 / 34 - Late Spring Session
February - April 2017
Evening Campus
1001 Rogers Street
Columbia, MO 65216
(800) 231-2391

Course Prefix and Number: MATH 155 A
Course Title: *Algebraic Reasoning for Elementary and Middle School Teachers
Semester Credit Hours: 3
Class Day and Time: Thu 
5:30 PM-8;30 PM
Additional Notes:

This is a virtual hybrid course which will meet weekly through Blackboard Collaborate (virtually) and online instruction through D2L using various resources, discussion and homework. The instructor will email instructions on how to access Blackboard Collaborate the week prior to the start of class. .


Catalog Description

This course introduces some basic concepts of number theory and modern algebra that underlie elementary and middle grade arithmetic and algebra, with a focus on collaborative learning and technology. Cross-listed as MATH 155. Prerequisites: MATH 102 and MATH 150 (or higher).


MATH 102 and MATH 150 (or higher).


Developing Essential Understanding of Algebraic Thinking; Grades 3-5 2011 edition
Author: Blanton, M., Levi, L., Crites, T., and Dougherty, B.J. (NCTM)
ISBN: 978-0-87353-668-4
Developing Essential Understanding of Expressions, Equations & Functions; Grades 6-8 2011 edition
Author: Lloyd, G., Herbel-Eisenmann, B., and Star, J. R. (NCTM)
ISBN: 978-0-87353-670-7

Course Learning Outcomes

  1. Demonstrate knowledge of the basic properties of the real numbers including commutativity, associativity, identity, distributivity.
  2. Use the basic properties of the real numbers to determine equivalent algebraic equations and solve algebraic equations.
  3. Use equations to model problem solving situations.
  4. Use a variable to generalize a pattern, to represent a fixed but unknown number, to represent a quantity that varies in relation to another quantity and understand that a variable can be a discrete or continuous quantity.
  5. Use quantitative reasoning to generalize relationships.
  6. Use functional thinking to generalize relationships between covarying quantities and to express those relationships in words, symbols, tables, or graphs and reason with those relationships to analyze function behavior.
  7. Represent patterns algebraically.
  8. Compare and contrast the concepts of equality or equivalence.
  9. Find values that make two expressions equal.
  10. Demonstrate understanding that an inequality can describe a relationship between quantities and solve these inequalities.
  11. Describe recursive relationships.
  12. Classify functions based on the rate at which the variables change and the situations that they model.
  13. Solve equations using symbolic, graphical and numerical methods.
  14. Demonstrates knowledge of the academic language of the appropriate discipline applicable to the certification area(s) sought as defined by the Subject Competencies for Beginning Teachers in Missouri. (1.1)
  15. Demonstrates content knowledge and ability to use multiple subject specific methodologies for specific instructional purposes to engage students. (1.2)
  16. Demonstrates understanding of how to engage students in the methods of inquiry and research in his or her respective discipline. (1.3)
  17. Understands how to select appropriate strategies for addressing individual student needs in meeting curriculum objectives. (3.2)
  18. Demonstrates knowledge of current instructional resources to support complex thinking and technological skills. (4.2)
  19. Develops skills in using a variety of technology media communication tools. (6.4)

Special Course Requirements

Items Required for this Class:

  • Desmos Free Online Grapher:
  • TI-84 Graphing Calculator
  • Microsoft Excel

Topical Outline:

  • Arithmetic as a context for algebraic thinking
  • Equations and equivalence
  • Variables
  • Quantitative reasoning and generalizations
  • Representing functions
  • The symbolic language of algebra
  • Expressions as building blocks
  • Variables for studying varying quantities
  • Equality vs. Equivalence
  • Functions for modeling
  • Rates of change
  • Solving equations, graphically, symbolically and numerically


Instructional Methods

The instructional methods will include lecture, small group work, and individual exploration. We will have the opportunity to explore mathematics through the use of mathematical manipulatives and technology, such as the calculator, software programs, and online manipulatives and applets.

Graded Activities

Discussion Questions16@10 points = 160 Points
Description -

You will be expected to participate in 2 discussion questions each week. These discussions will relate to the readings and activities both inside and outside of class that completed during that week.

Activities8@20 points = 160 Points
Description -

You will be expected to complete and out of class activity each week that will be and extension to the class activities for the week.

Quizzes8@10 points = 80 Points
Description -

You will be asked to complete a short quiz each week over the mathematics we have covered through readings, the activities in and out - of class.

