Algebra 1 for 9th or 10th Grade

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Chapter 1: Foundations of Algebra

0 1.1 Introduction to Course 05:26

In this short introduction to the course, I share a bit about myself and my approach to teaching Algebra. I explain why I consider this to be an extremely important course to take and master.

1 1.2 LESSON: Classification of Real Numbers 15:52

NO HOMEWORK FOR THIS LESSON

2 1.3 LESSON: Adding & Subtracting Positive & Negative Numbers (Part 1) 13:49

This lesson introduces the concept of positive and negative numbers and shows one method for adding them together.

2 1.3 HOMEWORK VIDEO: Adding & Subtracting Positive & Negative Numbers (Part 1) 06:03

Homework Video for Lesson 1.3

3 1.4 LESSON: Adding & Subtracting Positive & Negative Numbers (Part 2) 14:53

This lesson shows a more sophisticated method for combining positive and negative integers.

3 1.4 HOMEWORK VIDEO: Adding & Subtracting Positive & Negative Numbers (Part 2) 15:05

Homework Video for Lesson 1.4

4 1.5 LESSON: Multiplying & Dividing Positive and Negative Numbers 10:38

This lessons discusses the unique rules regarding multiplying and dividing positive and negative numbers.

4 1.5 HOMEWORK VIDEO: Multiplying & Dividing Positive and Negative Numbers 09:22

Homework Video for Lesson 1.5

5 1.6 LESSON: Evaluating Algebraic Expressions 17:38

This lesson illustrates how to evaluate an algebraic expression with variables when those variables are given specific values.

5 1.6 HOMEWORK VIDEO: Evaluating Algebraic Expressions 10:01

Homework Video for Lesson 1.6

6 1.7 LESSON: Order of Operations 24:26

This lesson explains Order of Operation. This rule is used for simplifying expressions and is a foundational principle that all Mathematicians must follow.

6 1.7 HOMEWORK VIDEO: Order of Operations 14:52

Homework Video for Lesson 1.7

7 1.8 LESSON: Some Key Properties in Algebra 18:47

This lesson focuses on the most common algebraic properties you will see and use in Algebra.

7 1.8 HOMEWORK VIDEO: Some Key Properties in Algebra 13:19

Homework Video for Lesson 1.8

Chapter 2: Linear Equations

8 2.1 LESSON: Solving One-Step Equations 11:26

This lesson explains the basics of solving very simple equations. These techniques will be applied in future lessons to more complicated equations.

8 2.1 HOMEWORK VIDEO: Solving One-Step Equations 13:10

Homework Video for Lesson 2.1

9 2.2 LESSON: Solving Two-Step Equations 07:06

This lesson continues with an explanation of solving slightly more difficult equations which require 2 steps to solve.

9 2.2 HOMEWORK VIDEO: Solving Two-Step Equations 12:37

Homework Video for Lesson 2.2

10 2.3 LESSON: Solving Multi-Step Equations 13:52

This lesson adds a bit more complexity, showing you how to solve equations that require multiple steps.

10 2.3 HOMEWORK VIDEO: Solving Multi-Step Equations 22:11

Homework Video for Lesson 2.3

11 2.4 LESSON: Equations With Infinite and Zero Solutions 06:50

Sometimes an equation will have no solution or an infinite number of solutions. This lesson explores this concept.

11 2.4 HOMEWORK VIDEO: Equations With Infinite and Zero Solutions 15:43

Homework Video for Lesson 2.4

12 2.5 LESSON: Solving Equations with Fractions (Same Denominator) 08:35

Fractions have often been challenging for students. This lesson shows a very powerful yet simple method for eliminating all fractions so that it can be solved effortlessly.

12 2.5 HOMEWORK VIDEO: Solving Equations with Fractions (Same Denominator) 09:14

Homework Video for Lesson 2.5

13 2.6 LESSON: Solving Equations with Fractions (Different Denominators) 09:32

This lesson continues the discussion of removing fractions from your equation. It is a brilliant method!

13 2.6 HOMEWORK VIDEO: Solving Equations with Fractions (Different Denominators) 13:23

Homework Video for Lesson 2.6

14 2.7 LESSON: Solving Proportions 05:49

Proportions are a unique type of equation with Fractions. This lesson explains how to solve these equations easily and effortlessly.

14 2.7 HOMEWORK VIDEO: Solving Proportions 12:52

Homework Video for Lesson 2.7

15 2.8 LESSON: Solving Equations with Decimals 06:09

This lesson discusses the different ways in which you can easily solve equations with decimals.

15 2.8 HOMEWORK VIDEO: Solving Equations with Decimals 09:45

Homework Video for Lesson 2.8

16 2.9 LESSON: Solving Absolute Value Equations 17:51

This lesson illustrates how to solve equations that have absolute value expressions within an equation.

16 2.9 HOMEWORK VIDEO: Solving Absolute Value Equations 16:55

Homework Video for Lesson 2.9

17 2.10 LESSON: Solving Literal Equations 14:02

Sometimes equations have several different variables. This lesson discusses how to solve an equation for any given variable.

