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I. Introduction to Algebra

Lesson: Verbal to Algebraic Expressions & Equations

Example: How do you write 5 greater than x algebraically?

Lesson: Declaring Variables

Example: Mike is 3 inches taller than Semande. If Semande is s inches tall, express Mike’s height in terms of s.

Lesson: Order of Operations

Example: Evaluate 3 - (5-8)^2

Lesson: Real Numbers (Including Rational vs. Irrational Numbers)

Lesson: Order of Operations with Substitution

Example: If x=2, what is the value of 2x^2-3x?

Lesson: Adding and Subtracting Real Numbers

Example: Evaluate 5 - (-2)

Lesson: Multiplying and Dividing Real Numbers

Example: Evaluate -3 \times 4

Lesson: Properties of Real Numbers

Example: Which property justifies the following equation: 5(x+2y)+5=5x+10y+5

Lesson: Distributive Property

Example: Simplify 3(4x-5)

Lesson: Finding the Solution to an Equation

Example: Is 7 a solution to the equation 12 = 3x - 9?

II. Solving Equations

Lesson: Solving Algebraic Equations (One-Step)

Example: Solve for x.
x+7=12

Lesson: Solving Multi-Step Equations

Example: Solve for x.
2x + 4 = 18

Lesson: Multi-Step Equations (Variable on Both Sides)

Example: Solve for x.
2x - 4 = -3x + 11

Lesson: Linear Equations

Example: Solve for y.
3y + 2x = 12

Lesson: Solving Proportions

Example: Solve for x.
\dfrac{x}{6} = \dfrac{20}{15}

Lesson: Solving Complex Proportions

Example: Solve for x.
\dfrac{x+5}{4} = \dfrac{3}{8}

Lesson: Percents

Example: What is 48% of 30?

Lesson: Percent Change

Example: What is the percent change from 50 to 72?

III. Solving Inequalities

Lesson: Graphing Inequalities

Example: Graph k < 1
Algebra 1 Lessons

Lesson: Solving Inequalities Using Addition or Subtraction

Example: Solve for x.
x - 12 > 8

Lesson: Solving Inequalities Using Multiplication or Division

Example: Solve for x.
-4x \geq 12

Lesson: Solving Inequalities

Example: Solve for x.
-7x + 19 \leq -2

Lesson: Solving Compound Inequalities

Example: Solve for x.
-3 \leq 2x -5 < 21

Lesson: Solving and Graphing Compound Inequalities

Example: Solve for x and graph.
 0 \leq r + 5 < 9
Algebra 1 Lessons

Lesson: Absolute Value Equations

Example: Solve for p.
 9 + |5p + 1| = 18

Lesson: Absolute Value Inequalities

Example: Solve for x.
3|5x + 1| > 12

IV. Functions

Lesson: Using Graphs to Relate Two Quantities

Example: A bird flies above ground in search of worms. This is represented in the table below.
Algebra 1 Lessons
What does A represent?

Lesson: Patterns and Linear Functions

Example: Is the following graph linear?
Algebra 1 Lessons

Example: For each set of ordered pairs, write the rule that represents the function.
(0, 3), (1, 8), (2, 13), (3, 18), (4, 23)

Lesson: Patterns and Non-Linear Functions

Example: Is the following a linear or nonlinear function?
Algebra 1 Lessons

Example: For the set of ordered pairs, write the rule that represents the function.
(0,1),(1,3),(2,9),(3,27),(4,81)

Lesson: Graphing a Function Rule

Example: Match the function with its graph.
Algebra 1 Lessons

Lesson: Writing a Function Rule

Example: Write the function rule for the table of values.
Algebra 1 Lessons

Lesson: Formalizing Relations and Functions

Example: Is the following relation shown a function?
(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)

V. Linear Functions

Lesson: Slope

Example: What is the slope of the line below?
Algebra 1 Lessons
Example: What is the slope of the line that passes through the points (2, 7) and (5, 12)?

