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Why should you take this course? 1) Huge amount of resources 2) Step-by-step instruction 3) Highly qualified instructor 4) Build your mathematics confidence

Objectives:

- Be able to determine all of the factors of a given natural number.
- Be able to determine the prime factorization for a given natural number.
- Be able to determine the least common multiple for a given set of natural numbers.

Objectives:

- Be able to determine all of the factors of a given natural number.
- Be able to determine the prime factorization for a given natural number.
- Be able to determine the least common multiple for a given set of natural numbers.

Objectives:

- Understand why no number can be written as a fraction with a denominator of zero
- Be able to write any fraction as a reduced fraction where the numerator and denominator have no common factors other than 1.
- Be able to create an equivalent fraction with a given denominator.
- Be able to multiply and divide fractions and write the result as a reduced fraction.

Objectives:

- Understand why no number can be written as a fraction with a denominator of zero
- Be able to write any fraction as a reduced fraction where the numerator and denominator have no common factors other than 1.
- Be able to create an equivalent fraction with a given denominator.
- Be able to multiply and divide fractions and write the result as a reduced fraction.

Objectives:

- Be familiar with the basic definition of a set and the notation used to define a set.
- Be able to give examples and non-examples of natural numbers.
- Be able to give examples and non-examples of whole numbers.
- Be able to give examples and non-examples of integers.
- Be able to give examples and non-examples of rational numbers.
- Be able to give examples and non-examples of irrational numbers.
- Be able to identify problems that can be addressed with each subset of the real numbers.
- Be familiar with the basic definition of the absolute value of a real number.
- Be able to determine the absolute value of a given real number

Objectives:

- Be familiar with the basic definition of a set and the notation used to define a set.
- Be able to give examples and non-examples of natural numbers.
- Be able to give examples and non-examples of whole numbers.
- Be able to give examples and non-examples of integers.
- Be able to give examples and non-examples of rational numbers.
- Be able to give examples and non-examples of irrational numbers.
- Be able to identify problems that can be addressed with each subset of the real numbers.
- Be familiar with the basic definition of the absolute value of a real number.
- Be able to determine the absolute value of a given real number

Objectives:

- Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
- Understand and be able to utilize the rule for simplifying the power of an exponential expression.
- Understand and be able to utilize the rule for simplifying the powers of products and quotients.
- Be able to interpret and simplify an exponential with a zero as an exponent.
- Be able to interpret and simplify an exponential with a negative number exponent.

Objectives:

- Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
- Understand and be able to utilize the rule for simplifying the power of an exponential expression.
- Understand and be able to utilize the rule for simplifying the powers of products and quotients.
- Be able to interpret and simplify an exponential with a zero as an exponent.
- Be able to interpret and simplify an exponential with a negative number exponent.

Objective:

- Be able to use the order of operations to evaluate and simplify an expression.

Objective:

- Be able to use the order of operations to evaluate and simplify an expression.

Objectives:

- Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
- Be able to simplify variable expressions using the distributive property.

Objectives:

- Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
- Be able to simplify variable expressions using the distributive property.

**Objectives**:

- Define polynomial.
- Add and subtract polynomials.

**Objectives**:

- Define polynomial.
- Add and subtract polynomials.

**Objectives**:

- Multiply terms, any two polynomials, binomials, and polynomial functions.
- Find the product of the sum and difference of two terms.
- Find the square of a binomial.

**Objectives**:

- Multiply terms, any two polynomials, binomials, and polynomial functions.
- Find the product of the sum and difference of two terms.
- Find the square of a binomial.

**Objectives**:

- Multiply terms, any two polynomials, binomials, and polynomial functions.
- Find the product of the sum and difference of two terms.
- Find the square of a binomial.

**Objectives**:

- Divide a polynomial by a monomial.
- Divide a polynomial by a polynomial of two or more terms.

**Objectives**:

- Divide a polynomial by a monomial.
- Divide a polynomial by a polynomial of two or more terms.

**Objectives**:

- Factor out the greatest common factor.
- Factor by grouping.

**Objectives**:

- Factor out the greatest common factor.
- Factor by grouping.

**Objectives**:

- Factor out the greatest common factor.
- Factor by grouping.

