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Developmental Emporium
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Lumen Learning: Waymaker Developmental Math Emporium Learning Outcomes is licensed under CC-BY 4.0
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OutcomesShort Title
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Module 1: Evaluate expressions and solve problems involving whole numbersWhole Numbers
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1.1Understand the basics of whole numbersWhole Number Basics
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1.1.1Identify whole numbers from a list of numbersCounting Numbers and Whole Numbers
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1.1.2Identify the place value of a digitIdentifying Place Value
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1.1.3Write whole numbers as both digits and wordsWriting and Naming Whole Numbers
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1.1.4Round a whole number to a specific place valueRounding Whole Numbers
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1.2Add whole numbers using the properties of additionAdding Whole Numbers
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1.2.1Add multiple-digit numbers using columns for place valueAdding Whole Numbers Without Models
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1.2.2Translate word phrases into mathematical notation representing additionTranslating Word Phrases to Addition Notation
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1.2.3Solve word problems by using additionAdding Whole Numbers in Applications
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1.3Subtract whole numbers using properties of subtractionSubtracting Whole Numbers
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1.3.1Model subtraction of whole numbersModeling Subtraction of Whole Numbers
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1.3.2Subtract multiple-digit numbers using columns for place valueSubtracting Whole Numbers Without Models
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1.3.3Translate word phrases into mathematical expressions representing subtraction Translating Subtraction Word Phrases
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1.3.4Solve word problems by using subtractionSubtracting Whole Numbers in Applications
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1.4Multiply whole numbers using properties of multiplicationMultiplying Whole Numbers
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1.4.1Identify and use the multiplication property of zeroUsing the Multiplication Property of Zero
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1.4.2Multiply multiple-digit numbers using columns for place valueMultiplying Whole Numbers Without Models
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1.4.3Translate word phrases into mathematical expressions representing multiplicationTranslating Word Phrases to Multiplication Notation
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1.4.4Solve word problems by using multiplication Multiplying Whole Numbers in Applications
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1.5Divide whole numbers using properties of divisionDividing Whole Numbers
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1.5.1Model division of whole numbersModeling Division of Whole Numbers
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1.5.2Identify and use the division properties of zeroUsing the Division Properties of Zero
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1.5.3Use the long division algorithm to divide multiple-digit numbersDividing Whole Numbers Without Models
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1.5.4Translate word phrases into mathematical expressions representing divisionTranslating Word Phrases to Division Notation
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1.5.5Solve word problems by using division Dividing Whole Numbers in Applications
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1.5.6Convert math expressions and word problems between division and multiplicationConverting Between Multiplication and Division
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Module 2: Manipulate mathematical expressions and equations using algebraic rulesLanguage of Algebra
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2.1Interpret expressions and equations that use words and algebraic symbolsUsing the Language of Algebra
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2.1.1Use variables to represent unknown quantities in an algebraic expressionUsing Variables and Algebraic Symbols
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2.1.2Identify the variables and constants in an algebraic expressionIdentifying Variables and Constants
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2.1.3Use symbols and words to represent algebraic operations on variables and constantsUsing Algebraic Symbols to Create Expressions
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2.1.4Use inequality symbols to compare two quantitiesUsing Inequality Symbols
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2.1.5Translate between words and inequality notationTranslating Sentences into Inequalities
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2.1.6Use exponential notation to express repeated multiplicationUsing Exponential Notation
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2.1.7Write an exponential expression in expanded formWriting Expanded Exponential Expressions
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2.1.8Simplify complex mathematical expressions involving addition, subtraction, multiplication, division, and exponentsSimplifying Complex Expressions with Operations
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2.2Evaluate algebraic expressions containing multiple termsEvaluating, Simplifying, and Translating Algebraic Expressions
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2.2.1Identify the coefficient of a variable termIdentifying Terms, Coefficients, and Like Terms
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2.2.2Use the order of operations to simplify expressions containing like termsCombining Like Terms
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2.2.3Evaluate algebraic expressions for different valuesEvaluating Algebraic Expressions
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2.2.4Translate word phrases into algebraic expressionsTranslating Words to Algebraic Expressions
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2.2.5Write an algebraic expression that represents the relationship between two measurementsWriting Algebraic Expressions Involving Measurements
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2.3Solve one-step equations using whole numbersSolving One-Step Equations Using Whole Numbers
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2.3.1Determine whether a number is a solution of an equationDetermine Whether a Whole Number is a Solution to an Equation
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2.3.2Solve equations using the Subtraction Property of EqualitySolving Equations Using the Subtraction Property of Equality