Midterm and Final Exams2@150 points = 300 Points
Description -

You will be expected to complete two exams each worth 150 points. The first will cover the material in the first four weeks of the course and the second exam will be the materials covered in the last four weeks of the course. The questions on the exams will relate to both the readings, discussions, quizzes, and activities for those weeks.


Grading Scale

90%-100% A
80%-89% B
70%-79% C
60%-69% D
0-59% F

Additional Information / Instructions

MATH 155 - Total Points Possible 700

Grades are based on accumulation of points. Points are assigned to each of the assignments. (See points at end of each assignment). Grades will be rounded from .5% and up, to the next whole number.

Your grade will be calculated by dividing the total points you earn in the course by the total points that are possible and then applying the Grade Scale above. Extra credit will not be provided, nor will grades be assigned based on a curved distribution.

The instructor reserves the right to adjust or make changes to the schedule and differentiated instruction as needed. All changes will be announced and each student will be responsible for recording and responding to the changes. 

Schedule of Activities and Assignments

Week 1
Algebraic Thinking and Arithmetic as a Context for Algebraic Thinking
  • Properties of Numbers Activity (commutative, associative, distributive zero product property, identity, inverses)
  • Number Systems (natural, whole, integers, relational, irrational, real, complex)
  • Using the properties to do mental math and alternative algorithms
  • Basic Number Theory Generalizations (even + even, odd + odd, etc)
  • Blanton et al Introduction and Chapter 1 (pp 1 - 24)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 1
  • Activity 1
Week 2
Equations as Statements of the Equivalence of Two Quantities and Variables as Versatile Tools
  • Understanding the equal sign
  • Reasoning about Equations and Nonstandard strategies for solving equations
  • Modeling with Equations
  • The roles of a variable
  • Blanton et al Chapter 1 (pp 25 - 38)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 2
  • Activity 2
Week 3
Using Quantitative Reasoning to Generalize Relationships and Functional Thinking as a Path into Algebra
  • Relational Understanding (=, <, >)
  • A Function as a Relationship between two sets
  • Covariation
  • Discrete vs Continuous Functions
  • Recursive Functions
  • Blanton et al Chapter 1 (pp 39 - 66)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 3
  • Activity 4
Week 4
Connecting Algebraic Thinking Across the Grades
  • Developing the Symbolic Language of Algebra
  • The Handshake Problem
  • Generalizing Arithmetic
  • Equal vs Equivalent
  • Blanton et al Chapter 2 (pp 67 - 80)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 4
  • Activity 4
  • Midterm Exam
Week 5
Understanding Expressions, Equations, and Functions and Expressions as Building Blocks
  • Expressions
  • Equivalent Expressions (using the properties)
  • Evaluating Expressions
  • Graphs and Tables
  • Lloyd et al Introduction and Chapter 1 (pp 1 - 24)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 5
  • Activity 5
Week 6
Variables as Useful Tools and Equality and Equivalence
  • More on the various roles of a variable (unknown quantity vs relationship between varying quantities)
  • Expressions vs Equations vs Functions
  • Finding the value to make two expressions equal
  • Solving an Equation
  • Inequalities and solving inequalities
  • Lloyd et al Chapter 1 (pp 25 - 43)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 6
  • Activity 6
Week 7
Representing and Analyzing Functions and Solving Functions
  • Functions as models
  • Patterns of change/Rates of Change
    • Constant Rates of Change (Linear)
    • Changing Rates of Change (Quadratic, Exponential)
  • Solving Linear Equations (symbolic, graphical and numerical methods)
  • Lloyd et al Chapter 1 (pp 44 - 82)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 7
  • Activity 7
Week 8
Connecting Expressions, Equations & Functions Across the Grades
  • Algebra Tiles for multiplying, dividing and factoring polynomials
  • Inverses
  • Patterns and Functions
  • Transformations of Functions/Families of Functions
  • Lloyd et al Chapter 2 (pp 83 - 100)
  • Discussion Question 1
  • Discussion Question 2
  • Quiz 8
  • Activity 8
  • Final Exam

Library Resources

Columbia College Resources - Online databases are available at the Columbia College Stafford Library.  You may access them using your CougarTrack login and password when prompted.

