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# Basic Math (Arithmetic)

#### Prerequisites

placement into MTH 20 and RD 90

## Course Description

Covers fractions, decimals, percents, integer, measurements to write, manipulate, interpret, and solve application and formula problems. Introduces concepts of basic statistics. A scientific calculator is required. Prerequisite: placement into MTH 20 and RD 90.

## Intended Outcomes

Upon successful completion students should be able to:

1. Choose and perform accurate arithmetic computations in a variety of situations with and without a calculator.
2. Creatively and confidently apply mathematical problem solving strategies.
3. Meet the prerequisite for future course work.

## 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. At least one of the following additional measures must also be used:
1. Take-home examinations
3. Quizzes
4. Projects
5. In-class activities
6. Portfolios
7. Writing assignments

## Course Content (Themes, Concepts, Issues and Skills)

#### THEMES

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

#### SKILLS

1.0 ORDER OF OPERATIONS
1.1 Vocabulary (Define and use)
1.1.1 Grouping symbols
1.1.2 Exponents
1.1.3 Square roots (perfect squares)

2.0 SIGNED NUMBERS
2.1 Vocabulary (Define and use)
2.1.1 Absolute value
2.1.2 Opposite vs. negative vs. minus (subtract)
2.2 Number sense
2.2.1 Compare signed numbers using inequality and equality notations
2.2.2 Place signed numbers on a number line
2.3 Computation
2.3.1 Add, subtract, multiply, and divide signed numbers
2.3.2 Simplify signed numbers to exponents
2.4 Order of operations with signed numbers
2.5 Applications with signed numbers

3.0 FRACTIONS
3.1 Vocabulary (Define and use)
3.1.1 Proper fractions, improper fractions, mixed numbers
3.1.2 Reciprocal
3.1.3 Prime number
3.1.4 Composite number
3.1.5 Divisibility Rules 2, 3, 5, 9, and 10
3.2 Number Sense
3.2.1 Compare fractions using inequality and equality notations
3.2.2 Place signed fractions on a number line
3.3 Computation
3.3.1 Add, subtract, multiply, and divide signed fractions
3.4 Order of operations with fractions
3.5 Applications involving fractions
3.5.1 Write answers to application problems as complete sentences and using proper units
3.5.2 Ratios and rates

4.0 DECIMALS
4.1 Vocabulary (Define and use)
4.1.1 Place values
4.1.2 Powers of ten
4.1.3 Terminating, repeating and non-terminating
4.2 Number sense
4.2.1 Compare decimals using inequality and equality notations
4.2.2 Place signed decimals on a number line
4.2.3 Rounding decimals
4.3 Computation
4.3.1 Add, subtract, multiply, and divide signed decimals
4.3.2 Convert between fractions and decimals
4.4 Order of operations with decimals
4.4.1 Round at the end of the calculation
4.5 Applications
4.5.1 Write answers to application problems as complete sentences and using proper units
4.5.2 Rates and ratios
4.5.3 Unit rate and unit price

5.0 PROPORTION AND PERCENT
5.1 Vocabulary
5.1.1 Proportion
5.1.2 Percent
5.2 Number sense
5.2.1 Convert between fractions, decimals, and percents
5.3 Computation
5.3.1 Solve proportion problems for missing value
5.3.2 Solve percent problems
5.4 Applications
5.4.1 Write answers to application problems as complete sentences and using proper units
5.4.2 Identify and solve problems that involve reasoning about proportions
5.4.3 Solving percent increase and percent decrease problems
5.5 Technology

6.0 GRAPHS
6.1 Introduce, read and interpret graphs

7.0 FORMULAS AND CONVERSIONS
7.1 Perimeter and area of rectangles, squares and triangles
7.2 Computing mean, median, and mode
7.3 Introduce unit conversions within each measurement system
7.4 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.

Vertical Format

Horizontal Format

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.

## Department Notes

• 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.