17 2.10 HOMEWORK VIDEO: Solving Literal Equations 18:42

Homework Video for Lesson 2.10

18 2.11 LESSON: Solving Percent Equations 14:19

This lesson discusses how to work with percents mathematically.

18 2.11 HOMEWORK VIDEO: Solving Percent Equations 17:41

Homework Video for Lesson 2.11

19 2.12 LESSON: Percent Increase or Decrease 07:17

This lesson discusses the concept of Percent Change and shows how to find the percent increase or decrease of data that has changed over time.

19 2.12 HOMEWORK VIDEO: Percent Increase or Decrease 14:42

Homework Video for Lesson 2.12

Chapter 3: Introduction to Word Problems

20 3.1 LESSON: Translating English into Math 13:25

This lesson is an introduction to words and phrases commonly used in the English language that translate directly into mathematical expressions and equations.

20 3.1 HOMEWORK VIDEO: Translating English into Math 12:16

Homework Video for Lesson 3.1

21 3.2 LESSON: Number Word Problems 13:57

This lesson shares one approach to solving number word problems.

21 3.2 HOMEWORK VIDEO: Number Word Problems 14:33

Homework Video for Lesson 3.2

22 3.3 LESSON: Consecutive Integer Word Problems (Part 1) 09:24

This lesson describes an approach for solving consecutive integer word problems.

22 3.3 HOMEWORK VIDEO: Consecutive Integer Word Problems (Part 1) 12:08

Homework Video for Lesson 3.3

23 3.4 LESSON: Consecutive Integer Word Problems (Part 2) 08:33

In this video I explain how to solve consecutive integer word problems where you have consecutive even or consecutive odd numbers.

23 3.4 HOMEWORK VIDEO: Consecutive Integer Word Problems (Part 2) 10:35

Homework Video for Lesson 3.4

24 3.5 LESSON: Geometry Word Problems 17:37

This video shares ways of solving a variety of geometry word problems.

24 3.5 HOMEWORK VIDEO: Geometry Word Problems 14:54

Homework Video for Lesson 3.5

25 3.6 LESSON: Age Word Problems 18:45

This lesson shows an approach that I use to organize data in a way that allows you to solve the problem easily and effortlessly.

25 3.6 HOMEWORK VIDEO: Age Word Problems 20:24

Homework Video for Lesson 3.6

26 3.7 LESSON: Ratio Word Problems 16:43

Ratios are an important and useful concept in math. This video shows how to solve ratio word problems.

26 3.7 HOMEWORK VIDEO: Ratio Word Problems 19:00

Homework Video for Lesson 3.7

27 3.8 LESSON: Percent Word Problems 13:30

This lesson explains how to solve word problems that utilize percents.

27 3.8 HOMEWORK VIDEO: Percent Word Problems 12:39

Homework Video for Lesson 3.8

28 3.9 LESSON: Simple Interest Word Problems 10:52

This lesson discusses what Simple Interest is and how to solve word problems that relate to simple interest.

28 3.9 HOMEWORK VIDEO: Simple Interest Word Problems 15:56

Homework Video for Lesson 3.9

29 3.10 LESSON: Distance/Motion Word Problems (Part 1) 17:43

This is the first of 3 lessons on solving distance or motion word problems.

29 3.10 HOMEWORK VIDEO: Distance/Motion Word Problems (Part 1) 15:39

Homework Video for Lesson 3.10

30 3.11 LESSON: Distance/Motion Word Problems (Part 2) 09:57

This is the second of 3 lessons on solving distance or motion word problems.

30 3.11 HOMEWORK VIDEO: Distance/Motion Word Problems (Part 2) 14:03

Homework Video for Lesson 3.11

31 3.12 LESSON: Distance/Motion Word Problems (Part 3) with Headwind and Current 14:40

This is the third of 3 lessons on solving distance or motion word problems.

31 3.12 HOMEWORK VIDEO: Distance/Motion Word Problems (Part 3) with Headwind and Current 20:34

Homework Video for Lesson 3.12

Chapter 4: Linear Inequalities

32 4.1 LESSON: Graphing & Writing Single Variable Inequalities 11:56

This lesson explains how to graph a single variable inequality. It also shows how to write an inequality to describe a graph.

32 4.1 HOMEWORK VIDEO: Graphing & Writing Single Variable Inequalities 14:29

Homework Video for Lesson 4.1

33 4.2 LESSON: Solving Single Variable Inequalities 11:08

Sometimes an inequality needs to be simplified before it can be graphed. This lesson shows how to do this.

33 4.2 HOMEWORK VIDEO: Solving Single Variable Inequalities 25:06

Homework Video for Lesson 4.2

34 4.3 LESSON: More Practice Solving Inequalities Plus Examples of Zero & Infinite Solutions 10:23

This lesson begins with a practice session on solving inequalities. It concludes with a discussion on inequalities that may have no solution or an infinite number of solutions.

34 4.3 HW VIDEO: Practice Solving Inequalities + Examples of Zero & Infinite Solutions 22:25

Homework Video for Lesson 4.3

35 4.4 LESSON: Solving & Graphing Compound Inequalities with "AND" 19:33

Compound inequalities are made up of two inequalities. This lesson discusses what it means to join the two inequalities with the word "AND".

