Connections in Mathematics

Stephen C. Smith, Ed.D., Director; Email: ssmith@cvgs.k12.va.us 
Office Hours: After class as needed or as scheduled by email

Course Description:
This course provides students with introductory experiences in symbolic logic, binary and other bases, probability, conditional probability, set theory, voting schemes and apportionment theory, and topics of personal finance and investment. Both EXCEL and a variety of website-based applications will be used throughout the year. Emphasis is placed on conceptual understanding, solving real world applications, and fostering mathematical reasoning and communication.

Required Course Materials:
The primary text for this course will be The Nature of Mathematics, 10th ed., by Smith (no relation). You will be responsible for any text while it is in your possession; scanned pages of the text are available in a shared Google folder for your convenience.

Methodology:
The beginning of most class periods will be used to answer questions on the material that is due for that day. The rest of the class period will consist of a variety of activities including lecture, individual and group problem solving, and exploration of questions and concepts. You will prepare for each class meeting by working assigned homework problems and by reading and taking notes on the text to be covered in the next class meeting.

Study Aids:
There are many reference books and web sites widely available that can serve as study aids for this course. However, it is unlikely that any materials beyond those provided in class will be necessary. If you feel at any time that you require additional assistance, please discuss this with me at the beginning or end of the next class meeting.

Participation:
You should plan to be actively involved in class. This means being attentive and participating in class discussions and activities. Points may be deducted for a lack of participation.

Absences (consult the Student Handbook for additional information):
When you miss any amount of class time, for any reason, it is your responsibility to contact a classmate to obtain the information you missed. Foreseeable absences for any reason need to be discussed with the instructor in advance.

If a student is absent, upon return he/she is expected to have completed the work that was due on the day of absence. If a test was missed, the student is expected to take the test on the day of return. If a student misses several consecutive class meetings, he/she should email the instructor to devise a plan to catch up. 

Tardiness (consult the Student Handbook for additional information):
You are expected to be in our class, ready to learn, by our starting time. Given my responsibilities as the Director of the Governor’s School, I might not be in the room; that does not relieve you of your responsibility to be in the class, ready to learn, by the beginning of class. Students will begin class at the assigned time regardless of my presence or absence. I will permit one unexcused tardy without any grade penalty.  After that, each unexcused tardy may result in a reduction in your semester grade of ½ pt.

Honor Code:
Students are required to pledge all work that they turn in for a grade.  The pledge should be written out and signed PRIOR to completing the work.  The pledge is as follows: 

I have neither given nor received any unauthorized assistance on this assignment.  (Student's signature)

Grading:
The grading scale is a standard 11/10/10/10 percentage scale.

 

Point Total and Grade Equivalent Chart

97-100   A+

87-89     B+

77-79     C+

67-69     D+

93-96     A

83-86     B

73-76     C

63-66     D

90-92     A-

80-82     B-

70-72     C-

60-62     D-

Earning less than 60 percent of the available points will result in a failing grade for the course.

All progress reports will show the grade thus far in the course.  There is no average of progress report grades for a final semester grade.

Students are responsible for maintaining a spreadsheet of their grades so that, at any given time, they know the total number of possible points to date and the total number of points earned.  Students may be asked at any time to show their points.

FIRST SEMESTER Specific Course Content and Objectives:
the student will be able to:

  • translate sentences to symbolic form,
  • construct truth tables,
  • state the converse, inverse and contrapositive of statements,
  • determine the validity of an argument,
  • design a simple circuit as a logic application,
  • understand and use basic set theory concepts, including intersections, unions, complements, distributive and De Morgan’s laws, and cardinality,
  • convert numbers in the decimal, binary, octal, and hexadecimal systems,
  • recall and be able to compare and contrast voting methods, voting dilemmas, apportionment methods and paradoxes
  • recall the processes necessary and properly solve problems related to the Fundamental Counting Principle, permutations, and combinations,
  • compute probabilities and evaluate expected values,
  • compute conditional probabilities,
  • identify and solve problems using an Euler Circuit
  • identify a Hamiltonian Cycle
  • identify and construct a minimal spanning tree
  • solve Traveling Salesman problems

The FIRST SEMSTER grade will be determined as follows:  

Item Type

Description

Point Value

Total Points

Tests (5)

50 minutes

(about ½ recall and ½ application)

120

600

Test Corrections (5)

Specific requirements must be met…

20

100

Final Exam (1)

Comprehensive semester final based on tests and new content (if any)

200

200

Projects (3)

Application problems (some individual, some in pairs or groups)

30

90

Class Participation

Asking or answering questions well, putting problems on the board

(the goal is to average at least one every other instructional period)

10

10

TOTAL POINTS

PER SEMESTER

 

1,000

 

SECOND SEMESTER Specific Course Content and Objectives:
the student will be able to:

  • Identify how payroll related taxes affect income; topics include
  • Gross, taxable and adjusted incomes, W2 and W4 forms
  • Social Security Tax/Medicare, Federal, State, Local payroll taxes
  • Tax brackets
  • Compute origination fees, discounts, repayments, and total cost of loans
  • compute simple interest
  • compute compound interest (including discrete and continuous compounding)
  • Identify a house for sale and complete all the calculations for the cost to purchase the house
  • Explore credit card benefits and fees, debit card information, etc.
  • Define the terms “stocks,” “bonds,” “mutual funds,” and “annuities”
  • compute the present and future value (given certain assumptions) of annuities
  • create an amortization schedule for a home purchase
  • Learn how to follow stocks
  • Define the terms “traditional IRA,” “ROTH IRA,” and “401K” and explain their various tax advantages and limitations
  • Identify, research, estimate, and present on some type of life expense. Past projects have included the following topics:
  • Housing and miscellaneous living expenses, medical insurance, vacation costs, college costs, costs of smoking, pet ownership, having a baby, etc.
  • Use Microsoft Excel throughout the semester
  • Complete the Senior Science Scenario Project

                              The semester grade will be determined as follows      

Item Type

Description

Point Value

Total Points

Tests (3)

50 minutes

(about ½ recall and ½ application)

150

450

Final Exam (1)

Comprehensive semester final based on tests and new content (if any)

200

200

Finance Project (1)

In a pair, includes a PowerPoint and presentation to the class

100

100

Smaller Projects (2)

Application problems (some individual, some in pairs or groups)

50

100

S-Cubed

A group project, paper, and presentation completed the last 5 weeks of the semester

150

150

TOTAL POINTS

PER SEMESTER

 

1,000