**Objectives**:

- Factor out the greatest common factor.
- Factor by grouping.

**Objectives/Hints**:

- Use the “OI” to factor.
- Can you factor out a monomial?
- Negative leading coefficients should be factored out.

**Objectives/Hints**:

- Use the “OI” to factor.
- Can you factor out a monomial?
- Negative leading coefficients should be factored out.

**Objectives**:

- Factor a difference of squares.
- Factor a perfect square trinomial.

**Objectives**:

- Factor a difference of squares.
- Factor a perfect square trinomial.

**Objectives**:

- Define rational expressions and functions and describe their domain.
- Write rational expressions in lowest terms.

**Objectives**:

- Define rational expressions and functions and describe their domain.
- Write rational expressions in lowest terms.

**Objectives**:

- Define rational expressions and functions and describe their domain.
- Write rational expressions in lowest terms.
- Multiply and divide rational expressions.
- Find reciprocals of rational expressions.

**Objectives**:

- Define rational expressions and functions and describe their domain.
- Write rational expressions in lowest terms.
- Multiply and divide rational expressions.
- Find reciprocals of rational expressions.

**Objectives**:

- Add and subtract rational expressions with common denominators.
- Find a least common denominator.
- Add and subtract rational expressions with different denominators.

**Objectives**:

- Add and subtract rational expressions with common denominators.
- Find a least common denominator.
- Add and subtract rational expressions with different denominators.

**Objectives**:

- Find roots of numbers.
- Find principal roots.

**Objectives**:

- Find roots of numbers.
- Find principal roots.

**Objectives**:

- Use the product and quotient rule for radicals.
- Simplify radicals.
- Simplify products and quotients of radicals with different indexes.

**Objectives**:

- Use the product and quotient rule for radicals.
- Simplify radicals.
- Simplify products and quotients of radicals with different indexes.

**Objectives**:

- Use the product and quotient rule for radicals.
- Simplify radicals.
- Simplify products and quotients of radicals with different indexes.

**Objectives**:

- Write from logarithmic form to exponential form.
- Write from exponential form to logarithmic form.
- Evaluate logarithmic expressions.

**Objectives**:

- Write from logarithmic form to exponential form.
- Write from exponential form to logarithmic form.
- Evaluate logarithmic expressions.

**Objectives**:

- List elements of sets.
- Graph inequalities.
- Write inequalities in interval notation.
- Express intervals as inequalities.
- Write sets using the roster method.

**Objectives**:

- List elements of sets.
- Graph inequalities.
- Write inequalities in interval notation.
- Express intervals as inequalities.
- Write sets using the roster method.

**Objectives**:

- Determine if a given number is a solution or is not a solution of a given equation.
- Write a given sentence as an equation or inequality.
- Solve equations.

**Objectives**:

- Determine if a given number is a solution or is not a solution of a given equation.
- Write a given sentence as an equation or inequality.
- Solve equations.

**Objectives**:

- Solve equations.
- Solve application problems.

**Objectives**:

- Solve equations.
- Solve application problems.

**Objectives**:

- Solve absolute value equations.
- Write solutions in solution sets.

**Objectives**:

- Solve absolute value equations.
- Write solutions in solution sets.

**Objectives**:

- Learn and use the zero-factor property.
- Solve applied problems that require the zero-factor property.

**Objectives**:

- Learn and use the zero-factor property.
- Solve applied problems that require the zero-factor property.

**Objectives**:

- Determine the domain of the variable in a rational equation.
- Solve rational equations.

**Objectives**:

- Determine the domain of the variable in a rational equation.
- Solve rational equations.

**Objectives**:

- Determine the domain of the variable in a rational equation.
- Solve rational equations.

**Objectives**:

- Solve radical equations by using the power rule.
- Solve radical equations that require additional steps.
- Solve radical equations with indexes greater than 2.

**Objectives**:

- Solve radical equations by using the power rule.
- Solve radical equations that require additional steps.
- Solve radical equations with indexes greater than 2.

**Objectives**:

- Learn the square root property.
- Solve quadratic equations by extending the square root property.
- Solve quadratic equations by completing the square.

**Objectives**:

- Learn the square root property.
- Solve quadratic equations by extending the square root property.
- Solve quadratic equations by completing the square.

