CCOG for MTH 20 Winter 2023
 Course Number:
 MTH 20
 Course Title:
 Fundamentals of Mathematics
 Credit Hours:
 4
 Lecture Hours:
 30
 Lecture/Lab Hours:
 20
 Lab Hours:
 0
Course Description
Addendum to Course Description
 Students will be evaluated not only on their ability to get correct answers and perform correct steps, but also on the accuracy of the presentation itself.
 Application problems must be answered in complete sentences.
Intended Outcomes for the course
Upon completion of the course students should be able to:
 Perform accurate arithmetic computations in a variety of expressions and applications.
 Apply mathematical problem solving strategies.
 Effectively communicate mathematical reasoning.
Course Activities and Design
A portion of the course is designed to be lab based. Students will be expected to regularly work collaboratively in class.
Outcome Assessment Strategies
1. The following must be assessed in a proctored", closedbook nonote and nocalculator setting: basic arithmetic with fractions, decimals, and signed numbers, and order of operations.
2. At least two proctored", closedbook nonote examinations (one of which is the comprehensive final) must be given. These exams must consist primarily of free response questions although a limited number of multiplechoice and/or fill in the blank questions may be used where appropriate.
3. Assessment must include evaluation of the student’s ability to arrive at correct and appropriate conclusions using proper mathematical procedures and proper mathematical notation. Additionally", each student must be assessed on their ability to use appropriate organizational strategies and their ability to write conclusions appropriate to the problem.
4. Participate in, and contribute to, class discussions and activities.
5. At least one of the following additional measures must also be used
 Takehome examinations
 Graded homework
 Quizzes
 Projects
 Inclass activities
 Portfolios
 Writing assignments
Course Content (Themes, Concepts, Issues and Skills)
THEMES:
 Mathematical vocabulary
 Number sense
 Computational proficiency
 Critical thinking
 Appropriate use of technology
 Team (group) work
SKILLS:

ORDER OF OPERATIONS
 Vocabulary (Define and use)
 Grouping symbols
 Exponents
 Square roots (perfect squares)
 Vocabulary (Define and use)

SIGNED NUMBERS
 Vocabulary (Define and use)
 Absolute value
 Opposite vs. negative vs. minus (subtract)
 Number sense
 Compare signed numbers using inequality and equality notations
 Place signed numbers on a number line
 Computation
 Add", subtract, multiply, and divide signed numbers
 Simplify signed numbers to exponents
 Order of operations with signed numbers
 Applications with signed numbers
 Vocabulary (Define and use)

FRACTIONS
 Vocabulary (Define and use)
 Proper fractions", improper fractions, mixed numbers
 Reciprocal
 Prime number
 Composite number
 Divisibility Rules 2",3,5,9, and 10
 Number Sense
 Compare fractions using inequality and equality notations
 Place signed fractions on a number line
 Computation
 Add", subtract, multiply, and divide signed fractions
 Order of operations with fractions
 Applications involving fractions
 Write answers to application problems as complete sentences and using proper units
 Ratios and rates
 Vocabulary (Define and use)

DECIMALS
 Vocabulary (Define and use)
 Place values
 Powers of ten
 Terminating", repeating and nonterminating
 Number sense
 Compare decimals using inequality and equality notations
 Place signed decimals on a number line
 Rounding decimals
 Computation
 Add", subtract, multiply, and divide signed decimals
 Convert between fractions and decimals
 Order of operations with decimals
 Round at the end of the calculation
 Applications
 Write answers to application problems as complete sentences and using proper units
 Rates and ratios
 Unit rate and unit price
 Vocabulary (Define and use)

PROPORTION AND PERCENT
 Vocabulary
 Proportion
 Percent
 Number sense
 Convert between fractions", decimals, and percents
 Computation
 Solve proportion problems for missing value
 Solve percent problems
 Applications
 Write answers to application problems as complete sentences and using proper units
 Identify and solve problems that involve reasoning about proportions
 Solving percent increase and percent decrease problems
 Technology
 Vocabulary

GRAPHS
 Introduce", read and interpret graphs

FORMULAS AND CONVERSIONS
 Perimeter and area of rectangles", squares and triangles
 Computing mean", median, and mode
 Introduce unit conversions within each measurement system
 Money", $0.35 vs. 35¢ (students often write 0.35¢)
ADDENDUM:
Prerequisites 
The students in this course come from mathematically diverse backgrounds", from those who need a refresher and decide to start at the beginning, to those who have never been successful at mathematics.
Intended Course Goals –
Mth 20 is a review of arithmetic skills and provides a good foundation for students to take Mth 60", beginning algebra. Beginning algebra students often encounter difficulty operating with fractions and negative numbers, resulting in the need to take Mth 20. Thus, it would be beneficial to incorporate these topics throughout the course, whenever possible, so that students have ample exposure. This will lead to greater success in Mth 60.
When performing addition and subtraction operations with fractions (not mixed numbers) traditionally students perform the operations in a vertical format. This format however does not serve them at all in algebra", in which many cases the work is shown horizontally. Thus, to help students prepare for algebra, it is suggested that we have students perform computations in a horizontal format also.
\[
\begin{array}{cc}
\text{Vertical format} & \text{Horizontal format} \\
\begin{array}{r}
\frac{4}{9}\\
\rule{0pt}{1em}+\frac{2}{3}\\
\hline
\end{array}
&
\begin{aligned}
\frac{4}{9} + \frac{2}{3} &= \frac{4}{9} + \frac{2}{3}\left( \frac{3}{3} \right ) \\
&= \frac{4}{9} + \frac{6}{9} \\
&= \frac{10}{9}
\end{aligned}
\end{array}
\]
The Mathematics SAC recognizes that how one presents the steps to a problem that lead to the desired goal is as important as the answer itself. We want all of our students to recognize this fact; thus an instructor will need to emphasize the importance of how to write mathematics properly. All students in a Math 20 course should consistently write proper mathematical steps; students must adhere to correct use of syntax. A portion of the grade for any problem", when applicable, should be based on mathematical syntax.