35 4.4 HOMEWORK VIDEO: Solving & Graphing Compound Inequalities with "AND" 21:48

Homework Video for Lesson 4.4

36 4.5 LESSON: Solving & Graphing Compound Inequalities with "OR" 09:48

Compound inequalities are made up of two inequalities. This lesson discusses what it means to join the two inequalities with the word "OR".

36 4.5 HOMEWORK VIDEO: Solving & Graphing Compound Inequalities with "OR" 21:12

Homework Video for Lesson 4.5

37 4.6 LESSON: Absolute Value Inequalities 07:31

Absolute Value Inequalities are examples of Compound Inequalities. This lesson discusses what needs to be done to solve absolute value inequalities.

37 4.6 HOMEWORK VIDEO: Absolute Value Inequalities 28:23

Homework Video for Lesson 4.6

Chapter 5: Graphing and Writing Functions

38 5.1 LESSON: Intro to Equations with Two Variables 11:08

This lesson is an introduction of the unique features of equations with 2 variables. Much of Algebra utilizes these types of equations.

38 5.1 HOMEWORK VIDEO: Intro to Equations with Two Variables 25:53

Homework Video for Lesson 5.1

39 5.2 LESSON: Relations versus Functions 22:07

This lesson discusses an important distinction between Relations and Functions. Most of what we will be discussing in this course will involve Functions.

39 5.2 HOMEWORK VIDEO: Relations versus Functions 12:13

Homework Video for Lesson 5.2

40 5.3 LESSON: Graphing on a Cartesian Plane with T-charts 17:04

This lesson shows how to graph functions on a Cartesian Plane using T-charts.

40 5.3 HOMEWORK VIDEO: Graphing on a Cartesian Plane with T-charts 14:51

Homework Video for Lesson 5.3

41 5.4 LESSON: Graphing Equations in Slope Intercept Form (a Shortcut) 11:25

This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Slope-Intercept Form.

41 5.4 HOMEWORK VIDEO: Graphing Equations in Slope Intercept Form (a Shortcut) 08:53

Homework Video for Lesson 5.4

42 5.5 LESSON: Graphing Equations in Point Slope Form 20:03

This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Point-Slope Form.

42 5.5 HOMEWORK VIDEO: Graphing Equations in Point Slope Form 11:26

Homework Video for Lesson 5.5

43 5.6 LESSON: Graphing Equations in Standard Form 18:21

This lesson shows a shortcut on how to easily and quickly graph an equation that is written in Standard Form.

43 5.6 HOMEWORK VIDEO: Graphing Equations in Standard Form 09:21

Homework Video for Lesson 5.6

44 5.7 LESSON: Graphing Practice 10:40

It is always good to take extra time to practice graphing so that you can do it effortlessly. This lesson gives you the opportunity to practice the three methods discussed in the last 3 lessons.

44 5.7 HOMEWORK VIDEO: Graphing Practice 10:05

Homework Video for Lesson 5.7

45 5.8 LESSON: Finding The Slope Using The Slope Formula 13:39

This lesson discusses the Slope Formula and how to use it to find the slope of a line passing through two points.

45 5.8 HOMEWORK VIDEO: Finding The Slope Using The Slope Formula 18:13

Homework Video for Lesson 5.8

46 5.9 LESSON: Writing Equations With Given Data 15:33

Sometimes you need to write equations of lines that have certain data points. This lesson discusses how to do this.

46 5.9 HOMEWORK VIDEO: Writing Equations With Given Data 19:22

Homework Video for Lesson 5.9

47 5.10 LESSON: Converting Equations From One Form to Another 17:46

This lesson shows you how to easily convert equations from one form to another.

47 5.10 HOMEWORK VIDEO: Converting Equations From One Form to Another 22:01

Homework Video for Lesson 5.10

48 5.11 LESSON: Parallel and Perpendicular Lines 13:02

This lesson illustrates how to write equations of lines that are parallel or perpendicular to another line.

48 5.11 HOMEWORK VIDEO: Parallel and Perpendicular Lines 11:30

Homework Video for Lesson 5.11

49 5.12 LESSON: Scatter Plots and Trend Lines 17:08

This lesson explains how to take data and identify trends, if any, of the data. It shows how to graph the data and create trend lines when trends exist.

49 5.12 HOMEWORK VIDEO: Scatter Plots and Trend Lines 19:46

Homework Video for Lesson 5.12

50 5.13 LESSON: Direct Variation 15:28

This lesson discusses the unique qualities of an equation that represents Direct Variation.

50 5.13 HOMEWORK VIDEO: Direct Variation 23:28

Homework Video for Lesson 5.13

51 5.14 LESSON: Graphing Absolute Value Functions 13:00

This lesson illustrates how to graph absolute value functions.

51 5.14 HOMEWORK VIDEO: Graphing Absolute Value Functions 21:05

Homework Video for Lesson 5.14

52 5.15 LESSON: Graphing One Variable Inequalities on Cartesian Plane 11:21

This lesson demonstrates how to graph one-variable inequalities on a Cartesian Plane.