Course Policies and Procedures


Columbia College Policy - Columbia College students are expected to attend all classes and laboratory periods for which they are enrolled.  Students are directly responsible to instructors for class attendance and work missed during an absence for any cause.  If absences jeopardize progress in a course, an instructor may withdraw a student from the course with a grade of "F" or "W" at the discretion of the instructor.  For additional information, see the Columbia College policy on Student Attendance.

Instructor Policy -

  1. Attendance and Participation: Students are expected to come to class, and therefore a loss of points for unexcused or excessive absences will occur. It is impossible to ever duplicate the time spent in class, and the professor cannot use class time to try to “catch-up” those students who were absent. If you must miss class, it is your responsibility to obtain notes from a fellow student. Do not ask the instructor to provide this for you. Note that any assignments that are not turned in because you are absent will be counted as late. To avoid the late penalty, assignments may be submitted via Dropbox prior to the start of class time. Additionally, when you are late to class, it will be your responsibility to insure that you have been marked present by the professor. Students expecting a superior grade must demonstrate superior attendance. A grade of “A” will not be issued for any student missing more than one class session. The instructor reserves the right to issue a grade of F, U, W, or I for any student who, for any reason, misses three or more classes or more than one hour of field experience. Finally, students must come to class prepared with a notebook and pen or pencil to take notes, and any assignments that are due. Also be prepared to ask questions and participate in class discussion. Borderline grades will be influenced by class participation.

  2. Late Assignments: If the student have justifiable cause for missing student will have 1 day from due date to makeup assignment with a -10% deduction from the maximum possible score. If turned in later than 1 day will receive a 0.

  3. In Class Work: (Weekly Assignments, Class Activities, Discussions, and Group Activities) No Makeup.

Academic Integrity

Columbia College Policy - Columbia College students must fulfill their academic obligations through honest, independent effort.  Dishonesty is considered a serious offense subject to strong disciplinary actions.  Activities which constitute academic dishonesty include plagiarism, unauthorized joint effort on exams or assignments, falsification of forms or records, providing false or misleading information, or aiding another in an act of academic dishonesty.  For more information, see the Columbia College Academic Integrity Policy and Procedures.

Instructor Policy -

  1. All work must be original and represent the thinking and understanding of the student. Sources must be credited for the ideas, content and quotations used in the development of the assignment and must be cited using APA format.

  2. Plagiarism will not be tolerated. Those found plagiarizing will be dropped from the course and receive an F.

Class Conduct and Personal Conduct

Columbia College Policy - Students must conduct themselves so others will not be distracted from the pursuit of learning.  Students may be disciplined for any conduct which constitutes a hazard to the health, safety, or well-being of members of the College community or which is deemed detrimental to the College's interests. Discourteous or unseemly conduct may result in a student being asked to leave the classroom.  For more information, see the Columbia College Student Code of Conduct and Student Behavioral Misconduct Policy and Procedures.

Cancelled Class Make-Up

Columbia College Policy - Classes cancelled because of inclement weather or other reasons must be rescheduled.  For more information, see the Columbia College Inclement Weather Policy.

Make-Up Examinations

Columbia College Policy - Make-up examinations may be authorized for students who miss regularly scheduled examinations due to circumstances beyond their control.  Make-up examinations must be administered as soon as possible after the regularly scheduled examination period and must be administered in a controlled environment.

Campus Policy - Make up examinations are scheduled on designated Saturday mornings 9am in 103 Buchanan. Students must present a picture I.D. in order to be admitted to the testing session. Students must arrange with the instructor to take the exam before or after it is given in class and permission to take a makeup examination (or any graded activity) is granted at the discretion of the instructor.

Instructor Policy -

  1. Midterm and Final Exams: If the student has justifiable cause for missing, student will have 1 day from the due date to makeup the Exam with a 10% deduction from the maximum possible score. If turned in later than 1 day will receive a 0.

Adding, Dropping, or Withdrawing from a Course

Columbia College Policy - Students may add a course through Wednesday of the first week of the session and drop a course without academic or financial liability through close of business on Monday of the second week of the session.  Once enrolled, a student is considered a member of that class until he or she officially drops or withdraws in accordance with College policy.  An official drop/withdrawal takes place only when a student has submitted a Drop/Add/Withdrawal form.  A failure to attend class, or advising a fellow student, staff or adjunct faculty member of an intent to withdraw from a class does not constitute official drop/withdrawal.  The drop/add/withdrawal periods begin the same day/date the session starts, not the first day a particular class begins. If a student stops attending a class but does not submit the required Drop/Withdrawal form a grade of "F" will be awarded.  For more information, see the Columbia College Registration Policy and Procedures.

