Module 1: Whole Numbers<\/h2>\r\nEvaluate expressions and solve problems involving whole numbers<\/h3>\r\n\r\n \t- Understand the basics of whole numbers<\/li>\r\n \t
- Add whole numbers using the properties of addition<\/li>\r\n \t
- Subtract whole numbers using properties of subtraction<\/li>\r\n \t
- Multiply whole numbers using properties of multiplication<\/li>\r\n \t
- Divide whole numbers using properties of division<\/li>\r\n<\/ul>\r\n\r\n
Module 2: The Language of Algebra<\/h2>\r\nManipulate mathematical expressions and equations using algebraic rules<\/h3>\r\n\r\n \t- Interpret expressions and equations that use words and algebraic symbols<\/li>\r\n \t
- Evaluate algebraic expressions containing multiple terms<\/li>\r\n \t
- Solve one-step equations using whole numbers<\/li>\r\n \t
- Find multiples and factors of whole numbers<\/li>\r\n \t
- Use prime factorization to find the least common multiple of two numbers<\/li>\r\n<\/ul>\r\n
Module 3: Integers<\/h2>\r\nSolve problems that involve integers<\/h3>\r\n\r\n \t- Write integer expressions and evaluate integer expressions involving absolute value<\/li>\r\n \t
- Simplify and evaluate expressions that involve the addition of integers<\/li>\r\n \t
- Simplify and evaluate expressions that involve the subtraction of integers<\/li>\r\n \t
- Simplify and evaluate expressions that involve the multiplication or division of integers<\/li>\r\n \t
- Solve simple one-step algebraic equations<\/li>\r\n<\/ul>\r\n
Module 4: Fractions<\/h2>\r\nUnderstand how to manipulate fractions and demonstrate how they relate to one another<\/h3>\r\n\r\n \t- Use fractions to represent parts of a whole and understand their value<\/li>\r\n \t
- Multiply and divide fractions by whole numbers, other fractions, and variable expressions<\/li>\r\n \t
- Multiply, divide, and simplify mixed numbers and complex fractions<\/li>\r\n \t
- Add and subtract fractions with common denominators<\/li>\r\n \t
- Add and subtract fractions with different denominators<\/li>\r\n \t
- Manipulate fractions to add or subtract mixed numbers<\/li>\r\n \t
- Solve equations that contain fractions or have fractional solutions<\/li>\r\n<\/ul>\r\n
Module 5: Decimals<\/span><\/h2>\r\nUnderstand how to make calculations with decimals and demonstrate how they relate to one another<\/h3>\r\n\r\n \t- Write and identify characteristics of decimals<\/li>\r\n \t
- Use various operations to solve applications involving decimals<\/li>\r\n \t
- Understand the relationship between decimals and fractions<\/li>\r\n \t
- Solve equations with decimals using properties of addition and subtraction<\/li>\r\n<\/ul>\r\n
Module 6: Ratios, Rates, Probabilities, and Averages<\/span><\/h2>\r\nApply knowledge of decimals to real world scenarios<\/h3>\r\n\r\n \t- Find the average and other reportable measures of a set of numbers<\/li>\r\n \t
- Write ratios as fractions and calculate unit rates<\/li>\r\n \t
- Use square roots to simplify expressions and solve application problems<\/li>\r\n<\/ul>\r\n
Module 7: Percents<\/span><\/h2>\r\nDemonstrate an understanding of percents and how they relate to other number formats<\/h3>\r\n\r\n \t- Write percents using words, ratios, and fractions and complete conversions<\/li>\r\n \t
- Solve general applications of percent<\/li>\r\n \t
- Solve sales tax, commission, and discount applications<\/li>\r\n \t
- Solve simple interest applications involving rate, time, and principal<\/li>\r\n \t
- Solve proportions and their applications<\/li>\r\n<\/ul>\r\n
Module 8: Geometry<\/span><\/h2>\r\nUse measurements and geometric equations to analyze shapes and structures<\/h3>\r\n\r\n \t- Use properties of angles, triangles, and the Pythagorean Theorem to solve problems<\/li>\r\n \t
- Use properties of rectangles, triangles, and trapezoids to solve problems<\/li>\r\n \t
- Use the properties of circles and irregular figures to solve problems<\/li>\r\n \t
- Solve problems using the volume and surface area of solid figures<\/li>\r\n \t
- Make conversions between units in the U.S. and Metric systems of measurement<\/li>\r\n<\/ul>\r\n
Module 9: Real Numbers<\/span><\/h2>\r\nIdentify and use properties of real numbers to evaluate expressions and equations<\/h3>\r\n\r\n \t- Identify the different types of real numbers<\/li>\r\n \t
- Use the commutative and associative properties to simplify expressions<\/li>\r\n \t
- Use the distributive property to simplify and evaluate expressions<\/li>\r\n \t
- Apply the identify, inverse, and zero properties<\/li>\r\n<\/ul>\r\n
Module 10: Linear Equations<\/span><\/h2>\r\nSolve linear equations that contain a variety of operations and number types<\/h3>\r\n\r\n \t- Solve equations using the properties of equality<\/li>\r\n \t
