Detailed Course Information

Number Sense: Integers

• Multiplication is Commutative
• Multiplication is Associative
• Division is not Commutative
• Division is Not Associative
• Word Problems with Commutative and Associative Laws
• Distributive Law for Multiplication Over Addition
• Definition of 2 Forms of Distributive Law for Mult. over Add.
• Distributive Law for Multiplication over Subtraction
• Distributive Law for Division over Addition
• Only One Form of Distributive Law for Division
• Review of Binary Operations
• Multiple Binary Operations
• Adding Parentheses to Make Equations True
• Distributive Laws for Multiplication
• Distributive Laws for Division
• Identity Element in Addition, Subtraction, Multiplication, and Division
• Multiplying and Dividing by Zero
• Giving Reason for Each Equation by Law
• Review Multiplication by Ten, One-Hundred, and One-Thousand
• Review Multiplication by Multiples of Ten Using Distributive Law
• Multiplication Using the Distributive Law
• Multiplication of a Single Digit and a 2, 3, and 4 Digit Numbers
• Multiplication of Single Digit and 2 Digit Number, Shortened Notation
• Multiplication of 2 Digit Number by a 2 Digit Number
• Multiplication of a 2 Digit by a 2 Digit Number, Shortened Notation
• Multiplication of a 2 Digit by a 3 Digit Number, Shortened Notation
• Multiplication w/Money, Word Problems
• Multiplication (3 Digit by 3 Digit, 3 digit by 4 Digit, 4 Digit by 4 Digit)
• Division as Inverse of Multiplication
• Long Division, 2 Digit by 1 Digit
• Estimation
• Multiplication Tables are also Division Tables
• Hundreds
• Dividing Tens and Hundreds
• Multiple of 10, 100 or 1000 Divided by 1 Digit
• Estimation and Division
• Multiples
• Multiples of 2, 3, 5, 7, and 9
• Finding Factors
• Prime Numbers 
• Prime Factors
• Multiplication by 10's, 100's, and 1000's
• Multiplying Multiples of Ten
• Division by Tens
• Multiplying Multiples of Ten by Multiples of Ten
• Dividing by Multiples of Ten
• Multiplication and division of Tens and Hundreds
• Estimating to the Nearest Multiple of Ten
• Using Estimates in Division
• Estimation
• Multiples of 10, 100, and 1000
• Checking Division with Multiplication

Number Sense:  Decimals and Fractions

• Fractions, Equal Mixed Numbers
• Mixed Numbers Equal to a Fraction
• Expressing a Fraction as a Whole or Mixed Number
• Expressing a Whole or Mixed Number as a Fraction
• Equal Fractions
• Equal and Unequal Fractions
• Renaming Fractions
• Definition of Renaming Fractions
• Multiplying Fractions  
• Equal and Unequal Fractions
• Addition of Fractions
• Subtraction of Fractions
• Word Problems: Renaming and Multiplication of Fractions
• Lowest Terms
• Finding Lowest Terms 
• Express in Lowest Terms, Dividing More than Once
• Common Multiples
• Finding the Least Common Multiple
• Which are Multiples of 2, 5, and 10?
• Which are divisible by 2, 5, and 10?
• Finding the Least Common Denominator and Rewriting Fractions
• Addition and Subtraction of Fractions Word Problems
• Unequal Fractions, Find Common Denominators
• Equal and Unequal Fractions, Find Common Denominators
• Addition and Subtraction with Unlike Denominators  
• Whole Numbers, Fractions, Mixed Numbers on a Number Line with Addition
• Addition of Fractions with Unlike Denominators
• Addition of Mixed Numbers, Like Fractions
• Addition of Mixed Numbers
• Renaming Fraction by Multiplying both Numerator/Denominator by Same Number
• Addition and Subtraction with Unlike Denominators, Answer in Lowest Terms
• Addition of Fractions Word Problems
• Addition of Fractions, Column Form
• Subtraction of Fractions, Column Form
• Addition and Subtraction of Fractions, Column Form 
• Addition and Subtraction of Fractions and Mixed Numbers Word Problems
• Addition of Mixed Numbers and Renaming Improper Mixed Numbers
• Addition of Mixed Numbers
• Subtraction of Mixed Numbers, Regrouping
• Subtraction of Mixed Numbers
• Addition and Subtraction of Mixed Numbers 
• Multiplication and Subtraction of Fractions, Addition of Mixed Numbers Word Problems
• Subtraction of Mixed Numbers
• Subtraction of Mixed Numbers with Borrowing, Lowest Terms
• Word Problems, Addition and Subtraction of Mixed Numbers
• Intro to Multiplying a Fraction by a Whole Number
• Multiplication Fractions by a Whole Number
• Multiplication of a Whole Number by a Whole Number/Multiplication of a Fraction by a Whole Number
• Multiplication Fractions by a Whole Number
• Distributive Law for Multiplying a Mixed Number by a Whole Number
• Word Problems, Multiplication of Fractions and Mixed Numbers
• Operations on Fractions and Mixed Numbers 
• Word Problems, Addition and Subtractions of Mixed Numbers
• Multiplying a Fraction by a Fraction
• Multiplication of Fractions 
• Fractions Equal to One 
• Intro to Multiplicative Inverse 
• Definition of Multiplicative Inverse
• Word Problems, Multiplicative Inverse and Multiplication of Fractions
• Division of Fractions
• Division of and by Fractions
• Multiplying and Dividing Mixed Numbers
• Dividing Mixed Numbers
• Word Problems, Dividing Mixed Numbers
• Dividing Fractions and Whole Numbers by Fractions 
• Multiplying Mixed Numbers by Fractions and Mixed Numbers
• Dividing Mixed Numbers by Fractions and Mixed Numbers
• Decimal Fractions and Decimal Points
• Converting Decimals to Fractions 
• Converting Fractions to Decimals 
• Finding Decimals on the Number Line, Patterns of Decimal Numbers
• Equal and Unequal Decimals  
• Decimal Tables
• Adding Fractions and Adding Decimals
• Converting Fraction Equations to Decimal Equations
• Using Decimals to Name More Place Values
• Converting Mixed Numbers to Decimal Numbers
• Decimals as English Words
• Expressing Decimals as Addition of Fractions
• Expressing Addition of Fractions as Decimals
• Addition of Decimals
• Addition of Decimals, Column Form
• Addition of Fractions and Addition of Decimals, Column Form 
• Decimal Equalities
• Addition of Decimals 
• Expressing Improper Fractions as Mixed Numbers and Decimals
• Subtraction of Decimal Fractions
• Subtraction of Decimal Fractions with Borrowing
• Addition and Subtraction of Fractions and Decimals
• Addition of Fractions resulting in Decimals
• Addition of Decimals
• Subtraction of Decimals
• Word Problems, Addition and Subtraction of Decimals and Fractions
• Equal and Unequal Decimals
• Place Value: Thousandths to Millionths
• Adding Decimals of More than Two Places
• Comparing Decimals, Equal, Lesser, or Greater Than
• Expressing Fractions as Decimals 
• Expressing Parts as Decimals
• Money and Decimals
• Word Problems, Addition and Subtraction of Decimals, Money and Decimals

