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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:

 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!!