- Use problem solving strategies for word problems<\/li>\r\n \t
- Solve word problems containing decimals<\/li>\r\n \t
- Solve word problems by using common formulas<\/li>\r\n<\/ul>\r\n
Module 11: Linear Inequalities<\/span><\/h2>\r\nSolve both simple and compound linear inequalities and express the solution with the correct notation<\/h3>\r\n\r\n \t- Solve single- and multi-step inequalities<\/li>\r\n \t
- Solve compound inequalities<\/li>\r\n<\/ul>\r\n
Module 12: Exponents<\/h2>\r\nManipulate expressions containing exponents<\/h3>\r\n\r\n \t- Apply exponent rules to simplify expressions<\/li>\r\n \t
- Use scientific notation to represent and do arithmetic with large and small values<\/li>\r\n<\/ul>\r\n
Module 13: Polynomials<\/span><\/h2>\r\nManipulate and complete calculations with polynomials<\/h3>\r\n\r\n \t- Identify characteristics of polynomial expressions<\/li>\r\n \t
- Perform operations on polynomials<\/li>\r\n \t
- Divide polynomials<\/li>\r\n \t
- Write polynomials to represent real world situations<\/li>\r\n<\/ul>\r\n
Module 14: Factoring<\/h2>\r\nFactor polynomials using a variety of methods<\/h3>\r\n\r\n \t- Solve simple polynomial equations<\/li>\r\n \t
- Use a variety of factoring methods on polynomials<\/li>\r\n \t
- Factor special case polynomials<\/li>\r\n<\/ul>\r\n
Module 15: Graphs<\/span><\/h2>\r\nUse graphs and slope to identify points and write equations for lines<\/h3>\r\n\r\n \t- Graph points on the coordinate plane<\/li>\r\n \t
- Find the slope of a line<\/li>\r\n \t
- Use intercepts to graph lines<\/li>\r\n \t
- Write the equation for a line<\/li>\r\n \t
- Graph linear inequalities<\/li>\r\n \t
- Solve application problems involving graphs<\/li>\r\n<\/ul>\r\n
Module 16: Linear Systems<\/span><\/h2>\r\nSolve systems of linear equations using a variety of methods<\/h3>\r\n\r\n \t- Evaluate solutions to systems of equations<\/li>\r\n \t
- Solve systems of two variable equations using various methods<\/li>\r\n \t
- Solve systems of three variable equations using various methods<\/li>\r\n \t
- Solve application problems involving systems of equations<\/li>\r\n \t
- Solve systems of linear inequalities<\/li>\r\n<\/ul>\r\n
Module 17: Rational Expressions and Equations<\/span><\/h2>\r\nPerform operations on rational expressions and equations<\/h3>\r\n\r\n \t- Multiply and divide rational expressions<\/li>\r\n \t
- Add and subtract rational expressions<\/li>\r\n \t
- Use rational equations to solve application problems<\/li>\r\n \t
- Solve problems involving each type of variation<\/li>\r\n<\/ul>\r\n
Module 18: Roots and Rational Exponents<\/span><\/h2>\r\nUse properties of exponents to simplify expressions with radicals<\/h3>\r\n\r\n \t- Simplify expressions involving roots<\/li>\r\n \t
- Simplify expressions with radicals and rational exponents<\/li>\r\n \t
- Use algebraic operations to simplify radical expressions<\/li>\r\n \t
- Solve equations containing radicals<\/li>\r\n<\/ul>\r\n
Module 19:\u00a0<\/span>Quadratic Equations and Complex Numbers<\/span><\/h2>\r\nSolve quadratic equations and express non-real solutions as complex numbers<\/h3>\r\n\r\n \t- Use a variety of methods to solve quadratic equations<\/li>\r\n \t
- Express imaginary and complex numbers<\/li>\r\n \t
- Solve quadratic equations with complex solutions<\/li>\r\n<\/ul>\r\n
Module 20: Linear Functions and Function Notation<\/span><\/h2>\r\nIdentify and evaluate functions and find their domain and range<\/h3>\r\n\r\n \t- Define and evaluate functions<\/li>\r\n \t
- Graph and write equations for linear functions<\/li>\r\n \t
- Find the domain and range of a function<\/li>\r\n<\/ul>\r\n
Module 21:\u00a0<\/span>Quadratic, Polynomial, and\u00a0<\/span>Piecewise Functions<\/span><\/h2>\r\nEvaluate and graph quadratic, polynomial, and\u00a0piecewise functions<\/h3>\r\n\r\n \t- Evaluate, graph, and write piecewise functions<\/li>\r\n \t
- Graph quadratic and radical functions<\/li>\r\n \t
- Identify characteristics of polynomial functions<\/li>\r\n \t
- Solve problems involving projectile motion<\/li>\r\n<\/ul>\r\n
Module 22:\u00a0<\/span>Exponential and Logarithmic Functions<\/span><\/h2>\r\nEvaluate and graph exponential and logarithmic functions<\/h3>\r\n\r\n \t- Evaluate and graph exponential functions<\/li>\r\n \t
- Evaluate and graph logarithmic functions<\/li>\r\n<\/ul>\r\n
Module 23: Exponential and Logarithmic Equations<\/span><\/h2>\r\nUse logarithmic properties to solve exponential and logarithmic equations<\/h3>\r\n\r\n \t- Use logarithmic properties to simplify expressions<\/li>\r\n \t
