Math Logic & Problem Solving Honors
Course Description:
Logic and Problem Solving Honors is a course designed to strengthen the
skills essential to
mathematical reasoning and problem solving. Participants will learn about the
major elements of
mathematical logic including but not limited to validity, soundness, formal
proof and counter
example, inductive and deductive reasoning, truth tables, and set theory. These
concepts will be
applied to proof writing and analysis, problem solving, and other mathematical
units of study such
as probability, statistics, algebra, geometry, and number theory. Successful
completion of this
course will prepare the student for advanced math and logic courses.
Outcomes: Upon successful completion of this course, the student will:
a. understand and apply the concepts of inductive and deductive
reasoning
b. apply inductive and deductive reasoning in mathematical proofs and
problem solving situations
c. understand and apply the concepts and symbols of set theory
d. understand and apply the concepts and symbols relating to the rules of
logic
e. understand and apply the definitions of symbolic logic
f. construct and apply truth tables for specific cases and for determining
validity
g. construct and use Euler diagrams to determine validity
h. apply reasoning skills to early numeration systems and number bases in
positional systems
i. apply logic concepts and problem solving to topics of mathematical
study including, Number Theory, Algebra, Geometry, Trigonometry, Counting
Methods and Probability Theory, Statistics, and Mathematical Systems
Student Evaluation and Grading Policies for Credit
Courses Only:
CTD Grading scale
| A+ |
100-98% |
A |
97-93% |
A- |
92-90% |
| B+ |
89-87% |
B |
86-83% |
B- |
82-80% |
| C+ |
79-77% |
C |
76-73% |
C- |
72-70% |
| D+ |
69-67% |
D |
66-63% |
D- |
62-60% |
| F |
below 60% |
|
|
|
|
The final semester grade will be based on completion of
daily assignments (25%) and test grades
(75%).
Instructor Biography:
Lynn Tremmel is a middle school math teacher with 18 years
of experience teaching Math, Pre-
Algebra, and Algebra I in grades 6-8. She has a B.A. degree in elementary
education with a
mathematics concentration (receiving honors in mathematics) along with a M.Ed.
in mathematics
education, both from National College of Education (National Louis University).
She is also an
article reviewer for the Illinois Council of Teachers of Mathematics.
Mrs. Tremmel has taught for the Saturday Enrichment
Program through the Center for Talent
Development and is excited to be teaching her first summer session for the
Summer Spectrum
Program.
Schedule:
The following is a flexible schedule of topics covered in
class. These will be adjusted as students’
needs dictate. Instructional strategies that will be utilized include large
group instruction, small
group work, individual work, and class discussions.
| Date(s) |
Topic(s) |
Activities |
Assignments
and/or
Assessment |
| Week 1 |
|
|
|
| Monday |
Problem Solving
and Critical
Thinking
(Chapter 1) |
-inductive/deductive reasoning
-estimation, graphs, and mathematical models
-problem solving |
Pre-Test
Chapter 1
assignment |
| Tuesday |
Set Theory
(Chapter 2) |
-basic set concepts
-subsets
-Venn diagrams and set operations
-problem solving applications |
Test Chp. 1
Chapter 2
assignment |
| Wednesday |
Logic
(Chapter 3) |
-statements, negations, and
quantified
statements
-compound statements and connectives
-truth tables for negation, conjunctions, and
disjunctions
-truth table for the conditional and the
biconditional
-equivalent statements, variations of
conditional statements, and De Morgan’s laws |
Test Chp. 2
Chapter 3
assignment
(part 1) |
| Thursday |
Logic
(Chapter 3) |
-arguments and truth tables
-arguments and Euler Diagrams |
Chapter 3
assignment
(part 2) |
| Friday |
Number
Representations
and Calculations
(Chpater 4) |
-Hindu-Arabic System and early
positional
systems
-number bases in positional systems
computations in positional systems
-early numeration systems
-groups develop their own numeration system |
Test Chp. 3
Chapter 4
assignment and
small group
project |
| Week 2 |
|
|
|
| Monday |
Number Theory
and the Real
Number System
(Chapter 5) |
-divisibility, prime, composite
-factors, multiples
-integers, order of operations
-rational numbers
-real numbers and their properties
-exponents and scientific notation
-arithmetic and geometric sequences |
Test Chp. 4
Chapter 5
assignment |
| Tuesday |
Mathematical
Systems
(Chapter 13) |
-determine what a mathematical
system is
-properties of certain mathematical systems
-groups and clock arithmetic |
Test Chp. 5
Chapter 13
assignment |
| Wednesday |
Algebra:
Equations and
Inequalities
(Chapter 6) |
-algebraic expressions and formulas
-linear equations in one variable
-applications of linear equations
-ratio, proportion and variation
-linear inequalities in one variable
-quadratic equations
-proofs involving linear equations |
Test Chp. 13
Chapter 6
assignment |
| Thursday |
Algebra:
Graphs,
Functions, and
Linear Systems
(Chapter 7) |
-graphing and functions
-linear functions and their graphs
-systems of linear equations in two variables
-linear inequalities in two variables
-linear programming
-approximating reality with nonlinear models:
exponential functions, logarithmic functions,
quadratic functions |
Test Chp. 6
Chapter 7
assignment |
| Friday |
Measurement
(Chapter 9)
Geometry
(Chapter 10) |
-linear measurement
-using dimensional analysis to convert units
within and between measurement systems
-area and volume
-weight and temperature
-points, lines, planes, and angles
-triangles
-polygons, perimeter, tessellations
-area and circumference
-volume
-right triangle trigonometry
-beyond Euclidean geometry |
Test Chp. 7
Chapters 9 and
10 assignment |
| Week 3 |
|
|
|
| Monday |
Graph Theory
(Chapter 15) |
-graphs, paths, circuits
-Euler Paths and Euler Circuits
-Hamilton Paths and Hamilton Circuits
-trees |
Test Chp. 9,10
Chapter 15
assignment |
| Tuesday |
Counting
Methods and
Probability
(Chapter 11) |
-fundamental counting principle
-permutations and combinations and their
applications to probability
-fundamentals of probabilities
-events involving “not” and “or”, odds
-events involving “and” conditional
probability
-expected value |
Test Chp.15
Chapter 11
assignment |
| Wednesday |
Statistics
(Chapter 12) |
-sampling, frequency distributions,
and
graphs
-measures of central tendency
-measures of dispersion
-the normal distribution
-scatter plots, correlation and regression lines |
Test Chp. 11
Chapter 12
assignment |
| Thursday |
Course overview |
-review for final exam |
Final Exam |
| Friday |
Course overview |
-complete final exam I
-applications of logic- “Numb3rs” T.V. show
(CBS) and activities |
Have a great
rest of the
summer and a
great 2008-09
school year!! |
|