52 5.15 HOMEWORK VIDEO: Graphing One Variable Inequalities on Cartesian Plane 09:49

Homework Video for Lesson 5.15

53 5.16 LESSON: Graphing Two Variable Inequalities on Cartesian Plane 17:29

This lesson demonstrates how to graph two-variable inequalities on a Cartesian Plane.

53 5.16 HOMEWORK VIDEO: Graphing Two Variable Inequalities on Cartesian Plane 19:27

Homework Video for Lesson 5.16

Chapter 6: Systems of Equations and Inequalities

54 6.1 LESSON: Solving Systems of Equations by Graphing 23:26

Solving Systems of Equations by Graphing

54 6.1 HOMEWORK VIDEO: Solving Systems of Equations by Graphing 17:25

Homework Video for Lesson 6.1

55 6.2 LESSON: Solving Systems of Equations by Substitution (Part 1) 17:23

This is the first of two lessons explaining how to "solve" linear systems algebraicly using a substitution method.

55 6.2 HOMEWORK VIDEO: Solving Systems of Equations by Substitution (Part 1) 19:27

Homework Video for Lesson 6.2

56 6.3 LESSON: Solving Systems of Equations by Substitution (Part 2) 10:38

This is the last of two lessons explaining how to "solve" linear systems algebraicly using a substitution method.

56 6.3 HOMEWORK VIDEO: Solving Systems of Equations by Substitution (Part 2) 19:33

Homework Video for Lesson 6.3

57 6.4 LESSON: Solving Systems of Equations by Elimination (Part 1) 07:59

This is the first of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

57 6.4 HOMEWORK VIDEO: Solving Systems of Equations by Elimination (Part 1) 17:33

Homework Video for Lesson 6.4

58 6.5 LESSON: Solving Systems of Equations by Elimination (Part 2) 07:06

This is the second of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

58 6.5 HOMEWORK VIDEO: Solving Systems of Equations by Elimination (Part 2) 19:45

Homework Video for Lesson 6.5

59 6.6 LESSON: Solving Systems of Equations by Elimination (Part 3) 09:23

This is the third of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

59 6.6 HOMEWORK VIDEO: Solving Systems of Equations by Elimination (Part 3) 21:52

Homework Video for Lesson 6.6

60 6.7 LESSON: Solving Systems of Equations by Elimination (Part 4) 10:00

This is the last of four lessons explaining how to "solve" linear systems algebraicly using a method called "Elimination".

60 6.7 HOMEWORK VIDEO: Solving Systems of Equations by Elimination (Part 4) 20:21

Homework Video for Lesson 6.7

61 6.8 LESSON: Systems With No Solutions or Infinite Solutions 09:58

Some linear systems have no solutions or an infinite number of solutions. This lesson explores these situations.

61 6.8 HOMEWORK VIDEO: Systems With No Solutions or Infinite Solutions 18:10

Homework Video for Lesson 6.8

62 6.9 LESSON: Systems of Equations Word Problems - Type 1 16:43

This is the first of 5 types of word problems in which systems of equations are used in finding the solution.

62 6.9 HOMEWORK VIDEO: Systems of Equations Word Problems - Type 1 13:21

Homework Video for Lesson 6.9

63 6.10 LESSON: Systems of Equations Word Problems - Type 2 26:05

This is the second of 5 types of word problems in which systems of equations are used in finding the solution.

63 6.10 HOMEWORK VIDEO: Systems of Equations Word Problems - Type 2 19:27

Homework Video for Lesson 6.10

64 6.11 LESSON: Systems of Equations Word Problems - Type 3 15:33

This is the third of 5 types of word problems in which systems of equations are used in finding the solution.

64 6.11 HOMEWORK VIDEO: Systems of Equations Word Problems - Type 3 17:19

Homework Video for Lesson 6.11

65 6.12 LESSON: Systems of Equations Word Problems - Type 4 11:24

This is the fourth of 5 types of word problems in which systems of equations are used in finding the solution.

65 6.12 HOMEWORK VIDEO: Systems of Equations Word Problems - Type 4 16:12

Homework Video for Lesson 6.12

66 6.13 LESSON: Systems of Equations Word Problems - Type 5 15:22

This is the last of 5 types of word problems in which systems of equations are used in finding the solution.

66 6.13 HOMEWORK VIDEO: Systems of Equations Word Problems - Type 5 12:43

Homework Video for Lesson 6.13

67 6.14 LESSON: Solving Systems of Inequalities by Graphing 21:18

You can also solve "systems" of inequalities by graphing. This lesson explains the process.

67 6.14 HOMEWORK VIDEO: Solving Systems of Inequalities by Graphing 13:17

Homework Video for Lesson 6.14

68 6.15 LESSON: Graphing Systems of Inequalities with Parallel Boundary Lines 13:54

When your system involves two inequalities that are parallel to each other, you can have some interesting effects. This lesson explores these cases.

68 6.15 HOMEWORK VIDEO: Graphing Systems of Inequalities with Parallel Boundary Lines 10:12

Homework for Lesson 6.15

69 6.16 LESSON: Systems of Inequalities Word Problems 13:12

This lessons illustrates how to solve word problems which include inequalities.

