Learning Outcomes

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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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