**Objective**:

- Solve quadratic equations by using the quadratic formula.

**Objective**:

- Solve quadratic equations by using the quadratic formula.

**Objectives**:

- Solve linear inequalities by using the addition property.
- Solve linear inequalities by using the multiplication property.
- Solve applied problems by using linear inequalities.

**Objectives**:

- Solve linear inequalities by using the addition property.
- Solve linear inequalities by using the multiplication property.
- Solve applied problems by using linear inequalities.

**Objectives**:

- Use the definition of absolute value.
- Solve inequalities. graph the solution set, and write in interval notation.

**Objectives**:

- Use the definition of absolute value.
- Solve inequalities. graph the solution set, and write in interval notation.

**Objectives**:

- Distinguish between independent and dependent variables.
- Define and identify relations and functions.
- Find the domain and range.
- Identify functions defined by graphs and equations.

**Objectives**:

- Distinguish between independent and dependent variables.
- Define and identify relations and functions.
- Find the domain and range.
- Identify functions defined by graphs and equations.

**Objectives**:

- Find the x- and y-coordinates of labeled points. State in which quadrant or on which axis the point lies.
- Complete tables of ordered pairs for linear equations.

**Objectives**:

- Find the x- and y-coordinates of labeled points. State in which quadrant or on which axis the point lies.
- Complete tables of ordered pairs for linear equations.

**Objectives**:

- Graph linear equations.
- Graph linear equations by finding and plotting its intercepts.
- Write the coordinates of x- and y-intercepts.

**Objectives**:

- Graph linear equations.
- Graph linear equations by finding and plotting its intercepts.
- Write the coordinates of x- and y-intercepts.

**Objectives**:

- Graph a line, given its slope and a point on the line.
- Use slopes to determine whether two lines are parallel, perpendicular, or neither.
- Solve problems involving average rate of change.

**Objectives**:

- Graph a line, given its slope and a point on the line.
- Use slopes to determine whether two lines are parallel, perpendicular, or neither.
- Solve problems involving average rate of change.

**Objectives**:

- Use the slope-intercept form to graph the equations.
- Find an equation of the line passing through the pair of points.
- Solve problems involving average rate of change.

**Objectives**:

- Use the slope-intercept form to graph the equations.
- Find an equation of the line passing through the pair of points.
- Solve problems involving average rate of change.

**Objective**:

- Recognize the graphs of elementary functions and graph their translations.
- Determine a graph's domain and range.

**Objective**:

- Recognize the graphs of elementary functions and graph their translations.
- Determine a graph's domain and range.

**Objective**:

- Solve linear systems by graphing, substitution, and elimination.

**Objective**:

- Solve linear systems by graphing, substitution, and elimination.

**TOPICS COVERED**:

This course is an intermediate course in algebra that begins with a review of introductory algebra concepts. The course is comprised of three units: Manipulating and Simplifying Expressions, Solving Equations and Inequalities, and Graphing Equations and Inequalities. Each unit will consider real-world applications of the associated concepts and procedures and will incorporate the following expression types: linear, quadratic, general polynomial, rational, roots and radicals, exponential, and logarithmic.

**IDEA COURSE OBJECTIVES**:

This course will involve the following objectives:

- Objective 1: Gaining factual knowledge (terminology, classifications, methods, trends).

- Objective 2: Learning fundamental principles, generalizations, and/or theories

**COURSE INCLUDES**:

- 37 Video-Lessons
- 36 Practice Worksheets
- 18 hr 37 min 26 sec of video-lessons
- PDF versions of guided notes for each lesson
- Guided powerpoint for each lesson
- 36 Practice worksheet review videos
- 22 Quizzes (Quick concept/vocabulary checks)
- 10 Comprehension Tests
- PDF versions of each test
- Answer keys to all practice worksheets and tests (Additional Resources for Parents)
- Completed copies of all of the notes (Additional Resources for Parents)