69 6.16 HOMEWORK VIDEO: Systems of Inequalities Word Problems 20:23

Homework Video for Lesson 6.16

Chapter 7: Exponents and Exponential Functions

70 7.1 LESSON: Intro to Exponents; Rules for Zero and Negative Exponents 27:07

In this lesson, I introduce exponents and discuss rules relating to zero exponents and negative exponents.

70 7.1 HOMEWORK VIDEO: Intro to Exponents; Rules for Zero and Negative Exponents 14:23

Homework Video for Lesson 7.1

71 7.2 LESSON: Multiplication Properties of Exponents 19:42

This lesson explains the rules you need to follow when multiplying same bases with exponents.

71 7.2 HOMEWORK VIDEO: Multiplication Properties of Exponents 13:27

Homework Video for Lesson 7.2

72 7.3 LESSON: Division Properties of Exponents 24:06

This lesson explains the rules you need to follow when dividing same bases with exponents.

72 7.3 HOMEWORK VIDEO: Division Properties of Exponents 14:07

Homework Video for Lesson 7.3

73 7.4 LESSON: Division Property: A Cool Little Trick... 09:07

For some types of problems when dividing same bases with exponents, there is a cool little trick that makes it easy and effortless. This lesson explains this trick.

73 7.4 HOMEWORK VIDEO: Division Property: A Cool Little Trick... 15:35

Homework Video for Lesson 7.4

74 7.5 LESSON: Scientific Notation 17:29

Scientific Notation is a practical application of exponents when dealing with numbers that are very large or very small. This lesson illustrates these cases.

74 7.5 HOMEWORK VIDEO: Scientific Notation 15:56

Homework Video for Lesson 7.5

75 7.6 LESSON: Exponential Functions and Their Graphs 20:20

This lesson explores what exponential functions look like on a Cartesian Plane.

75 7.6 HOMEWORK VIDEO: Exponential Functions and Their Graphs 16:44

Homework Video for Lesson 7.6

76 7.7 LESSON: Exponential Growth and Decay 18:35

This lesson discusses exponential growth and decay, demonstrating their respective formulas and how to use them in real-life situations.

76 7.7 HOMEWORK VIDEO: Exponential Growth and Decay 15:03

Homework Video for Lesson 7.7

77 7.8 LESSON: Compound Interest 15:04

This lesson explores compound interest, showing the formula and the powerful results that this type of interest can create.

77 7.8 HOMEWORK VIDEO: Compound Interest 24:37

Homework Video for Lesson 7.8

Chapter 8: Radicals and Radical Functions

78 8.1 LESSON: Introduction to Radicals; Simplifying Radicals with Numbers 22:05

In this lesson, I introduce radicals and show how to simplify radicals with numbers.

78 8.1 HOMEWORK VIDEO: Introduction to Radicals; Simplifying Radicals with Numbers 12:58

Homework Video for Lesson 8.1

79 8.2 LESSON: Simplifying Radicals with Variables 23:50

In this lesson, I show how to simplify radicals with variables.

79 8.2 HOMEWORK VIDEO: Simplifying Radicals with Variables 14:12

Homework Video for Lesson 8.2

80 8.3 LESSON: Adding and Subtracting Radicals 17:57

This lesson explains the rules and process regarding adding and subtracting radicals.

80 8.3 HOMEWORK VIDEO: Adding and Subtracting Radicals 21:37

Homework Video for Lesson 8.3

81 8.4 LESSON: Multiplying Radicals - Part 1 14:41

This is the first of two lessons explaining the rules and processes used to multiply radicals.

81 8.4 HOMEWORK VIDEO: Multiplying Radicals - Part 1 15:16

Homework Video for Lesson 8.4

82 8.5 LESSON: Multiplying Radicals - Part 2 14:42

This is the last of two lessons explaining the rules and processes used to multiply radicals.

82 8.5 HOMEWORK VIDEO: Multiplying Radicals - Part 2 12:14

Homework Video for Lesson 8.5

83 8.6 LESSON: Dividing Radicals and Rationalizing the Denominator 29:47

This lesson demonstrates the rules and processes used when dividing radicals. It also shows how to "rationalize" the denominator and when to use it.

83 8.6 HOMEWORK VIDEO: Dividing Radicals and Rationalizing the Denominator 19:20

Homework Video for Lesson 8.6

84 8.7 LESSON: Practicing With Radicals 29:11

Since students sometimes struggle with all the different rules regarding radicals, I put together this lesson to allow you to practice these techniques.

84 8.7 HOMEWORK VIDEO: Practicing With Radicals 18:43

Homework Video for Lesson 8.7

85 8.8 LESSON: Solving Radical Equations - Part 1 08:55

This is the first of two lessons explaining how to solve simple radical equations.

85 8.8 HOMEWORK VIDEO: Solving Radical Equations - Part 1 13:55

Homework Video for Lesson 8.8

86 8.9 LESSON: Solving Radical Equations - Part 2 10:58

This is the last of two lessons explaining how to solve simple radical equations.

86 8.9 HOMEWORK VIDEO: Solving Radical Equations - Part 2 14:32

Homework Video for Lesson 8.9

87 8.10 LESSON: Graphing Radical Equations 11:49

In this lesson, I show how to graph radical equations.

