# Developmental Math Modules Course Descriptions

## DMA 010 Operations With Integers

This course provides a conceptual study of integers and integer operations. Topics include integers, absolute value, exponents, square roots, perimeter and area of basic geometric figures, Pythagorean theorem, and use of the correct order of operations. Upon completion, students should be able to demonstrate an understanding of pertinent concepts and principles and apply this knowledge in the evaluation of expressions.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: None
Corequisite: None
DMA 010 Course Outline: Not Available

### Competencies:

• Visually represent an integer and its opposite on the number line
• Explain the concept of the absolute value of an integer
• Demonstrate the conceptual understanding of operations with integers to solve application problems
• Correctly apply commutative and associative properties to integer operations
• Apply the proper use of exponents and calculate the principal square root of perfect squares
• Simplify multi-step expressions using the rules for order of operations
• Solve geometric application problems involving area and perimeter of rectangles and triangles, angles, and correctly apply the Pythagorean theorem

### Student Learning Outcomes:

• 1.1 Demonstrate an understanding of the concept of integers within contextual application problems
• 1.2 Correctly represent integers on a number line
• 1.3 Demonstrate the correct use of additive inverses
• 1.4 Evaluate the absolute value of a number
• 1.5 Apply integer operations in solving contextual application problems
• 1.6 Correctly apply the associative and commutative properties
• 1.7 Demonstrate understanding of exponents by converting between exponential and expanded form
• 1.8 Evaluate exponents
• 1.9 Calculate the square root of numbers containing perfect squares
• 1.10 Evaluate integer expressions by using the correct order of operations
• 1.11 Distinguish between appropriate use of area and perimeter formulas to solve geometric application problems
• 1.12 Use the Pythagorean Theorem to solve geometric problems
• 1.13 Represent the events of a geometric application problem included in this module pictorially and evaluate the correct solution using the appropriate formula
• 1.14 Demonstrate an understanding of what a variable represents
• 1.15 Evaluate variable expressions and formulas

## DMA 020 Fractions and Decimals

This course provides a conceptual study of the relationship between fractions and decimals and covers related problems. Topics include application of operations and solving contextual application problems, including determining the circumference and area of circles with the concept of pi. Upon completion, students should be able to demonstrate an understanding of the connections between fractions and decimals.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: DMA 010
Corequisite: None
DMA 020 Course Outline: Not Available

### Competencies:

• Solve contextual application problems involving operations with fractions and decimals
• Visually represent fractions and their decimal equivalents
• Simplify fractions
• Find the lowest common denominator of two fractions
• Correctly perform arithmetic operations on fractions
• Explain the relationship between a number and its reciprocal
• Correctly order fractions and decimals on a number line
• Convert decimals between standard notation and word form
• Round decimals to a specific place value
• Estimate sums, differences, products, and quotients with decimals
• Demonstrate an understanding of the connection between fractions and decimals
• Convert between standard notation and scientific notation
• Solve geometric applications involving the circumference and area of circles

### Student Learning Outcomes:

• 2.1 Solve conceptual problems involving fractions and decimals
• 2.2 Visually represent fractions and decimals
• 2.3 Simplify fractions
• 2.4 Visually represent equivalent fractions and correctly place the values on the number line
• 2.5 Add and subtract fractions with like denominators
• 2.6 Write an equivalent fraction with a given denominator
• 2.7 Add and subtract fractions with unlike denominators using the correct LCD
• 2.8 Visually represent the sum and difference of two fractions with unlike denominators
• 2.9 Multiply fractions
• 2.10 Visually represent multiplication of fractions
• 2.11 Divide fractions using reciprocals
• 2.12 Correctly round decimals to a specific place value
• 2.13 Estimate sums, differences, products, and quotients with decimals
• 2.14 Demonstrate an understanding of the connection between fractions and decimals
• 2.15 Distinguish between the appropriate use of circumference and area of a circle in solving geometric applications
• 2.16 Represent events in geometric problems pictorially and evaluate the solution using correct formulas
• 2.17 Correlate negative exponents to fractions and decimals in base 10
• 2.18 Convert between standard notation and scientific notation