- Solve exponential and logarithmic equations<\/li>\r\n<\/ul>\r\n<\/div>\r\n
Contribute!<\/h2>Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"![\"icon](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2025\/2017\/07\/01225024\/outcomes.jpg\")
<\/p>\n
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:\u00a0Developmental Math Emporium Learning Outcomes<\/a>.<\/p>\nModule 1: Whole Numbers<\/h2>\nEvaluate expressions and solve problems involving whole numbers<\/h3>\n\n- Understand the basics of whole numbers<\/li>\n
- Add whole numbers using the properties of addition<\/li>\n
- Subtract whole numbers using properties of subtraction<\/li>\n
- Multiply whole numbers using properties of multiplication<\/li>\n
- Divide whole numbers using properties of division<\/li>\n<\/ul>\n\n
Module 2: The Language of Algebra<\/h2>\nManipulate mathematical expressions and equations using algebraic rules<\/h3>\n\n- Interpret expressions and equations that use words and algebraic symbols<\/li>\n
- Evaluate algebraic expressions containing multiple terms<\/li>\n
- Solve one-step equations using whole numbers<\/li>\n
- Find multiples and factors of whole numbers<\/li>\n
- Use prime factorization to find the least common multiple of two numbers<\/li>\n<\/ul>\n
Module 3: Integers<\/h2>\nSolve problems that involve integers<\/h3>\n\n- Write integer expressions and evaluate integer expressions involving absolute value<\/li>\n
- Simplify and evaluate expressions that involve the addition of integers<\/li>\n
- Simplify and evaluate expressions that involve the subtraction of integers<\/li>\n
- Simplify and evaluate expressions that involve the multiplication or division of integers<\/li>\n
- Solve simple one-step algebraic equations<\/li>\n<\/ul>\n
Module 4: Fractions<\/h2>\nUnderstand how to manipulate fractions and demonstrate how they relate to one another<\/h3>\n\n- Use fractions to represent parts of a whole and understand their value<\/li>\n
- Multiply and divide fractions by whole numbers, other fractions, and variable expressions<\/li>\n
- Multiply, divide, and simplify mixed numbers and complex fractions<\/li>\n
- Add and subtract fractions with common denominators<\/li>\n
- Add and subtract fractions with different denominators<\/li>\n
- Manipulate fractions to add or subtract mixed numbers<\/li>\n
- Solve equations that contain fractions or have fractional solutions<\/li>\n<\/ul>\n
Module 5: Decimals<\/span><\/h2>\nUnderstand how to make calculations with decimals and demonstrate how they relate to one another<\/h3>\n\n- Write and identify characteristics of decimals<\/li>\n
- Use various operations to solve applications involving decimals<\/li>\n
- Understand the relationship between decimals and fractions<\/li>\n
- Solve equations with decimals using properties of addition and subtraction<\/li>\n<\/ul>\n
Module 6: Ratios, Rates, Probabilities, and Averages<\/span><\/h2>\nApply knowledge of decimals to real world scenarios<\/h3>\n\n- Find the average and other reportable measures of a set of numbers<\/li>\n
- Write ratios as fractions and calculate unit rates<\/li>\n
- Use square roots to simplify expressions and solve application problems<\/li>\n<\/ul>\n
Module 7: Percents<\/span><\/h2>\nDemonstrate an understanding of percents and how they relate to other number formats<\/h3>\n\n- Write percents using words, ratios, and fractions and complete conversions<\/li>\n
- Solve general applications of percent<\/li>\n
- Solve sales tax, commission, and discount applications<\/li>\n
- Solve simple interest applications involving rate, time, and principal<\/li>\n
- Solve proportions and their applications<\/li>\n<\/ul>\n
Module 8: Geometry<\/span><\/h2>\nUse measurements and geometric equations to analyze shapes and structures<\/h3>\n\n- Use properties of angles, triangles, and the Pythagorean Theorem to solve problems<\/li>\n
- Use properties of rectangles, triangles, and trapezoids to solve problems<\/li>\n
- Use the properties of circles and irregular figures to solve problems<\/li>\n
- Solve problems using the volume and surface area of solid figures<\/li>\n
- Make conversions between units in the U.S. and Metric systems of measurement<\/li>\n<\/ul>\n
Module 9: Real Numbers<\/span><\/h2>\nIdentify and use properties of real numbers to evaluate expressions and equations<\/h3>\n\n- Identify the different types of real numbers<\/li>\n
- Use the commutative and associative properties to simplify expressions<\/li>\n
- Use the distributive property to simplify and evaluate expressions<\/li>\n
- Apply the identify, inverse, and zero properties<\/li>\n<\/ul>\n