87 8.10 HOMEWORK VIDEO: Graphing Radical Equations 22:07

Homework Video for Lesson 8.10

Chapter 9: Polynomials: Combining, Multiplying and Factoring

88 9.1 LESSON: Introduction to Polynomials 15:53

In this lesson, I introduce polynomials and several terms that you will need to know. I also show how to write them in standard form.

88 9.1 HOMEWORK VIDEO: Introduction to Polynomials 21:50

Homework Video for Lesson 9.1

89 9.2 LESSON: Adding and Subtracting Polynomials 19:29

This lesson illustrates how to add and subtract polynomials and identifies key issues that are sometimes overlooked by students.

89 9.2 HOMEWORK VIDEO: Adding and Subtracting Polynomials 21:12

Homework Video for Lesson 9.2

90 9.3 LESSON: Multiplying Polynomials 15:29

This lesson introduces rules needed in order to multiply polynomials.

90 9.3 HOMEWORK VIDEO: Multiplying Polynomials 23:01

Homework Video for Lesson 9.3

91 9.4 LESSON: Multiplying Binomials Using FOIL 10:39

This lesson shows a slightly different approach often used to multiply binomials together. The process is usually called "FOIL".

91 9.4 HOMEWORK VIDEO: Multiplying Binomials Using FOIL 08:45

Homework Video for Lesson 9.4

92 9.5 LESSON: Special Products of Binomials 14:29

This lesson focuses on special products that sometimes result from multiplying binomials together. It is useful to be aware to look for these scenarios.

92 9.5 HOMEWORK VIDEO: Special Products of Binomials 18:20

Homework Video for Lesson 9.5

93 9.6 LESSON: Factoring Polynomials: Factors, Tree Factorization, GCF 21:56

This lesson focuses on techniques for factoring polynomials. In particular I demonstrate tree factorization and the "upside-down birthday cake" method.

93 9.6 HOMEWORK VIDEO: Factoring Polynomials: Factors, Tree Factorization, GCF 14:08

Homework Video for Lesson 9.6

94 9.7 LESSON: Factoring Out the Greatest Common Factor (GCF) 22:38

Factoring out the Greatest Common Factor (GCF) is a key concept in Algebra. This lesson shows how to do this with polynomials.

94 9.7 HOMEWORK VIDEO: Factoring Out the Greatest Common Factor (GCF) 17:06

Homework Video for Lesson 9.7

95 9.8 LESSON: Factoring Out the Blobs (...or Binomials...) 08:30

Sometimes the Greatest Common Factor in two terms a binomial. This "blob" can be factored out of both terms easily. This lesson shows how.

95 9.8 HOMEWORK VIDEO: Factoring Out the Blobs (...or Binomials...) 11:57

Homework Video for Lesson 9.8

96 9.9 LESSON: Factoring By Grouping 25:58

This lesson focuses on a particular type of factoring in which there are four terms. It consists of grouping terms into pairs and factoring each pair individually.

96 9.9 HOMEWORK VIDEO: Factoring By Grouping 17:41

Homework Video for Lesson 9.9

97 9.10 LESSON: Factoring Quadratic Trinomials: "a" Equals 1 26:52

This lesson identifies an extremely important approach for factoring quadratic trinomials.

97 9.10 HOMEWORK VIDEO: Factoring Quadratic Trinomials: "a" Equals 1 17:34

Homework Video for Lesson 9.10

98 9.11 LESSON: Factoring Quadratic Trinomials: "a" Is Not 1 25:11

This lesson shows how to factor quadratic trinomials in which the leading coefficient is a number other than "one".

98 9.11 HOMEWORK VIDEO: Factoring Quadratic Trinomials: "a" Is Not 1 23:43

Homework Video for Lesson 9.11

99 9.12 LESSON: Gary's Terrific Trick for Factoring Quadratic Trinomials "a" not 1 16:22

This lesson demonstrates and extremely helpful trick in factoring quadratic trinomials where the leading coefficient is not "one".

99 9.12 HOMEWORK VIDEO: Gary's Terrific Trick for Factoring Quadratic Trinomials "a" not 1 17:28

Homework Video for Lesson 9.12

100 9.13 LESSON: Factoring The Difference of Two Squares 13:27

This lesson shows how to factor expressions where there is a difference (subtraction) of two perfect squares.

100 9.13 HOMEWORK VIDEO: Factoring The Difference of Two Squares 09:13

Homework Video for Lesson 9.13

101 9.14 LESSON: Factoring Practice 09:42

Students always need extra practice in factoring expressions. This lesson gives you the opportunity to do just that!

101 9.14 HOMEWORK VIDEO: Factoring Practice 26:04

Homework Video for Lesson 9.14

Chapter 10: Quadratic Functions and Equations

102 10.1 LESSON: Understanding and Solving Quadratic Equations - Part 1 21:19

Now it is time to learn the true power of the skills you learned in the last chapter. This lesson focuses on solving quadratic equations.

102 10.1 HOMEWORK VIDEO: Understanding and Solving Quadratic Equations - Part 1 13:09

Homework Video for Lesson 10.1

103 10.2 LESSON: Solving Quadratic Equations - Part 2 17:03

This lesson continues the conversation on solving quadratic equations.

