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+ 
10098% 
A 
9793% 
A 
9290% 
B+ 
8987% 
B 
8683% 
B 
8280% 
C+ 
7977% 
C 
7673% 
C 
7270% 
D+ 
6967% 
D 
6663% 
D 
6260% 
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 68. 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 
PreTest
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) 
HinduArabic 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 200809
school year!! 
