Portland Community College | Portland, Oregon

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

• Choose and perform accurate basic computations in a variety of situations with and without a calculator.
• Solve problems at home or in an academic or work environment by creating a basic mathematical expression or equation that represents the situation and find the solution to the problem using correct basic mathematical steps.
• Creatively and confidently apply basic mathematical problem solving strategies.
• Be prepared for future course work.

Assessment shall include at least two of the following measures:

1. Tests
2. Attendance
3. Portfolios
4. Individual student conference

Basic Math (MTH 20)

THEMES:

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

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.