Module 10: Linear Equations<\/span><\/h2>\nSolve linear equations that contain a variety of operations and number types<\/h3>\n\n- Solve equations using the properties of equality<\/li>\n
- Use problem solving strategies for word problems<\/li>\n
- Solve word problems containing decimals<\/li>\n
- Solve word problems by using common formulas<\/li>\n<\/ul>\n
Module 11: Linear Inequalities<\/span><\/h2>\nSolve both simple and compound linear inequalities and express the solution with the correct notation<\/h3>\n\n- Solve single- and multi-step inequalities<\/li>\n
- Solve compound inequalities<\/li>\n<\/ul>\n
Module 12: Exponents<\/h2>\nManipulate expressions containing exponents<\/h3>\n\n- Apply exponent rules to simplify expressions<\/li>\n
- Use scientific notation to represent and do arithmetic with large and small values<\/li>\n<\/ul>\n
Module 13: Polynomials<\/span><\/h2>\nManipulate and complete calculations with polynomials<\/h3>\n\n- Identify characteristics of polynomial expressions<\/li>\n
- Perform operations on polynomials<\/li>\n
- Divide polynomials<\/li>\n
- Write polynomials to represent real world situations<\/li>\n<\/ul>\n
Module 14: Factoring<\/h2>\nFactor polynomials using a variety of methods<\/h3>\n\n- Solve simple polynomial equations<\/li>\n
- Use a variety of factoring methods on polynomials<\/li>\n
- Factor special case polynomials<\/li>\n<\/ul>\n
Module 15: Graphs<\/span><\/h2>\nUse graphs and slope to identify points and write equations for lines<\/h3>\n\n- Graph points on the coordinate plane<\/li>\n
- Find the slope of a line<\/li>\n
- Use intercepts to graph lines<\/li>\n
- Write the equation for a line<\/li>\n
- Graph linear inequalities<\/li>\n
- Solve application problems involving graphs<\/li>\n<\/ul>\n
Module 16: Linear Systems<\/span><\/h2>\nSolve systems of linear equations using a variety of methods<\/h3>\n\n- Evaluate solutions to systems of equations<\/li>\n
- Solve systems of two variable equations using various methods<\/li>\n
- Solve systems of three variable equations using various methods<\/li>\n
- Solve application problems involving systems of equations<\/li>\n
- Solve systems of linear inequalities<\/li>\n<\/ul>\n
Module 17: Rational Expressions and Equations<\/span><\/h2>\nPerform operations on rational expressions and equations<\/h3>\n\n- Multiply and divide rational expressions<\/li>\n
- Add and subtract rational expressions<\/li>\n
- Use rational equations to solve application problems<\/li>\n
- Solve problems involving each type of variation<\/li>\n<\/ul>\n
Module 18: Roots and Rational Exponents<\/span><\/h2>\nUse properties of exponents to simplify expressions with radicals<\/h3>\n\n- Simplify expressions involving roots<\/li>\n
- Simplify expressions with radicals and rational exponents<\/li>\n
- Use algebraic operations to simplify radical expressions<\/li>\n
- Solve equations containing radicals<\/li>\n<\/ul>\n
Module 19:\u00a0<\/span>Quadratic Equations and Complex Numbers<\/span><\/h2>\nSolve quadratic equations and express non-real solutions as complex numbers<\/h3>\n\n- Use a variety of methods to solve quadratic equations<\/li>\n
- Express imaginary and complex numbers<\/li>\n
- Solve quadratic equations with complex solutions<\/li>\n<\/ul>\n
Module 20: Linear Functions and Function Notation<\/span><\/h2>\nIdentify and evaluate functions and find their domain and range<\/h3>\n\n- Define and evaluate functions<\/li>\n
- Graph and write equations for linear functions<\/li>\n
- Find the domain and range of a function<\/li>\n<\/ul>\n
Module 21:\u00a0<\/span>Quadratic, Polynomial, and\u00a0<\/span>Piecewise Functions<\/span><\/h2>\nEvaluate and graph quadratic, polynomial, and\u00a0piecewise functions<\/h3>\n\n- Evaluate, graph, and write piecewise functions<\/li>\n
- Graph quadratic and radical functions<\/li>\n
- Identify characteristics of polynomial functions<\/li>\n
- Solve problems involving projectile motion<\/li>\n<\/ul>\n
Module 22:\u00a0<\/span>Exponential and Logarithmic Functions<\/span><\/h2>\nEvaluate and graph exponential and logarithmic functions<\/h3>\n\n- Evaluate and graph exponential functions<\/li>\n
- Evaluate and graph logarithmic functions<\/li>\n<\/ul>\n
Module 23: Exponential and Logarithmic Equations<\/span><\/h2>\nUse logarithmic properties to solve exponential and logarithmic equations<\/h3>\n\n- Use logarithmic properties to simplify expressions<\/li>\n
- Solve exponential and logarithmic equations<\/li>\n<\/ul>\n<\/div>\n
Contribute!<\/h2>\nDid you have an idea for improving this content? We\u2019d love your input.<\/div>\nImprove this page<\/a>Learn More<\/a><\/p>\n\n\t\t\t \n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp.