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2.3.3Solve equations using the Addition Property of EqualitySolving Equations Using the Addition Property of Equality
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2.3.4Translate statements into algebraic equations involving addition, subtraction, multiplication, and division and solveTranslating Word Phrases into Algebraic Equations and Solving
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2.4Find multiples and factors of whole numbersFinding Multiples and Factors
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2.4.1Identify multiples of whole numbersIdentifying Multiples of Numbers
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2.4.2Find all the factors of a numberFinding all the Factors of a Number
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2.4.3Determine whether a number is prime or compositePrime and Composite Numbers
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2.5Use prime factorization to find the least common multiple of two numbersPrime Factorization and the Least Common Multiple
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2.5.1Find the prime factorization of a number using the factor tree methodFinding the Prime Factorization of a Composite Number
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2.5.2Find the least common multiple of two numbers by listing multiplesFinding the Least Common Multiple of Two Numbers
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2.5.3Find the least common multiple of two numbers by prime factorizationUse Prime Factorization to Find the Least Common Multiple
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Module 3: Solve problems that involve integersIntegers
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3.1Write integer expressions and evaluate integer expressions involving absolute valueIdentifying and Writing Integers
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3.1.1Locate positive and negative numbers on the number lineLocating and Ordering Integers on the Number Line
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3.1.2Order positive and negative numbersOrdering Positive and Negative Numbers
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3.1.3Simplify expressions that contain absolute valueSimplifying Expressions with Absolute Value
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3.1.4Evaluate expressions that contain absolute valueEvaluating Expressions with Absolute Value
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3.2Simplify and evaluate expressions that involve the addition of integersAdding Integers
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3.2.1Simplify expressions using addition of integers Simplifying Expressions with Integer Addition
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3.2.2Evaluate variable expressions with addition of integersEvaluating Variable Expressions with Integer Addition
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3.2.3Translate word phrases involving addition to algebraic expressionsTranslating Addition Word Phrases to Algebraic Expressions
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3.2.4Add integers in applicationsAdding Integers in Applications
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3.3Simplify and evaluate expressions that involve the subtraction of integersSubtracting Integers
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3.3.1Simplify expressions using subtraction of integersSimplifying Expressions with Integer Subtraction
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3.3.2Evaluate variable expressions with subtraction of integersEvaluating Variable Expressions with Integer Subtraction
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3.3.3Translate words phrases involving subtraction to algebraic expressionsTranslating Subtraction Word Phrases into Algebraic Expressions
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3.3.4Subtract integers in applicationsSubtracting Integers in Applications
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3.4Simplify and evaluate expressions that involve the multiplication or division of integersMultiplying and Dividing Integers
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3.4.1Multiply integers Multiplying Integers
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3.4.2Divide integersDividing Integers
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3.4.3Simplify expressions using multiplication and division of integersSimplifying Expressions with Integer Multiplication and Division
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3.4.4Evaluate variable expressions with multiplication and division of integersEvaluating Variable Expressions with Integer Multiplication and Division
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3.4.5Translate word phrases involving multiplication or division to algebraic expressions and simplifyTranslating Multiplication and Division Word Phrases to Algebraic Expressions
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3.5Solve simple one-step algebraic equationsSolving One-Step Equations Using Integers
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3.5.1Determine whether an integer is a solution of an equationDetermining Whether an Integer is a Solution to an Equation
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3.5.2Solve equations with integers using the addition and subtraction properties of equalitySolving Equations with Integers Using Addition and Subtraction Properties of Equality
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3.5.3Solve equations using the multiplication and division properties of equalitySolving Equations Using the Division Property of Equality
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3.5.4Translate word problems to equations and solveTranslating and Solving Word Problems
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Module 4: Understand how to manipulate fractions and demonstrate how they relate to one another Fractions
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4.1Use fractions to represent parts of a whole and understand their valueRepresenting Parts of a Whole as Fractions
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4.1.1Convert between improper fractions and mixed numbersConverting Between Improper Fractions and Mixed Numbers
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4.1.2Find equivalent fractionsFinding Equivalent Fractions
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4.1.3Locate fractions and mixed numbers on the number lineLocating Fractions and Mixed Numbers on the Number Line
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4.1.4Order fractions and mixed numbers using lists and inequalitiesOrdering Fractions and Mixed Numbers
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4.2Multiply and divide fractions by whole numbers, other fractions, and variable expressionsMultiplying and Dividing Fractions
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4.2.1Simplify fractions by finding common factors between the numerator and denominatorSimplifying Fractions