**COURSE TOPICS**:

- Factors
- Fractions
- Real Numbers
- Exponents
- Order of Operations
- Simplifying and Evaluating Algebraic Expressions
- Polynomials
- Multiplying Polynomials
- Dividing Polynomials
- Factors and the Greatest Common Factor
- Factoring by Grouping
- Factoring Trinomials
- Special Factoring Formulas
- Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Radical Expressions
- Simplifying Radical Expressions
- Logarithmic Functions
- Sets and Notation for Sets
- Solutions of Equations and Properties of Equality
- Solving Linear Equations
- Solving Absolute Value Equations
- Solving Equations Using the Zero-Factor Property
- Solving Rational Equations
- Solving Equations with Radical Terms
- Extracting Square Roots to Solve an Equation
- Quadratic Formula
- Solving Linear Inequalities
- Solving Inequalities that Contain an Absolute Value Term
- Functions
- Two-Variable Equations and Graphs
- Linear Equations and their Graphs
- Slope of a Line
- Determining the Equation for a Line
- Graphs of Common Functions and Basic Transformations
- Solving Systems of Equations

- Teacher: Amy
- Areas of expertise: Mathematics
- Education: Bachelor of Science in Math Education, Masters in Educational Leadership and Policy
- Interests: Running, hiking, reading, swimming, playing at the park with my kids, crocheting
- Skills: I have earned many teaching awards: Jordan School District Teacher of the Year, Canyons School District Teacher of the Year, and Utah State University's Teaching Adjunct of the Year (Twice)
- Associations: NCTM, UCTM
- Issues I care about: I am passionate about making math accessible to all types of learners. You can do this!

I am an outstanding teacher-leader who has served in numerous leadership capacities. I taught at the middle school level for eight consecutive years, then at the university level for four consecutive years, and I currently work at a local high school helping at-risk students.

Test Preparation Document

Digital Quizzes and Tests Answer Keys Document

Practice Worksheet Key

Filled-in notes

Blank powerpoint, but the key to the homework is included at the end.

Adding, Subtracting, Multiplying, Dividing, and Writing Equivalent Fractions

Sets of Numbers, Absolute Value

Objectives:

- Understand and be able to utilize the rules for multiplying and dividing exponential expressions.
- Understand and be able to utilize the rule for simplifying the power of an exponential expression.
- Understand and be able to utilize the rule for simplifying the powers of products and quotients.
- Be able to interpret and simplify an exponential with a zero as an exponent.
- Be able to interpret and simplify an exponential with a negative number exponent.

Objective:

- Be able to use the order of operations to evaluate and simplify an expression.

Objectives:

- Be able to simplify variable expressions using the algebraic properties of addition and multiplication.
- Be able to simplify variable expressions using the distributive property.

**Objectives**:

- Define polynomial.
- Add and subtract polynomials.

**Objectives**:

- Multiply terms, any two polynomials, binomials, and polynomial functions.
- Find the product of the sum and difference of two terms.
- Find the square of a binomial.

**Objectives**:

- Divide a polynomial by a monomial.
- Divide a polynomial by a polynomial of two or more terms.

Factors, GCF

GCF, Factoring by Grouping

FOIL, Factoring

Factoring, Difference of Squares, Perfect Square Trinomials

Domain, Simplifying Rational Expressions

Domain, Multiplying and Dividing Rational Expressions

Rational Expressions, LCD, Add, & Subtract

Radical Expressions, Roots, Principal Roots, Negative Roots

Simplify radicals, product rule, quotient rule

Logarithmic Form, Exponential Form, Solving Logarithms

Sets, Inequalities, Interval Notation, Graphing Intervals, Roster Method

Solve equations, determine solutions and non-solutions, write sentences as equations or inequalities

Solve equations and application problems

Equations containing absolute values, solution sets

Zero-Factor Property, Zero-Product Property

Domain, rational equations

Radical Equations, Power Rule, Indexes Greater than 2

Square Root Property

Quadratic Formula

Linear Inequalities

Absolute Value Inequalities

Relations, Functions, Domain, Range, Graphs

Quadrants, Ordered Pairs, Linear Equations

Graph Linear Equations, Intercepts

Graph Lines, Parallel and Perpendicular Slopes, Average Rate of Change

Slope-Intercept Form, Point-Slope Form, Parallel and Perpendicular

Absolute Value Function, Parabolic Function, Square Root Function, Domain and Range

Graphing, Substitution, Elimination