- \r\n \t
- Understand the basics of whole numbers<\/li>\r\n \t
- Add whole numbers using the properties of addition<\/li>\r\n \t
- Subtract whole numbers using properties of subtraction<\/li>\r\n \t
- Multiply whole numbers using properties of multiplication<\/li>\r\n \t
- Divide whole numbers using properties of division<\/li>\r\n<\/ul>\r\n\r\n
Module 2: The Language of Algebra<\/h2>\r\n
Manipulate mathematical expressions and equations using algebraic rules<\/h3>\r\n
- \r\n \t
- Interpret expressions and equations that use words and algebraic symbols<\/li>\r\n \t
- Evaluate algebraic expressions containing multiple terms<\/li>\r\n \t
- Solve one-step equations using whole numbers<\/li>\r\n \t
- Find multiples and factors of whole numbers<\/li>\r\n \t
- Use prime factorization to find the least common multiple of two numbers<\/li>\r\n<\/ul>\r\n
Module 3: Integers<\/h2>\r\n
Solve problems that involve integers<\/h3>\r\n
- \r\n \t
- Write integer expressions and evaluate integer expressions involving absolute value<\/li>\r\n \t
- Simplify and evaluate expressions that involve the addition of integers<\/li>\r\n \t
- Simplify and evaluate expressions that involve the subtraction of integers<\/li>\r\n \t
- Simplify and evaluate expressions that involve the multiplication or division of integers<\/li>\r\n \t
- Solve simple one-step algebraic equations<\/li>\r\n<\/ul>\r\n
Module 4: Fractions<\/h2>\r\n
Understand how to manipulate fractions and demonstrate how they relate to one another<\/h3>\r\n
- \r\n \t
- Use fractions to represent parts of a whole and understand their value<\/li>\r\n \t
- Multiply and divide fractions by whole numbers, other fractions, and variable expressions<\/li>\r\n \t
- Multiply, divide, and simplify mixed numbers and complex fractions<\/li>\r\n \t
- Add and subtract fractions with common denominators<\/li>\r\n \t
- Add and subtract fractions with different denominators<\/li>\r\n \t
- Manipulate fractions to add or subtract mixed numbers<\/li>\r\n \t
- Solve equations that contain fractions or have fractional solutions<\/li>\r\n<\/ul>\r\n
Module 5: Decimals<\/span><\/h2>\r\n
Understand how to make calculations with decimals and demonstrate how they relate to one another<\/h3>\r\n
- \r\n \t
- Write and identify characteristics of decimals<\/li>\r\n \t
- Use various operations to solve applications involving decimals<\/li>\r\n \t
- Understand the relationship between decimals and fractions<\/li>\r\n \t
- Solve equations with decimals using properties of addition and subtraction<\/li>\r\n<\/ul>\r\n
Module 6: Ratios, Rates, Probabilities, and Averages<\/span><\/h2>\r\n
Apply knowledge of decimals to real world scenarios<\/h3>\r\n
- \r\n \t
- Find the average and other reportable measures of a set of numbers<\/li>\r\n \t
- Write ratios as fractions and calculate unit rates<\/li>\r\n \t
- Use square roots to simplify expressions and solve application problems<\/li>\r\n<\/ul>\r\n
Module 7: Percents<\/span><\/h2>\r\n
Demonstrate an understanding of percents and how they relate to other number formats<\/h3>\r\n
- \r\n \t
- Write percents using words, ratios, and fractions and complete conversions<\/li>\r\n \t
- Solve general applications of percent<\/li>\r\n \t
- Solve sales tax, commission, and discount applications<\/li>\r\n \t
- Solve simple interest applications involving rate, time, and principal<\/li>\r\n \t
- Solve proportions and their applications<\/li>\r\n<\/ul>\r\n
Module 8: Geometry<\/span><\/h2>\r\n
Use measurements and geometric equations to analyze shapes and structures<\/h3>\r\n
- \r\n \t
- Use properties of angles, triangles, and the Pythagorean Theorem to solve problems<\/li>\r\n \t
- Use properties of rectangles, triangles, and trapezoids to solve problems<\/li>\r\n \t
- Use the properties of circles and irregular figures to solve problems<\/li>\r\n \t
- Solve problems using the volume and surface area of solid figures<\/li>\r\n \t
- Make conversions between units in the U.S. and Metric systems of measurement<\/li>\r\n<\/ul>\r\n
Module 9: Real Numbers<\/span><\/h2>\r\n
Identify and use properties of real numbers to evaluate expressions and equations<\/h3>\r\n
- \r\n \t
- Identify the different types of real numbers<\/li>\r\n \t
- Use the commutative and associative properties to simplify expressions<\/li>\r\n \t
- Use the distributive property to simplify and evaluate expressions<\/li>\r\n \t
- Apply the identify, inverse, and zero properties<\/li>\r\n<\/ul>\r\n
Module 10: Linear Equations<\/span><\/h2>\r\n
Solve linear equations that contain a variety of operations and number types<\/h3>\r\n
- \r\n \t
- Solve equations using the properties of equality<\/li>\r\n \t
