IB Math Studies I – MTH151
First Semester 2006
Mrs. Jones (bjones@salem.k12.va.us)
Course Description
Presents topics in inductive and deductive reasoning, sets, logic, numeration and
mathematical systems, number theory, real numbers and their applications, geometric
systems, and computer concepts.
Prerequisites
Algebra I, Algebra II, and Geometry, or equivalent.
Textbook
Mathematical Ideas, 9th Edition, Miller, Heeren, & Hornsby, Addison-Wesley Publishers
Course Goals and Objectives
1. Confidence and belief in mathematical reasoning when the truth has been reached
through undeniable demonstrations.
2. An appreciation of the evolution of those mathematical ideas that define the subject.
3. An understanding of the foundations of mathematics which involve (i) the fundamental
concept of set (finite and infinite); (ii) the properties of numeration systems (historical
and contemporary); (iii) selected topics from Number Theory; (iv) the concept of
number and the properties of real numbers; (v) the laws that govern mathematical
systems.
4. The use of the graphing calculator as an algorithmic method of solving selected
problems.
5. Independent inquiry and research that enhances mathematical knowledge.
6. An appreciation of the aesthetic nature of mathematics.
I.
Course materials -- -- needed every day
1. Textbook
2. Paper (should be loose leaf in a 3 ring notebook
3. Pencil (work done in ink will not be graded)
4. Previous assignments
5. Student planning and agenda book
6. graphing calculator (a TI 83, TI 83+, TI84, or TI 84+ is required for Math Studies II)
II. Six-weeks evaluation
Grading will be by cumulative points. Letter grades will be assigned according to
the Salem City School grading scale.
1. Tests
There will be approximately three tests per six week and each will usually count as
100 points
2. Quizzes
a. Notebook quizzes will be closed book but opened notebook and consist of
working problems or answering with short answer. These will usually count 5-25
points.
b. Problem quizzes will be closed book and consist of working problems or answering
with short answer. These will usually count 5-25 points.
3. Homework
Homework should always be completed conscientiously and on time. In an effort to
encourage you to do this, I will check your assignments often. The following scale will
usually be used:
0 points for less than 1/5 completed
1 point for more than 1/5 but less than 2/5 completed
2 points for more than 2/5 but less than 3/5 completed
3 points for more than 3/5 but less than 4/5 complete
4 points for more than 4/5 but less than all completed
5 points for all completed
Homework will be taken up occasionally and graded as to content. You may receive help if
necessary. If you have received help, you must understand the process necessary to solve the
problems well enough to explain all of your work in class. Copying will be considered as
cheating. All work must be shown. No work means no credit given.
III. Class rules:
1. Be in your seat ready to work when the bell rings. If you are late to class, you will need to
make up your time by doing extra work with me during your lunch period.
2. Bring all books and materials to class. Either bring your own sharpened pencils to class
or sharpen your pencils before the tardy bell rings. You will not be allowed to return to
your locker to retrieve “forgotten” items.
3. Sit in your assigned seat each day and remain there until class is dismissed.
4. Follow directions the first time they are given.
5. Conduct yourself in a manner not disruptive to class. Do not bring grooming items,
drinks, food, hats, electronic games, etc. into the classroom.
IV.
Make-up work.
1. Arrangements to make up a test due to an excused absence must be made within two days
of your return to school. You should always try to make up your test on the first day back
in school.
2. Makeup tests will usually be given during Math Lab (AM or PM). You will need to make
arrangements with me prior to the test time in order for your test to be available. It will be
easier for you if you are present on test days.
3. If you make an appointment to make up a test and do not make up test at that time, you
may receive is a zero on that test.
4. If you are in class the day a test is announced and in class the day that test is given, you are
expected to take the test at the regular time.
5. If you are taking a test at a time different from the rest of the class, you should expect a
different test.
6. If you are suspended from school or have an unexcused absence, you will be given two
days to make up work for each day of unexcused absence. The maximum grade given for
such make-up work shall be a “69”. Time extensions will not be granted.
7. If you are absent due to an excused absence, you must make up the work missed within 2
days of your return to school.
8. If you are absent due to a preplanned event (athletic events, field trips, etc.), you should
have all work completed on the day following the absence.
9. Homework must be completed by the beginning of class.
10.The responsibility of making arrangements to make up work rest with YOU!
V. Conferences and extra help
I will be glad to help you at any time you feel you need extra help. If you will see me before
or after class, we will arrange a convenient time to work. Help is also available in the math
Lab (room 258) which is open before school beginning at 6:30 am and after school beginning
at 3:00 pm. All work will be covered in class, but if after class discussion you still have a
question or problems, please make me aware of the situation so we can arrange for extra help.
Topical Description
Chapter 1: The Art of Problem Solving
1.1 Solving Problems by Inductive Reasoning
1.2 An Application of Inductive Reasoning: Number Patterns
1.3 Strategies for Problem Solving
1.4 Calculating, Estimating, and Reading Graphs
Extension: Using Writing to Learn About Mathematics
Chapter 2: The Basic Concepts of Set Theory
2.1 Symbols and Terminology
2.2 Venn Diagrams and Subsets
2.3 Set Operations and Cartesian Products
2.4 Cardinal Numbers and Surveys
2.5 Infinite Sets and Their Cardinalities
Chapter 3: Introduction to Logic
3.1 Statements and Quantifiers
3.2 Truth Tables and Equivalent Statements
3.3 The Conditional and Circuits
3.4 More on the Conditional
3.5 Analyzing Arguments and Euler Diagrams
3.6 Using Truth Tables to Analyze Arguments
Chapter 4: Numeration and Mathematical Systems
4.1 Historical Numeration Systems
4.2 Arithmetic in the Hindu-Arabic System
4.3 Conversion Between Number Bases
4.4 Finite Mathematical Systems
4.5 Groups
Chapter 5: Number Theory
5.1 Prime and Composite Numbers
5.2 Selected Topics from Numbers Theory
5.3 Greatest Common Factor and Least Common Multiple
5.4 Modular Systems
5.5 The Fibonacci Sequence and the Golden Rule
Chapter 6: Real Numbers and Their Representations
6.1 Real Numbers, Order, and Absolute Value
6.2 Operations, Properties, and Applications of Real Numbers
6.3 Rational Numbers and Decimal Representation
6.4 Irrational Numbers and Decimals and Decimal Representation
6.5 Applications of Decimals and Percents
Extension: Complex Numbers
Plus assorted topics as time permits