Course Description:
The fundamental purpose of the Algebra 1 course is to formalize and extend the mathematics that students learned in the middle grades. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, and Statistics and Probability. Some standards are repeated in multiple higher mathematics courses; therefore instructional notes, which appear in brackets, indicate what is appropriate for study in this particular course. For example, the scope of Algebra 1 is limited to linear, quadratic, and exponential expressions and functions as well as some work with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include references to logarithms or trigonometry, those functions are not to be included in course work for Algebra 1; they will be addressed later in Algebra 2. Successful completion of Algebra 1, or an equivalent sequence, is a graduation requirement.
Student Resources:
Algebra 1A:
Chapter 1
Foundations of Algebra
Topic 1 – Variables and Expressions
Topic 2 – Order of Operations and Evaluating Expressions
Topic 3 – Real Numbers and the Number Line
Topic 4 – Properties of Real Numbers
Topic 5 – Adding and Subtracting Real Numbers
Topic 6 – Multiplying and Dividing Real Numbers
Topic 7 – The Distributive Property
Topic 8 – An Introduction to Equations
Topic 9 – Patterns, Equations, and Graphs
Chapter 2
Solving Equations
Topic 1 – Solving One-Step Equations
Topic 2 – Solving Two-Step Equations
Topic 3 – Solving Multi-Step Equations
Topic 4 – Solving Equations With Variables on Both Sides
Topic 5 – Literal Equations and Formulas
Topic 6 – Ratios, Rates, and Conversations
Topic 7 – Solving Proportions
Topic 8 – Proportions and Similar Figures
Topic 9 – Percents
Topic 10 – Change Expressed as a Percent
Chapter 3
Solving Inequalities
Topic 1 – Inequalities and their Graphs
Topic 2 – Solving Inequalities Using Addition or Subtraction
Topic 3 – Solving Inequalities Using Multiplication or Division
Topic 4 – Solving Multi-Step Inequalities
Topic 5 – Working with Sets
Topic 6 – Compound Inequalities
Topic 7 – Absolute Value Equations and Inequalities
Topic 8 – Unions and Intersections of Sets
Chapter 4
An Introduction to Functions
Topic 1 – Using Graphs to Relate Two Quantities
Topic 2 – Patterns and Linear Functions
Topic 3 – Patterns and Nonlinear Functions
Topic 4 – Graphing a Function Rule
Topic 5 – Writing a Function Rule
Topic 6 – Formalizing Relations and Functions
Topic 7 – Arithmetic Sequences
Chapter 5
Linear Functions
Topic 1 – Rate of Change and Slope
Topic 2 – Direct Variation
Topic 3 – Slope-Intercept Form
Topic 4 – Point-Slope Form
Topic 5 – Standard Form
Topic 6 – Parallel and Perpendicular Lines
Topic 7 – Scatter Plots and Trend Lines
Topic 8 – Graphing Absolute Value Functions
Algebra 1B:
Chapter 6
Systems of Equations and Inequalities
Topic 1 – Solving Systems by Graphing
YouTube Link -> 6-1 Solving Systems By Graphing
YouTube Link -> Algebra: 6-1 Graphing Systems of Equations
Topic 2 – Solving Systems Using Substitution
YouTube Link -> 6-2 Solving Systems Using Substitution
Topic 3 – Solving Systems Using Elimination
YouTube Link -> Algebra 1 6-3 Solving Systems by Elimination
Topic 4 – Applications of Linear Equations
Mr. Tyler Videos: Pg. 17 – 23 Instructional Videos
YouTube Link -> 6-4 Applications of Linear Systems
YouTube Link – > Systems of Equations World Problems
Topic 5 – Linear Inequalities
YouTube Link -> Algebra 1 6-5 Solving Linear Inequalities
YouTube Link -> Solving Linear Inequalities Made Easy
Topic 6 – Systems of Linear Inequalities
YouTube Link -> 6-6 System of Linear Inequalities
YouTube Link -> Graphing Systems of Linear Inequalities Example #1
YouTube Link -> Graphing System of Linear Inequalities Example #2
Chapter 7
Exponents and Exponential Functions
Topic 1 – Zero and Negative Exponents
Topic 2 – Multiplying Power with the Same Base
Topic 3 – More Multiplication Properties of Exponents
Topic 4 – Division Properties of Exponents
Topic 5 – Rational Exponents and Radicals
Topic 6 – Exponential Functions
Topic 7 – Exponential Growth and Decay
Topic 8 – Geometric Sequences
Chapter 8
Polynomials and Factoring
Topic 1 – Adding and Subtracting Polynomials
Topic 2 – Multiplying and Factoring
Topic 3 – Multiplying Binomials
Topic 4 – Multiplying Special Cases
Topic 5 – Factoring X^2 + bx + c
Topic 6 – Factoring ax^2 + bx + c
Topic 7 – Factoring Special Cases
Topic 8 – Factoring Grouping
Chapter 9
Quadratic Functions and Equations
Topic 1 – Quadratic Graphs and Their Properties
YouTube Link -> 9-1 Quadratic Graphs and Their Properties
Topic 2 – Quadratic Functions
YouTube Link -> 9-2 Quadratic Functions
YouTube Link -> Algebra – Quadratic Functions (Parabolas)
Topic 3 – Solving Quadratic Equations
YouTube Link -> Solving Quadratic Equations by Factoring – Basic Examples
YouTube Link -> 9-3 Solving Quadratic Equations
Topic 4 – Factoring to Solve Quadratic Equations
YouTube Link -> 9-4 Factoring to Solve Quadratic Equations
Topic 5 – Completing the Square
YouTube Link -> 9-5 Completing the Square
Topic 6 – The Quadratic Formula and the Discriminant
YouTube -> 9-6 the quadratic formula and the discriminant
Topic 7 – Linear, Quadratic, and Exponential Models
YouTube-> 9-7 Linear, Quadratic, and Exponential Models
Topic 8 – Systems of Linear and Quadratic Equations
YouTube -> 9-8 Systems of Linear and Quadratic Equations
Chapter 10
Radical Expressions and Equations
Topic 1 – The Pythagorean Theorem
Topic 2 – Simplifying Radicals
Topic 3 – Operations with Radical Expressions
Topic 4 – Solving Radical Equations
Topic 5 – Graphing Square Root Functions
Topic 6 – Trigonometric Ratios
Chapter 11
Rational Expressions and Functions
Topic 1 – Simplifying Rational Expressions
Topic 2 – Multiplying and Dividing Rational Expressions
Topic 3 – Dividing Polynomials
Topic 4 – Adding and Subtracting Rational Expressions
Topic 5 – Solving Rational Equations
Topic 6 – Inverse Variation
Topic 7 – Graphing Rational Functions
Chapter 12
Data Analysis and Probability
Topic 1 – Organizing Data Using Matrices
Topic 2 – Frequency and Histograms
Topic 3 – Measures of Central Tendency and Dispersion
Topic 4 – Box and Whisker Plots
Topic 5 – Samples and Surveys
Topic 6 – Permutations and Combinations
Topic 7 – Theoretical and Experimental Probability
Topic 8 – Probability of Compound Events