- Use problem solving strategies for word problems<\/li>\r\n \t
- Solve word problems containing decimals<\/li>\r\n \t
- Solve word problems by using common formulas<\/li>\r\n<\/ul>\r\n
Module 11: Linear Inequalities<\/span><\/h2>\r\n
Solve both simple and compound linear inequalities and express the solution with the correct notation<\/h3>\r\n
- \r\n \t
- Solve single- and multi-step inequalities<\/li>\r\n \t
- Solve compound inequalities<\/li>\r\n<\/ul>\r\n
Module 12: Exponents<\/h2>\r\n
Manipulate expressions containing exponents<\/h3>\r\n
- \r\n \t
- Apply exponent rules to simplify expressions<\/li>\r\n \t
- Use scientific notation to represent and do arithmetic with large and small values<\/li>\r\n<\/ul>\r\n
Module 13: Polynomials<\/span><\/h2>\r\n
Manipulate and complete calculations with polynomials<\/h3>\r\n
- \r\n \t
- Identify characteristics of polynomial expressions<\/li>\r\n \t
- Perform operations on polynomials<\/li>\r\n \t
- Divide polynomials<\/li>\r\n \t
- Write polynomials to represent real world situations<\/li>\r\n<\/ul>\r\n
Module 14: Factoring<\/h2>\r\n
Factor polynomials using a variety of methods<\/h3>\r\n
- \r\n \t
- Solve simple polynomial equations<\/li>\r\n \t
- Use a variety of factoring methods on polynomials<\/li>\r\n \t
- Factor special case polynomials<\/li>\r\n<\/ul>\r\n
Module 15: Graphs<\/span><\/h2>\r\n
Use graphs and slope to identify points and write equations for lines<\/h3>\r\n
- \r\n \t
- Graph points on the coordinate plane<\/li>\r\n \t
- Find the slope of a line<\/li>\r\n \t
- Use intercepts to graph lines<\/li>\r\n \t
- Write the equation for a line<\/li>\r\n \t
- Graph linear inequalities<\/li>\r\n \t
- Solve application problems involving graphs<\/li>\r\n<\/ul>\r\n
Module 16: Linear Systems<\/span><\/h2>\r\n
Solve systems of linear equations using a variety of methods<\/h3>\r\n
- \r\n \t
- Evaluate solutions to systems of equations<\/li>\r\n \t
- Solve systems of two variable equations using various methods<\/li>\r\n \t
- Solve systems of three variable equations using various methods<\/li>\r\n \t
- Solve application problems involving systems of equations<\/li>\r\n \t
- Solve systems of linear inequalities<\/li>\r\n<\/ul>\r\n
Module 17: Rational Expressions and Equations<\/span><\/h2>\r\n
Perform operations on rational expressions and equations<\/h3>\r\n
- \r\n \t
- Multiply and divide rational expressions<\/li>\r\n \t
- Add and subtract rational expressions<\/li>\r\n \t
- Use rational equations to solve application problems<\/li>\r\n \t
- Solve problems involving each type of variation<\/li>\r\n<\/ul>\r\n
Module 18: Roots and Rational Exponents<\/span><\/h2>\r\n
Use properties of exponents to simplify expressions with radicals<\/h3>\r\n
- \r\n \t
- Simplify expressions involving roots<\/li>\r\n \t
- Simplify expressions with radicals and rational exponents<\/li>\r\n \t
- Use algebraic operations to simplify radical expressions<\/li>\r\n \t
- Solve equations containing radicals<\/li>\r\n<\/ul>\r\n
Module 19:\u00a0<\/span>Quadratic Equations and Complex Numbers<\/span><\/h2>\r\n
Solve quadratic equations and express non-real solutions as complex numbers<\/h3>\r\n
- \r\n \t
- Use a variety of methods to solve quadratic equations<\/li>\r\n \t
- Express imaginary and complex numbers<\/li>\r\n \t
- Solve quadratic equations with complex solutions<\/li>\r\n<\/ul>\r\n
Module 20: Linear Functions and Function Notation<\/span><\/h2>\r\n
Identify and evaluate functions and find their domain and range<\/h3>\r\n
- \r\n \t
- Define and evaluate functions<\/li>\r\n \t
- Graph and write equations for linear functions<\/li>\r\n \t
- Find the domain and range of a function<\/li>\r\n<\/ul>\r\n
Module 21:\u00a0<\/span>Quadratic, Polynomial, and\u00a0<\/span>Piecewise Functions<\/span><\/h2>\r\n
Evaluate and graph quadratic, polynomial, and\u00a0piecewise functions<\/h3>\r\n
- \r\n \t
- Evaluate, graph, and write piecewise functions<\/li>\r\n \t
- Graph quadratic and radical functions<\/li>\r\n \t
- Identify characteristics of polynomial functions<\/li>\r\n \t
- Solve problems involving projectile motion<\/li>\r\n<\/ul>\r\n
Module 22:\u00a0<\/span>Exponential and Logarithmic Functions<\/span><\/h2>\r\n
Evaluate and graph exponential and logarithmic functions<\/h3>\r\n
- \r\n \t
- Evaluate and graph exponential functions<\/li>\r\n \t
- Evaluate and graph logarithmic functions<\/li>\r\n<\/ul>\r\n
Module 23: Exponential and Logarithmic Equations<\/span><\/h2>\r\n
Use logarithmic properties to solve exponential and logarithmic equations<\/h3>\r\n
- \r\n \t
- Use logarithmic properties to simplify expressions<\/li>\r\n \t
- Solve exponential and logarithmic equations<\/li>\r\n<\/ul>\r\n<\/div>\r\n
Contribute!<\/h2>
Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"<\/p>\nThe 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:\u00a0Developmental Math Emporium Learning Outcomes<\/a>.<\/p>\n
Module 1: Whole Numbers<\/h2>\n
Evaluate expressions and solve problems involving whole numbers<\/h3>\n
- \n
- Understand the basics of whole numbers<\/li>\n
- Add whole numbers using the properties of addition<\/li>\n
- Subtract whole numbers using properties of subtraction<\/li>\n
- Multiply whole numbers using properties of multiplication<\/li>\n
- Divide whole numbers using properties of division<\/li>\n<\/ul>\n\n
Module 2: The Language of Algebra<\/h2>\n
Manipulate mathematical expressions and equations using algebraic rules<\/h3>\n
- \n
- Interpret expressions and equations that use words and algebraic symbols<\/li>\n
- Evaluate algebraic expressions containing multiple terms<\/li>\n
- Solve one-step equations using whole numbers<\/li>\n
- Find multiples and factors of whole numbers<\/li>\n
- Use prime factorization to find the least common multiple of two numbers<\/li>\n<\/ul>\n
Module 3: Integers<\/h2>\n
Solve problems that involve integers<\/h3>\n
- \n
- Write integer expressions and evaluate integer expressions involving absolute value<\/li>\n
- Simplify and evaluate expressions that involve the addition of integers<\/li>\n
- Simplify and evaluate expressions that involve the subtraction of integers<\/li>\n
- Simplify and evaluate expressions that involve the multiplication or division of integers<\/li>\n
- Solve simple one-step algebraic equations<\/li>\n<\/ul>\n
Module 4: Fractions<\/h2>\n
Understand how to manipulate fractions and demonstrate how they relate to one another<\/h3>\n
- \n
- Use fractions to represent parts of a whole and understand their value<\/li>\n
- Multiply and divide fractions by whole numbers, other fractions, and variable expressions<\/li>\n
- Multiply, divide, and simplify mixed numbers and complex fractions<\/li>\n
- Add and subtract fractions with common denominators<\/li>\n
- Add and subtract fractions with different denominators<\/li>\n
- Manipulate fractions to add or subtract mixed numbers<\/li>\n
- Solve equations that contain fractions or have fractional solutions<\/li>\n<\/ul>\n
Module 5: Decimals<\/span><\/h2>\n
Understand how to make calculations with decimals and demonstrate how they relate to one another<\/h3>\n
- \n
- Write and identify characteristics of decimals<\/li>\n
- Use various operations to solve applications involving decimals<\/li>\n
- Understand the relationship between decimals and fractions<\/li>\n
- Solve equations with decimals using properties of addition and subtraction<\/li>\n<\/ul>\n
Module 6: Ratios, Rates, Probabilities, and Averages<\/span><\/h2>\n
Apply knowledge of decimals to real world scenarios<\/h3>\n
- \n
- Find the average and other reportable measures of a set of numbers<\/li>\n
- Write ratios as fractions and calculate unit rates<\/li>\n
- Use square roots to simplify expressions and solve application problems<\/li>\n<\/ul>\n
Module 7: Percents<\/span><\/h2>\n
Demonstrate an understanding of percents and how they relate to other number formats<\/h3>\n
- \n
- Write percents using words, ratios, and fractions and complete conversions<\/li>\n
- Solve general applications of percent<\/li>\n
- Solve sales tax, commission, and discount applications<\/li>\n
- Solve simple interest applications involving rate, time, and principal<\/li>\n
- Solve proportions and their applications<\/li>\n<\/ul>\n
Module 8: Geometry<\/span><\/h2>\n
Use measurements and geometric equations to analyze shapes and structures<\/h3>\n
- \n
- Use properties of angles, triangles, and the Pythagorean Theorem to solve problems<\/li>\n
- Use properties of rectangles, triangles, and trapezoids to solve problems<\/li>\n
- Use the properties of circles and irregular figures to solve problems<\/li>\n
- Solve problems using the volume and surface area of solid figures<\/li>\n
- Make conversions between units in the U.S. and Metric systems of measurement<\/li>\n<\/ul>\n
Module 9: Real Numbers<\/span><\/h2>\n
Identify and use properties of real numbers to evaluate expressions and equations<\/h3>\n
- \n
- Identify the different types of real numbers<\/li>\n
- Use the commutative and associative properties to simplify expressions<\/li>\n
- Use the distributive property to simplify and evaluate expressions<\/li>\n
- Apply the identify, inverse, and zero properties<\/li>\n<\/ul>\n
Module 10: Linear Equations<\/span><\/h2>\n
Solve linear equations that contain a variety of operations and number types<\/h3>\n
- \n
- Solve equations using the properties of equality<\/li>\n
- Use problem solving strategies for word problems<\/li>\n