## DMA 030 Proportion/Ratio/Rate/Percent

This course provides a conceptual study of the problems that are represented by rates, ratios, percent, and proportions. Topics include rates, ratios, percent, proportion, conversion of English and metric units, and applications of the geometry of similar triangles. Upon completion, students should be able to use their understanding to solve conceptual application problems.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: DMA 010 and DMA 020
Corequisite: None
DMA 030 Course Outline: Not Available

### Competencies:

• Apply the concepts of ratio, rates, proportions, and percents to application problems
• Recognize and choose the correct units in application problems using ratios, rates, and proportions
• Calculate a unit rate
• Convert measurements within and between the U.S. customary and metric system using unit analysis
• Compare percents, decimals, and fractions
• Apply the concepts of part, whole, and percent to solve contextual applications

### Student Learning Outcomes:

• 3.1 Demonstrate an understanding of the concepts of ratios, rates, proportions, and percents in the context of application problems
• 3.2 Write a ratio using a variety of notations
• 3.3 Distinguish between events in a problem that should be represented by a ratio or a rate
• 3.4 Calculate a unit rate
• 3.5 Convert measurements within the U.S. customary and metric system using unit analysis
• 3.6 Convert measurements between the U.S customary and metric systems using unit analysis
• 3.7 Represent percent as "parts of 100"
• 3.8 Correctly convert between fractions, decimals, and percents
• 3.9 Solve application problems using ratios, rates, proportions, and percents
• 3.10 Recognize that two triangles are similar and solve for unknown sides using proportions in contextual applications

## DMA 040 Expressions/Linear Equalities/Inequalities

This course provides a conceptual study of problems involving linear expressions, equations, and inequalities. Emphasis is placed on solving contextual application problems. Upon completion, students should be able to distinguish between simplifying expressions and solving equations and apply this knowledge to problems involving linear expressions, equations, and inequalities.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: Take One Set:
Set 1: DMA 010, DMA 020 and DMA 030 OR
Set 2: MAT 060
Corequisite: None
DMA 040 Course Outline: Not Available

### Competencies:

• Differentiate between expressions, equations, and inequalities
• Simplify and evaluate, when appropriate, expressions, equations, and inequalities
• Effectively apply algebraic properties of equality
• Correctly represent the solution to an inequality on the number line
• Represent the structure of application problems pictorially and algebraically
• Apply effective problem solving strategies to contextual application problems
• Demonstrate conceptual knowledge by modeling and solving applications using linear equations and inequalities

### Student Learning Outcomes:

• 4.1 Demonstrate the use of a problem solving strategy to include multiple representations of the situation, organization of the information, and algebraic representation of linear equations or inequalities
• 4.2 Represent verbal statements as algebraic expressions, equations, and inequalities
• 4.3 Distinguish between problem events that use expressions, equations, or inequalities
• 4.4 Solve linear equations and inequalities in one variable using algebraic properties of equality
• 4.5 Demonstrate an understanding of the meaning of solutions to problems, i.e. identity, contradiction, conditional
• 4.6 Represent solutions of inequalities on a number line

## DMA 050  Graphs/Equations of Lines

This course provides a conceptual study of problems involving graphic and algebraic representations of lines. Topics include slope, equations of lines, interpretation of basic graphs, and linear modeling. Upon completion, students should be able to solve contextual application problems and represent real-world situations as linear equations in two variables.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: Take One Set:
Set 1: DMA 010, DMA 020, DMA 030 and DMA 040
Set 2: DMA 040 and MAT 060
Corequisite: None
DMA 050 Course Outline: Not Available

### Competencies:

• Apply the concept of slope as a rate of change in real-world situations
• Write and graph linear equations in two variables to model real-world situations
• Represent real-world situations as linear equations in two variables in tabular form, graphically, and algebraically

### Student Learning Outcomes:

• 5.1 Analyze and interpret basic graphs to solve problems
• 5.2 Represent real world situations in tabular, graphical, and algebraic equation form using two variables
• 5.3 Generate a table of values given an equation in two variables and plot in Cartesian plane to graph a line
• 5.4 Demonstrate an understanding of the concept of slope as a rate of change in real world situations using the slope formula
• 5.5 Find and interpret the x- and y-intercepts of linear models in real world situations
• 5.6 Graph linear equations using a variety of strategies
• 5.7 Given a contextual application, write a linear equation and use the equation to make predictions
• 5.8 Demonstrate a conceptual understanding of horizontal and vertical lines in terms of slope and graphically
• 5.9 Demonstrate a conceptual understanding of the concept of an algebraic function

