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CCOG for MTH 20 Fall 2022

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Course Number:
MTH 20
Course Title:
Fundamentals of Mathematics
Credit Hours:
Lecture Hours:
Lecture/Lab Hours:
Lab Hours:

Course Description

Develops arithmetic fluency and the conceptual basis, and applications of integers, fractions, decimals, percents, and measurements. A scientific calculator may be required. The TI-30XS or TI-30XIIS is recommended. The PCC math department recommends that students take MTH courses in consecutive terms. Prerequisites: (ABE 0782 or placement into MTH 20) and (placement into RD 80 or ESOL 250). Audit available.

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", closed-book no-note and no-calculator setting: basic arithmetic with fractions, decimals, and signed numbers, and order of operations. 

2.     At least two proctored", closed-book no-note 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 multiple-choice 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

  1. Take-home examinations
  2. Graded homework
  3. Quizzes
  4. Projects
  5. In-class activities
  6. Portfolios
  7. Writing assignments

Course Content (Themes, Concepts, Issues and Skills)


  1. Mathematical vocabulary
  2. Number sense
  3. Computational proficiency
  4. Critical thinking
  5. Appropriate use of technology
  6. Team (group) work


    1. Vocabulary (Define and use)
      1. Grouping symbols
      2. Exponents
      3. Square roots (perfect squares)
    1. Vocabulary (Define and use)
      1. Absolute value
      2. Opposite vs. negative vs. minus (subtract)
    2. Number sense
      1. Compare signed numbers using inequality and equality notations
      2. Place signed numbers on a number line
    3. Computation
      1. Add", subtract, multiply, and divide signed numbers
      2. Simplify signed numbers to exponents
    4. Order of operations with signed numbers
    5. Applications with signed numbers 
    1. Vocabulary (Define and use)
      1. Proper fractions", improper fractions, mixed numbers
      2. Reciprocal
      3. Prime number
      4. Composite number
      5. Divisibility Rules 2",3,5,9, and 10
    2. Number Sense
      1. Compare fractions using inequality and equality notations
      2. Place signed fractions on a number line
    3. Computation
      1. ​Add", subtract, multiply, and divide signed fractions
    4. Order of operations with fractions
    5. Applications involving fractions
      1. Write answers to application problems as complete sentences and using proper units
      2. Ratios and rates
    1. Vocabulary (Define and use)
      1. Place values
      2. Powers of ten
      3. Terminating", repeating and non-terminating
    2. Number sense
      1. Compare decimals using inequality and equality notations
      2. Place signed decimals on a number line
      3. Rounding decimals
    3. Computation
      1. Add", subtract, multiply, and divide signed decimals
      2. Convert between fractions and decimals
    4. Order of operations with decimals
      1. Round at the end of the calculation
    5. Applications
      1. Write answers to application problems as complete sentences and using proper units
      2. Rates and ratios
      3. Unit rate and unit price
    1. Vocabulary
      1. Proportion
      2. Percent
    2. Number sense
      1. ​Convert between fractions", decimals, and percents
    3. Computation
      1. Solve proportion problems for missing value
      2. Solve percent problems
    4. Applications
      1. Write answers to application problems as complete sentences and using proper units
      2. Identify and solve problems that involve reasoning about proportions
      3. Solving percent increase and percent decrease problems
    5. Technology
    1. Introduce", read and interpret graphs
    1. Perimeter and area of rectangles", squares and triangles
    2. Computing mean", median, and mode
    3. Introduce unit conversions within each measurement system
    4. Money", $0.35 vs. 35¢ (students often write 0.35¢)



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.

\text{Vertical format} & \text{Horizontal format} \\
\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}

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.