Withdrawal Excused

Columbia College Policy - A student may request an excused withdrawal (WE) under extraordinary circumstances by submitting a Drop/Withdrawal form accompanied by a complete explanation of the circumstances and supporting documentation to the location director.  The WE request must include all classes in which the student is currently enrolled.  The Vice President for Adult Higher Education is the approving authority for all WE requests.  A student who receives approval of their WE request may still be required to return some or all of the federal financial assistance received for the session.  For more information, see the Columbia College Withdrawal Policy.


Columbia College Policy - A student may request that the instructor award a grade of "I" due to extraordinary circumstances (unforeseen or unexpected circumstances beyond the student's control) that prevent a student from completing the requirements of a course by the end of a session.  An "I" will not be given because a student is failing, negligent or not meeting requirements.  If the instructor believes an "I" is appropriate, the instructor will specify the work needed to complete the course and the time allowed to complete the work.  Work missed must be made up within two subsequent sessions unless the instructor specifies an earlier date.  Extensions beyond two sessions must be approved by the Vice President for Adult Higher Education.  If the work is completed during the specified time period, the instructor will change the "I" to the grade earned.  If the work is not completed during the specified time, the instructor may allow the incomplete to remain on the student's permanent record or change it to any other letter grade.  For more information, see the Columbia College Undergraduate Grading Policy.

Grade Appeal

Columbia College Policy - A student may appeal any grade given if it is believed to be in error or in conflict with Columbia College policy and procedures.  The student must state in writing to the location director why the grade awarded is believed to be in error and request a desired remedy.  The faculty member who awarded the grade will be given the opportunity to comment on all student allegations.  If the issue cannot be resolved at the location the appeal will be transmitted through the location director to the Vice President for Adult Higher Education.  A grade appeal must be received for review by the Vice President for Adult Higher Education prior to the end of 60 days from the date the grade was awarded.  For more information, see the Columbia College Undergraduate Grading Policy.


Columbia College Policy - Course prerequisites are established to ensure that a student has adequate academic preparation to succeed in a particular course.  Staff members will attempt to ensure that students meet prerequisite requirements.  However, it is the student's responsibility to closely examine the course descriptions to determine if prerequisites exist and to enroll in courses in the proper sequence.  In some exceptional cases it may be apparent that the student possesses the required skills and knowledge to succeed in a particular course, even though they have not taken the prerequisite course.  In this case the prerequisite course may be waived by the location director.  Waiver of a course as a prerequisite does not remove the requirement to complete the course if it is a requirement for the student's degree program.


Columbia College Policy - The College provides all students access to CougarMail (the official means of e-mail communication for the College), online resources from the Stafford Library, and their Columbia College records (transcripts, grades, student schedules, etc.) through CougarTrack.

Instructor Policy - Student should check D2L Announcements and Cougar email each week for messages from the instructor.


Columbia College Policy - The official student email address (also known as CougarMail) will be used for all official correspondence from faculty and staff.  Students are responsible for the information received and are required to monitor their CougarMail account on a regular basis.  Students may forward their CougarMail to another email account but will be held responsible for the information sent over CougarMail, even if there is a problem with the alternate mail service.

Instructor Policy - Cougar email will be the official email address for students in this class. Instructor will reply to messages and emails. If student does not receive a reply, the message or email was not received.

Cell Phones

Columbia College Policy - Cell phones can be a distraction to the learning process.  Location directors or course instructors may require that cell phones be turned off or set to vibrate during class periods.  Students requiring special arrangements to receive a cell phone call during class should make prior arrangements with their location director or course instructor.

Instructor Policy - Cell phones should be put on silent in class.

Bookstore Information

Columbia College Policy - As part of Truition, students will receive their course materials automatically as described below. 

eText Information

If a course uses an eText, (see Textbook information above) the book will be available directly in Desire2Learn (D2L) and through the VitalSource eText reader the Friday before the session begins, if registered for courses prior to that date.  Students will have a VitalSource account created for them using their CougarMail email address.  Upon first login to VitalSource, students may need to verify their account and update their VitalSource password.  More information about how to use the VitalSource platform, including offline access to eTexts, can be found in D2L.  Students that would like to order an optional loose-leaf print-on-demand copy of eligible eTexts can do so through the VitalSource Bookshelf at an additional cost.  Once orders are placed, it can take approximately five to seven business days for students to receive their print-on-demand books.

