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Math Logic & Problem Solving Honors
Solving Quadratic Equations by Factoring
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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!!
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