- Solve word problems containing decimals<\/li>\n
- Solve word problems by using common formulas<\/li>\n<\/ul>\n
Module 11: Linear Inequalities<\/span><\/h2>\n
Solve both simple and compound linear inequalities and express the solution with the correct notation<\/h3>\n
- \n
- Solve single- and multi-step inequalities<\/li>\n
- Solve compound inequalities<\/li>\n<\/ul>\n
Module 12: Exponents<\/h2>\n
Manipulate expressions containing exponents<\/h3>\n
- \n
- Apply exponent rules to simplify expressions<\/li>\n
- Use scientific notation to represent and do arithmetic with large and small values<\/li>\n<\/ul>\n
Module 13: Polynomials<\/span><\/h2>\n
Manipulate and complete calculations with polynomials<\/h3>\n
- \n
- Identify characteristics of polynomial expressions<\/li>\n
- Perform operations on polynomials<\/li>\n
- Divide polynomials<\/li>\n
- Write polynomials to represent real world situations<\/li>\n<\/ul>\n
Module 14: Factoring<\/h2>\n
Factor polynomials using a variety of methods<\/h3>\n
- \n
- Solve simple polynomial equations<\/li>\n
- Use a variety of factoring methods on polynomials<\/li>\n
- Factor special case polynomials<\/li>\n<\/ul>\n
Module 15: Graphs<\/span><\/h2>\n
Use graphs and slope to identify points and write equations for lines<\/h3>\n
- \n
- Graph points on the coordinate plane<\/li>\n
- Find the slope of a line<\/li>\n
- Use intercepts to graph lines<\/li>\n
- Write the equation for a line<\/li>\n
- Graph linear inequalities<\/li>\n
- Solve application problems involving graphs<\/li>\n<\/ul>\n
Module 16: Linear Systems<\/span><\/h2>\n
Solve systems of linear equations using a variety of methods<\/h3>\n
- \n
- Evaluate solutions to systems of equations<\/li>\n
- Solve systems of two variable equations using various methods<\/li>\n
- Solve systems of three variable equations using various methods<\/li>\n
- Solve application problems involving systems of equations<\/li>\n
- Solve systems of linear inequalities<\/li>\n<\/ul>\n
Module 17: Rational Expressions and Equations<\/span><\/h2>\n
Perform operations on rational expressions and equations<\/h3>\n
- \n
- Multiply and divide rational expressions<\/li>\n
- Add and subtract rational expressions<\/li>\n
- Use rational equations to solve application problems<\/li>\n
- Solve problems involving each type of variation<\/li>\n<\/ul>\n
Module 18: Roots and Rational Exponents<\/span><\/h2>\n
Use properties of exponents to simplify expressions with radicals<\/h3>\n
- \n
- Simplify expressions involving roots<\/li>\n
- Simplify expressions with radicals and rational exponents<\/li>\n
- Use algebraic operations to simplify radical expressions<\/li>\n
- Solve equations containing radicals<\/li>\n<\/ul>\n
Module 19:\u00a0<\/span>Quadratic Equations and Complex Numbers<\/span><\/h2>\n
Solve quadratic equations and express non-real solutions as complex numbers<\/h3>\n
- \n
- Use a variety of methods to solve quadratic equations<\/li>\n
- Express imaginary and complex numbers<\/li>\n
- Solve quadratic equations with complex solutions<\/li>\n<\/ul>\n
Module 20: Linear Functions and Function Notation<\/span><\/h2>\n
Identify and evaluate functions and find their domain and range<\/h3>\n
- \n
- Define and evaluate functions<\/li>\n
- Graph and write equations for linear functions<\/li>\n
- Find the domain and range of a function<\/li>\n<\/ul>\n
Module 21:\u00a0<\/span>Quadratic, Polynomial, and\u00a0<\/span>Piecewise Functions<\/span><\/h2>\n
Evaluate and graph quadratic, polynomial, and\u00a0piecewise functions<\/h3>\n
- \n
- Evaluate, graph, and write piecewise functions<\/li>\n
- Graph quadratic and radical functions<\/li>\n
- Identify characteristics of polynomial functions<\/li>\n
- Solve problems involving projectile motion<\/li>\n<\/ul>\n
Module 22:\u00a0<\/span>Exponential and Logarithmic Functions<\/span><\/h2>\n
Evaluate and graph exponential and logarithmic functions<\/h3>\n
- \n
- Evaluate and graph exponential functions<\/li>\n
- Evaluate and graph logarithmic functions<\/li>\n<\/ul>\n
Module 23: Exponential and Logarithmic Equations<\/span><\/h2>\n
Use logarithmic properties to solve exponential and logarithmic equations<\/h3>\n
- \n
- Use logarithmic properties to simplify expressions<\/li>\n
- Solve exponential and logarithmic equations<\/li>\n<\/ul>\n<\/div>\n
Contribute!<\/h2>\n
Did you have an idea for improving this content? We\u2019d love your input.<\/div>\nImprove this page<\/a>Learn More<\/a><\/p>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Original<\/div>- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Magnify. Authored by<\/strong>: Eucalyp.
- Learning Outcomes. Provided by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>