The content, assignments, and assessments for Developmental Emporium are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Developmental Math Emporium Learning Outcomes.

## Module 1: Whole Numbers

### Evaluate expressions and solve problems involving whole numbers

- Understand the basics of whole numbers
- Add whole numbers using the properties of addition
- Subtract whole numbers using properties of subtraction
- Multiply whole numbers using properties of multiplication
- Divide whole numbers using properties of division

## Module 2: The Language of Algebra

### Manipulate mathematical expressions and equations using algebraic rules

- Interpret expressions and equations that use words and algebraic symbols
- Evaluate algebraic expressions containing multiple terms
- Solve one-step equations using whole numbers
- Find multiples and factors of whole numbers
- Use prime factorization to find the least common multiple of two numbers

## Module 3: Integers

### Solve problems that involve integers

- Write integer expressions and evaluate integer expressions involving absolute value
- Simplify and evaluate expressions that involve the addition of integers
- Simplify and evaluate expressions that involve the subtraction of integers
- Simplify and evaluate expressions that involve the multiplication or division of integers
- Solve simple one-step algebraic equations

## Module 4: Fractions

### Understand how to manipulate fractions and demonstrate how they relate to one another

- Use fractions to represent parts of a whole and understand their value
- Multiply and divide fractions by whole numbers, other fractions, and variable expressions
- Multiply, divide, and simplify mixed numbers and complex fractions
- Add and subtract fractions with common denominators
- Add and subtract fractions with different denominators
- Manipulate fractions to add or subtract mixed numbers
- Solve equations that contain fractions or have fractional solutions

## Module 5: Decimals

### Understand how to make calculations with decimals and demonstrate how they relate to one another

- Write and identify characteristics of decimals
- Use various operations to solve applications involving decimals
- Understand the relationship between decimals and fractions
- Solve equations with decimals using properties of addition and subtraction

## Module 6: Ratios, Rates, Probabilities, and Averages

### Apply knowledge of decimals to real world scenarios

- Find the average and other reportable measures of a set of numbers
- Write ratios as fractions and calculate unit rates
- Use square roots to simplify expressions and solve application problems

## Module 7: Percents

### Demonstrate an understanding of percents and how they relate to other number formats

- Write percents using words, ratios, and fractions and complete conversions
- Solve general applications of percent
- Solve sales tax, commission, and discount applications
- Solve simple interest applications involving rate, time, and principal
- Solve proportions and their applications

## Module 8: Geometry

### Use measurements and geometric equations to analyze shapes and structures

- Use properties of angles, triangles, and the Pythagorean Theorem to solve problems
- Use properties of rectangles, triangles, and trapezoids to solve problems
- Use the properties of circles and irregular figures to solve problems
- Solve problems using the volume and surface area of solid figures
- Make conversions between units in the U.S. and Metric systems of measurement

## Module 9: Real Numbers

### Identify and use properties of real numbers to evaluate expressions and equations

- Identify the different types of real numbers
- Use the commutative and associative properties to simplify expressions
- Use the distributive property to simplify and evaluate expressions
- Apply the identify, inverse, and zero properties

## Module 10: Linear Equations

### Solve linear equations that contain a variety of operations and number types

- Solve equations using the properties of equality
- Use problem solving strategies for word problems
- Solve word problems containing decimals
- Solve word problems by using common formulas

## Module 11: Linear Inequalities

### Solve both simple and compound linear inequalities and express the solution with the correct notation

- Solve single- and multi-step inequalities
- Solve compound inequalities

## Module 12: Exponents

### Manipulate expressions containing exponents

- Apply exponent rules to simplify expressions
- Use scientific notation to represent and do arithmetic with large and small values

## Module 13: Polynomials

### Manipulate and complete calculations with polynomials

- Identify characteristics of polynomial expressions
- Perform operations on polynomials
- Divide polynomials
- Write polynomials to represent real world situations

## Module 14: Factoring

### Factor polynomials using a variety of methods

- Solve simple polynomial equations
- Use a variety of factoring methods on polynomials
- Factor special case polynomials

## Module 15: Graphs

### Use graphs and slope to identify points and write equations for lines

- Graph points on the coordinate plane
- Find the slope of a line
- Use intercepts to graph lines
- Write the equation for a line
- Graph linear inequalities
- Solve application problems involving graphs

## Module 16: Linear Systems

### Solve systems of linear equations using a variety of methods

- Evaluate solutions to systems of equations
- Solve systems of two variable equations using various methods
- Solve systems of three variable equations using various methods
- Solve application problems involving systems of equations
- Solve systems of linear inequalities

## Module 17: Rational Expressions and Equations

### Perform operations on rational expressions and equations

- Multiply and divide rational expressions
- Add and subtract rational expressions
- Use rational equations to solve application problems
- Solve problems involving each type of variation

## Module 18: Roots and Rational Exponents

### Use properties of exponents to simplify expressions with radicals

- Simplify expressions involving roots
- Simplify expressions with radicals and rational exponents
- Use algebraic operations to simplify radical expressions
- Solve equations containing radicals

## Module 19: Quadratic Equations and Complex Numbers

### Solve quadratic equations and express non-real solutions as complex numbers

- Use a variety of methods to solve quadratic equations
- Express imaginary and complex numbers
- Solve quadratic equations with complex solutions

## Module 20: Linear Functions and Function Notation

### Identify and evaluate functions and find their domain and range

- Define and evaluate functions
- Graph and write equations for linear functions
- Find the domain and range of a function

## Module 21: Quadratic, Polynomial, and Piecewise Functions

### Evaluate and graph quadratic, polynomial, and piecewise functions

- Evaluate, graph, and write piecewise functions
- Graph quadratic and radical functions
- Identify characteristics of polynomial functions
- Solve problems involving projectile motion

## Module 22: Exponential and Logarithmic Functions

### Evaluate and graph exponential and logarithmic functions

- Evaluate and graph exponential functions
- Evaluate and graph logarithmic functions

## Module 23: Exponential and Logarithmic Equations

### Use logarithmic properties to solve exponential and logarithmic equations

- Use logarithmic properties to simplify expressions
- Solve exponential and logarithmic equations

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