Algebra 1

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