• Definition of Writing Segments Notation
• Describing Geometric Figures as the Union of Line Segments
• Set Descriptions
• Describing Circles as Sets of Points
• Definition of Plane
• Base and Height of a Triangle
• Area of a Triangle
• Area of Triangular and Rectangular Regions
• Definition of an Octagon and Comparison of Areas of Square, Circle, Pentagon, and Octagon
• Intro to Ratios
• Concave and Convex 2D Figures
• Lines of Symmetry
• Plane Intersecting an Object
• Examples of Planes Cutting Objects
• Planes of Symmetry
• Axis of Symmetry of 2D Figures
• Definition of Axis of Symmetry
• Naming Angles
• Measure of Angles
• Congruent Angles
• Measuring Angles in Degrees
• Using a Protractor to Measure Angles 
• Measuring Angles to Nearest Degree
• Positions
• Mirror Symmetry
• Mirror Reflections
• Identifying Lines of Mirror Reflection
• Rotational Symmetry
• Rotations and Indicating Rotations
• Identifying Missing Rotations
• Rotations and Mirror Reflections
• Rotation and Mirror Reflections (Motions)
• Rotations
• All Rotations of a Figure
• Identifying Missing Reflection or Rotation

Logic and Reasoning

• Using the "If-then" Rule
• Using the "If-then-not" Rule
• Antecedent or Consequent of a Conditional Sentence
• Denials
• Denial of a Sentence Whose Connective is "Not"
• Recognizing then or If-then-not Rule
• Rule of Adjunction
• Rule of Simplification
• Inferences about Disjunctions - The "Or" Rule
• Review Using a Capital Letter to Stand for a Set
• Probability of a Symmetrical Spinner
• Probability of an Asymmetrical Spinner
• Outcomes and Events
• Probability of Outcomes and Events
• Probability of Extended Outcomes and Events 
• Probability of Intersection or Union of Two Events
• Intersection of Events, Description and Probability
• Union of Events, Description and Probability 
• Union and Intersection of Events, Description and Probability
• Intersection of Events as Operation on Sets, Description and Probability 
• Union of Events as Operation on Sets, Description and Probability 
• Impossible Events
• Probability of an Event that is an Intersection of Two Events
• Probability of an Event that is a Union of Two Events
• Using Diagrams to Show Intersection, Union, and difference of Sets,
• Using Diagrams to Show Operations on Sets
• Using Diagrams to Show Union of More than Two Sets
• Using Diagrams to Show Intersection of More than Two Sets
• Using Diagrams to Show Operations on More than Two Sets
• Using Diagrams to Show Operations on Two of Three Sets

Measurement, Graphs, and Equations

• Definition of Picture Graphs
• Definition of Circle Graphs
• Line and Bar Graphs
• Writing a Mathematical Sentence to Correspond to an English Sentence
• Variables in Mathematical Sentences
• Expressing English Sentences as Mathematical Sentences
• Expressing Addition as Multiplication
• Omitting the Multiplication Sign in an Expression
• Equal or Not Equal Equations
• Is the Expression Clear? 
• Rewriting Equations without the Multiplication Sign
• Expressing English Sentences as Mathematical Sentences
• Mathematical Equations for Multiple English Sentences
• Simplifying Expressions Using the Distributive Law
• Equal and Unequal Equations 
• Simplifying Expressions and Word Problems
• Intro. of Metric System: km, dm, m, cm, and mm.
• Converting Units In The Metric System  
• Metric Word Problems
• Rule for Members of a Set
• Rule for Finding the Second Member of an Ordered Pair
• Ordered Pairs and Rules
• Finding the Rule by Looking at the Set of Ordered Pairs
• Definition of Function
• Graphs of Sets of Ordered Pairs
• Making a Table of Ordered Pairs
• Listing Ordered Pairs form a Table

Data/Statistics/Probability

• Computing the Mean
• Identifying Modes 1-2
• Identifying the Median
• Computing Mean, Median, and Mode
• Comparing Mean, Median, and Mode
• Circle Graphs 1-6
• Constructing Histograms
• Interpreting Histograms 1-3

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