103 10.2 HOMEWORK VIDEO: Solving Quadratic Equations - Part 2 24:11

Homework Video for Lesson 10.2

104 10.3 LESSON: Using Square Roots to Solve Quadratic Equations 11:17

This lesson shows another approach that can sometimes be utilized when solving quadratic equations.

104 10.3 HOMEWORK VIDEO: Using Square Roots to Solve Quadratic Equations 19:31

Homework Video for Lesson 10.3

105 10.4 LESSON: Vertical Motion Model Word Problems 27:15

This lesson looks at the Vertical Motion Model and shows its power in solving real-life word problems.

105 10.4 HOMEWORK VIDEO: Vertical Motion Model Word Problems 20:59

Homework Video for Lesson 10.4

106 10.5 LESSON: Completing The Square 28:23

Sometimes a quadratic equation cannot be factored. In this case, there is a powerful approach that can be used called Completing the Square. This lesson shows how.

106 10.5 HOMEWORK VIDEO: Completing The Square 24:50

Homework Video for Lesson 10.5

107 10.6 LESSON: Deriving The Quadratic Formula 15:47

NO HOMEWORK FOR THIS LESSON. In this lesson, I show how the famous Quadratic Formula was created.

108 10.7 LESSON: Using The Quadratic Formula 19:00

In this lesson, I show how to use the Quadratic Formula to find where a parabola crosses the x-axis. It is important to master using this formula!

108 10.7 HOMEWORK VIDEO: Using The Quadratic Formula 29:58

Homework Video for Lesson 10.7

109 10.8 LESSON: Understanding the Discriminant 18:52

In this lesson, we explore a part of the Quadratic Formula called the Discriminant, and we discuss what exactly this can tell you immediately about a given equation.

109 10.8 HOMEWORK VIDEO: Understanding the Discriminant 13:00

Homework Video for Lesson 10.8

110 10.9 LESSON: Quadratic Word Problems - Rectangles 18:41

In this lesson, we dive into word problems to see the power of factoring and solving quadratics.

110 10.9 HOMEWORK VIDEO: Quadratic Word Problems - Rectangles 24:30

Homework Video for Lesson 10.9

111 10.10 LESSON: Finding The Axis of Symmetry and Vertex 25:01

This lesson explores how to find the vertex of any parabola by first locating the Axis of Symmetry.

111 10.10 HOMEWORK VIDEO: Finding The Axis of Symmetry and Vertex 16:24

Homework Video for Lesson 10.10

112 10.11 LESSON: More Quadratic Word Problems 24:10

This lesson continues our exploration of quadratic word problems.

112 10.11 HOMEWORK VIDEO: More Quadratic Word Problems 20:53

Homework Video for Lesson 10.11

113 10.12 LESSON: Anatomy of A Quadratic Equation 25:19

In this lesson, I break the quadratic equation down into its parts and explain how each part affects the graph of a parabola.

113 10.12 HOMEWORK VIDEO: Anatomy of A Quadratic Equation 13:29

Homework Video for Lesson 10.12

114 10.13 LESSON: Graphing With Standard Parabola Guy 29:50

In this video, I demonstrate a very simple approach to graphing most quadratic equations.

114 10.13 HOMEWORK VIDEO: Graphing With Standard Parabola Guy 12:05

Homework Video for Lesson 10.13

115 10.14 LESSON: Reviewing Different Types of Graphs 08:02

NO HOMEWORK FOR THIS LESSON. This lesson takes a detour from the chapter and does a quick review of all the different types of graphs we have seen so far in this course.

116 10.15 LESSON: Functions, Set Notation, Domain and Range 22:33

This lesson explores the idea of functions and how to write the domain and range in set notation.

116 10.15 HOMEWORK VIDEO: Functions, Set Notation, Domain and Range 19:24

Homework Video for Lesson 10.15

Chapter 11: Rational Expressions and Equations

117 11.1 LESSON: Rational Expressions - Finding the Excluded Value 25:13

In this Video, I explain what a rational expression is and how you can identify values for x that are excluded, hence illegal, according to rules of mathematics.

117 11.1 HOMEWORK VIDEO: Rational Expressions - Finding the Excluded Value 13:44

Homework Video for Lesson 11.1

118 11.2 LESSON: Simplifying Rational Expressions 25:43

This lesson explains how to simplify Rational Expressions.

118 11.2 HOMEWORK VIDEO: Simplifying Rational Expressions 20:58

Homework Video for Lesson 11.2

119 11.3 LESSON: Simplifying Rational Expressions with Opposite Binomials 14:00

This lesson identifies an important trick that can be used in cases where you have "opposite binomials" in the numerator or denominator.

119 11.3 HOMEWORK VIDEO: Simplifying Rational Expressions with Opposite Binomials 18:08

Homework Video for Lesson 11.3

120 11.4 LESSON: Multiplying & Dividing Rational Expressions 20:27

This lesson demonstrates the steps necessary in order to easily multiply and divide Rational Expressions. By following these rules, your final fraction will be written in lowest terms.