Physical Course Materials Information

Students enrolled in courses that require physical materials will receive these materials automatically at the address on file with Columbia College.  Delivery date of physical materials is dependent on registration date and shipping location.  Please refer to confirmation emails sent from Ed Map for more details on shipping status.

Returns:  Students who drop a course with physical course materials will be responsible for returning those items to Ed Map within 30 days of receipt of the order.  More specific information on how to do so will be included in the package received from Ed Map.  See here for Ed Map's return policy.  Failure to return physical items from a dropped course will result in a charge to the student account for all unreturned items.

Students who opt-out of having their books provided as part of TruitionSM are responsible for purchasing their own course materials.  Visit for details.


Columbia College Policy - The Family Educational Rights and Privacy Act (FERPA) affords students certain rights with respect to their education records.  For more information, see the Columbia College Family Education Rights and Privacy Policy.

Student Accessibility Resources

Columbia College Policy - Students with documented disabilities who may need academic services for this course are required to register with the office of Student Accessibility Resources.  Until the student has been cleared through this office, accommodations do not have to be granted.  If you are a student who has a documented disability, it is important for you to read the entire syllabus as soon as possible.  The structure or the content of the course may make an accommodation not feasible.  Student Accessibility Resources is located in Student Affairs in AHSC 215 and can be reached by phone at (573) 875-7626.  For more information, see the Columbia College ADA and Section 504 Policy for Students.

Instructor Policy - Students needing accomodations must work with the office of ADA to get the accomodations approved and in place for the class.

Alcohol and Other Drugs: Columbia College Policies & Resources

Columbia College Policy - Columbia College recognizes the negative health effects associated with the use, possession, and distribution of controlled and/or illicit substances, and their detrimental impact on the quality of the educational environment.  Therefore, all members of the College community share in the responsibility of protecting the campus environment by exemplifying high standards of professional and personal conduct.  For more information and resources, see the Columbia College Alcohol and Other Drugs Policy.

Tobacco-Free Policy

Columbia College Policy - The following policy goes into effect on August 21, 2017.  Columbia College values and is concerned for the health and well-being of its students, employees and visitors. The College is committed to providing a healthful and productive educational and employment environment for members of the College community. Consistent with this commitment and in the interest of the general health and welfare of the College community, the College prohibits the use of all tobacco products and related devices on all College property and premises.  For more information, see the Columbia College Tobacco-Free Policy.


Columbia College Policy - Discrimination, harassment, and retaliation on the basis of protected status (see Notice of Non-Discrimination and Equal Opportunity for a definition of "protected status") are strictly prohibited. Persons who engage in such conduct are subject to discipline up to and including termination or dismissal.  For more information, see the Columbia College Non-Discrimination and Equal Opportunity Policy and Complaint Resolution Procedure.

Columbia College Policy Library

Columbia College Policy - The policies set forth in the Online Policy Library are the current official versions of College policies and supersede and replace any other existing or conflicting policies covering the same subject matter.  The Online Policy Library is currently under construction with new policies being added on a frequent basis and the policies currently listed are not comprehensive of every College policy.  Questions regarding the Online Policy Library should be directed to the Office of the General Counsel.  For more information on policies applicable to students, see Student Policies.  For more information on policies applicable to the entire Columbia College community, see College-Wide Policies.

Technical Support

Columbia College Policy - If you have problems accessing the course or posting your assignments, contact your instructor, the Columbia College Technology Solutions Center, or the D2L Helpdesk for assistance.  If you have technical problems with the VitalSource eText reader, please contact VitalSource.  Contact information is also available within the online course environment.

        - Columbia College Technology Solutions Center:, 1-800-231-2391 ext. 4357

        - D2L Helpdesk:, 1-877-325-7778

        - VitalSource:, 1-855-200-4146


Course Evaluations - All students are encouraged to complete the online course evaluations. Students are notified by way of CougarMail when the evaluations are available. The evaluations are used to help instructors improve their teaching techniques. They are reviewed carefully by the Evening Campus Director, Assistant Director, and several AHE Administrators. Student should know that all responses are completely confidential, instructors only view results after grades are posted. Your input is valued and appreciated.

Late graded assignment/activity policy - All graded assignments or activities are due when stated in the syllabus or by the instructor. Graded assignments or activities submitted after the stated due date/time will not receive any credit unless the instructor has specifically stated that full or partial credit may be awarded to late submissions.


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