Portland Community College | Portland, Oregon

This class is not intended to be a study hall for students to work on MTH assignments. The time needs to be spent working on material designated by your ALC instructor. If a student is co-enrolled in an MTH class, then this may include targeted materials which are intended to support the concepts being taught in that MTH class.

Upon successful completion of this course students will be able to:

• Perform appropriate basic computations in a wide variety of situations with and without a calculator.

• Apply basic mathematical problem solving strategies in multiple contexts.

• Address basic quantitative problems with increased confidence.

• Demonstrate progression through mathematical learning objectives established between the student and instructor.

Instructors may employ the use of worksheets, textbooks, online software, mini-lectures, and/or group work.

Assessment shall include at least two of the following measures:

1. Active participation/effort

2. Personal program/portfolios

3. Individual student conference

4. Assignments

5. Pre/post evaluations

6. Tests/Quizzes

Items from the course content may be chosen as appropriate for each student and some students may even work on content from other ALC courses as deemed appropriate by the instructor.

Basic Math (MTH 20)

THEMES:

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

SKILLS:

1. ORDER OF OPERATIONS
   1. Vocabulary (Define and use)
      1. Grouping symbols
      2. Exponents
      3. Square roots (perfect squares)
2. SIGNED NUMBERS
   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 
3. FRACTIONS
   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
4. DECIMALS
   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
5. PROPORTION AND PERCENT
   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
6. GRAPHS
   1. Introduce, read, and interpret graphs
7. FORMULAS AND CONVERSIONS
   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¢)

ADDENDUM: 

The mission of the Math ALC is to promote student success in MTH courses by tailoring the coursework to meet individual student needs.  

Specifically, the Math ALC:

• supports students concurrently enrolled in MTH courses;

• prepares students to take a MTH course the following term;

• allows students to work through the content of a MTH course over multiple terms;

• provides an accelerated pathway allowing students to work through the content of multiple MTH courses in one term, allowing placement into the subsequent courses(s) upon demonstrated competency;

• prepares students to take a math-placement exam.

The intended goals from the MTH 20 CCOG follow:

            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.