## Learning Outcomes 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
• 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

## 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
• 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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