Lesson: Equation of a Line

Example:

Lesson: Point Slope Form

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Lesson: Finding the Equation of a Line, Given the Slope and a Point

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Lesson: Standard Form of the Equations of a Line

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Lesson: Finding the Equation of a Line, Given Two Points

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Lesson: Equations of Parallel and Perpendicular Lines

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Lesson: Scatterplots and Trendlines

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Algebra 1 Lessons

Lesson: Graphing Absolute Value Functions

Example:

VI. Systems of Equations and Inequalities

Lesson: Solving a System of Equations Graphically

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Lesson: Solving a System of Equations Graphically

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Lesson: Solving a System of Equations Using Substitution

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Lesson: Solving a System of Equations Using Substitution

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Lesson: Solving a System of Equations Using Elimination

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Lesson: Solving a System of Equations Using Elimination

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Lesson: Applications of Linear Systems

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Lesson: Word Problems – System of Equations

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Lesson: Word Problems – System of Equations

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Lesson: Graphing Linear Inequalities

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Lesson: Graphing Linear Inequalities

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Algebra 1 Lessons

Lesson: Solving a System of Linear Inequalities

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VII. Exponents and Exponential Functions

Lesson: Positive Exponents

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Lesson: Negative Exponents

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Lesson: Multiplying & Dividing Terms that have Exponents

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Lesson: Multiplying & Dividing Terms that have Exponents

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Lesson: Graphs of Exponential Functions

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Lesson: Exponential Growth

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Lesson: Exponential Decay

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VIII. Polynomials and Factoring

Lesson: Adding & Subtracting Polynomials

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Lesson: Adding & Subtracting Polynomials

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Lesson: Multiplying a Polynomial by a Monomial

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Lesson: Dividing a Polynomial by a Monomial

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Lesson: Factor Out the Greatest Common Factor

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Lesson: Factor Out the Greatest Common Factor

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Lesson: Multiplying Binomials

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Lesson: Multiplying a Binomial by a Trinomial

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Lesson: Multiplying a Trinomial by a Binomial

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Lesson: Multiplying Binomials (Special Cases)

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Lesson: Factoring Quadratics

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Lesson: Factoring Quadratics

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Lesson: Difference of Perfect Squares

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Lesson: Factoring by Grouping

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IX. Quadratic Functions and Equations

Lesson: Evaluating Quadratic Functions

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Lesson: Properties of Quadratic Functions

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Lesson: Solving Quadratic Equations by Taking Square Roots

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Lesson: Solving Equations by Factoring

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Lesson: Completing the Square

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Lesson: Solve Equations by Completing the Square

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Lesson: Vertex Form of a Quadratic Function by Completing the Square

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Lesson: Solving a System of Equations Graphically (Linear & Quadratic)

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Lesson: Solving a System of Equations Using Substitution (Linear & Quadratic)

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X. Radical Expressions and Functions

Lesson: Pythagorean Theorem

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Lesson: Simplifying Radical Expressions

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Lesson: Adding and Subtracting Radical Expressions

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Lesson: Multiplying Radical Expressions

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Lesson: Dividing Radical Expressions

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Lesson: Solving Equations That Have Radical Terms

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Lesson: Solving Equations That Have Radical Terms

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Lesson: Graphing Square Root Functions

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Lesson: SOHCAHTOA (sine, cosine, tangent)

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Lesson: Inverse Trigonometric Functions

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XI. Rational Expressions and Functions

Lesson: Simplifying Rational Expressions

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Lesson: Multiplying and Dividing Rational Expressions

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Lesson: Dividing Polynomials

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Lesson: Adding and Subtracting Rational Expressions

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Lesson: Fractional Equations

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Lesson: Solving Rational Equations

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Lesson: Inverse Variation

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Lesson: Graphing Rational Functions

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XII. Data Analysis and Probability

Lesson: Matrices

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Algebra 1 Lessons

Lesson: Frequency, Cumulative Frequency, & Histograms

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Lesson: Measures of Central Tendency & Dispersion

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Lesson: Box & Whisker Plot

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Lesson: Samples and Surveys

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Lesson: Permutations and Combinations

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Lesson: Theoretical vs. Experimental Probability

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Lesson: Probability of Compound Events

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