This course provides a conceptual study of problems involving graphic and algebraic representations of quadratics. Topics include basic polynomial operations, factoring polynomials, and solving polynomial equations by means of factoring. Upon completion, students should be able to find algebraic solutions to contextual problems with quadratic applications.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: Take One Set:
Set 1: DMA 010, DMA 020, DMA 030, DMA 040 and DMA 050
Set 2: DMA 040, DMA 050, and MAT 060
Set 3: MAT 060 and MAT 070
Corequisite: None
DMA 060 Course Outline: Not Available

### Competencies:

• Represent real-world applications as quadratic equations in tabular, graphic, and algebraic forms
• Apply exponent rules
• Solve application problems involving polynomial operations
• Apply the principles of factoring when solving problems
• Represent contextual applications using function notation
• Analyze graphs of quadratic functions to solve problems

### Student Learning Outcomes:

• 6.1 Demonstrate the use of a problem solving strategy to include multiple representations of the situation, organization of the information, and algebraic representation of quadratic equations
• 6.2 Add and subtract polynomials
• 6.3 Apply exponent rules
• 6.4 Multiply polynomials
• 6.5 Divide a polynomial by a monomial
• 6.6 Factor trinomials using multiple methods
• 6.7 Factor the difference of two squares
• 6.8 Solve quadratic applications using the zero product property and critique the reasonableness of solutions found
• 6.9 Graph quadratic functions using the graphing calculator to identify and interpret the maximum, minimum, and y-intercept values and the domain and range in terms of the problem

## DMA 070 Rational Expressions/Equation

This course provides a conceptual study of problems involving graphic and algebraic representations of rational equations. Topics include simplifying and performing operations with rational expressions and equations, understanding the domain, and determining the reasonableness of an answer. Upon completion, students should be able to find algebraic solutions to contextual problems with rational applications.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: Take One Set:
Set 1: DMA 010, DMA 020, DMA 030, DMA 040 and DMA 050 and DMA-060
Set 2: DMA 040, DMA 050, and MAT 060
Set 3: DMA 060, MAT 060 and MAT 070
Set 4: DMA 010, DMA 020, DMA 030, DMA 060, AND MAT 070
Corequisite: None
DMA 070 Course Outline: Not Available

### Competencies:

• Solve contextual application problems involving operations on rational expressions and/or equations
• Represent real-world situations as rational equations and graphically using a graphing calculator
• Analyze the meaning of asymptotes using a graphing calculator
• Explain the reasonableness of solutions found

### Student Learning Outcomes:

• 7.1 Demonstrate the use of a problem solving strategy to include multiple representations of the situation, organization of the information, and algebraic representation of rational equations
• 7.2 Graph rational functions using the graphing calculator to identify and interpret the y-intercept values and domain in terms of the problem
• 7.3 Multiply and divide rational expressions
• 7.4 Add and subtract rational expressions
• 7.5 Solve rational equations

This course provides a conceptual study of the manipulation of radicals and the application of radical equations to real-world problems. Topics include simplifying and performing operations with radical expressions and rational exponents, solving equations, and determining the reasonableness of an answer. Upon completion, students should be able to find algebraic solutions to contextual problems with radical applications.

Course Hours Per Week: Class, 0.75; Lab, 0.50
Semester Hours Credit: 1
Prerequisite: Take One Set:
Set 1: DMA 010, DMA 020, DMA 030, DMA 040 and DMA 050, DMA 060 and DMA 070
Set 2: DMA 060, DMA 070, MAT 060 and MAT 070
Set 3: DMA 040, DMA 050, DMA 060, DMA 070, and MAT 060
Set 4: DMA 010, DMA 020, DMA 030, DMA 060, DMA 070, and MAT 070
Corequisite: None
DMA 080 Course Outline: Not Available

### Competencies:

• Solve contextual application problems involving operations on radical expressions and/or equations
• Represent real world situations as radical equations and graphically using a graphing calculator
• Explain the reasonableness of solutions found
• Correctly perform operations with radical expressions
• Use a graphing calculator to analyze radical functions

### Student Learning Outcomes:

• 8.1 Demonstrate the use of a problem solving strategy to include multiple representations of the situation, organization of the information, and algebraic representation of radical equations
• 8.2 Correctly use rational exponents to rewrite radical expressions