120 11.4 HOMEWORK VIDEO: Multiplying & Dividing Rational Expressions 08:16

Homework Video for Lesson 11.4

121 11.5 LESSON: Adding & Subtracting Rational Expressions - Same Denominator 27:17

In this lesson, I show how to add and subtract rational expressions that already have common denominators.

121 11.5 HOMEWORK VIDEO: Adding & Subtracting Rational Expressions - Same Denominator 20:26

Homework Video for Lesson 11.5

122 11.6 LESSON: Adding & Subtracting Rational Expressions - Different Denominator 29:46

In this lesson, I show how to add and subtract rational expressions and how to find and create common denominators.

122 11.6 HOMEWORK VIDEO: Adding & Subtracting Rational Expressions - Different Denominator 22:37

Homework Video for Lesson 11.6

123 11.7 LESSON: Dividing Polynomials Using Long Division 17:02

This lesson demonstrates how to divide polynomials using long division. This is one way to find factors of a polynomial.

123 11.7 HOMEWORK VIDEO: Dividing Polynomials Using Long Division 15:43

Homework Video for Lesson 11.7

124 11.8 LESSON: Solving Rational Equations - Proportions 24:22

A proportion is one example of a simple rational equation. This lesson shows how to solve rational proportions and identify any excluded values.

124 11.8 HOMEWORK VIDEO: Solving Rational Equations - Proportions 14:23

Homework Video for Lesson 11.8

125 11.9 LESSON: Solving Rational Equations - Multiplying by LCD 24:18

Most Rational Equations are not proportions and therefore need a different approach for solving them. This lesson discusses this important approach.

125 11.9 HOMEWORK VIDEO: Solving Rational Equations - Multiplying by LCD 17:17

Homework Video for Lesson 11.9

126 11.10 LESSON: Solving Rational Equations - Extraneous Solutions 13:32

Sometimes you will solve a rational equation and get more than one answer. This lesson identifies how to know if both answers are valid and "legal". Illegal or invalid answers are called Extraneous solutions.

126 11.10 HOMEWORK VIDEO: Solving Rational Equations - Extraneous Solutions 19:53

Homework Video for Lesson 11.10

127 11.11 LESSON: Understanding & Graphing Inverse Variation 17:25

Inverse variation is an example of a rational equation. This lesson shows how to graph inverse variation equations.

127 11.11 HOMEWORK VIDEO: Understanding & Graphing Inverse Variation 18:39

Homework Video for Lesson 11.11

128 11.12 LESSON: Direct Variation vs. Inverse Variation 17:30

In this video, we explore the differences between direct variation and inverse variation.

128 11.12 HOMEWORK VIDEO: Direct Variation vs. Inverse Variation 11:45

Homework Video for Lesson 11.12

129 11.13 LESSON: Graphing Rational Functions Using Asymptotes & T-charts 29:19

This lesson illustrates how to graph rational functions using asymptotes and T-charts.

129 11.13 HOMEWORK VIDEO: Graphing Rational Functions Using Asymptotes & T-charts 26:22

Homework Video for Lesson 11.13

130 11.14 LESSON: Work Word Problems 24:31

In this lesson, we dive into solving work word problems which involve creating and solving rational equations.

130 11.14 HOMEWORK VIDEO: Work Word Problems 20:35

Homework Video for Lesson 11.14

131 11.15 LESSON: Inverse Variation & Rational Word Problems 21:25

This lesson focuses on more types of rational word problems, how to set them up and how to solve them.

131 11.15 HOMEWORK VIDEO: Inverse Variation & Rational Word Problems 16:44

Homework Video for Lesson 11.15

Chapter 12: End of Course Review

132 12.1 LESSON: Final Exam Prep #1 19:03

This lesson is the first of four review lessons in which I cover a large percentage of the material we covered in this course.

132 12.1 HOMEWORK VIDEO: Final Exam Prep #1 23:55

Homework Video for Lesson 12.1

133 12.2 LESSON: Final Exam Prep #2 18:44

This lesson is the second of four review lessons in which I cover a large percentage of the material we covered in this course.

133 12.2 HOMEWORK VIDEO: Final Exam Prep #2 26:24

Homework Video for Lesson 12.2

134 12.3 LESSON: Final Exam Prep #3 25:20

This lesson is the third of four review lessons in which I cover a large percentage of the material we covered in this course.

134 12.3 HOMEWORK VIDEO#1: Final Exam Prep #3 (Problems 1-9) 23:56

Homework Video for Lesson 12.3 (Part 1)

134 12.3 HOMEWORK VIDEO#2: Final Exam Prep #3: (Problems 10-15) 13:33

Homework Video for Lesson 12.3 (Part 2)

135 12.4 LESSON: Final Exam Prep #4 19:42

This lesson is the last of four review lessons in which I cover a large percentage of the material we covered in this course.

135 12.4 HOMEWORK VIDEO: Final Exam Prep #4 21:11

Homework Video for Lesson 12.4

136 12.5 FINAL EXAM Wrap-Up (Optional) 02:03

In this video I present a short introduction and explanation of the FINAL EXAM. (This exam is optional, but recommended)

136 12.5 FINAL EXAM SOLUTIONS (Problems 1-15) (Optional) 18:21

Final Exam Solutions Video (Problems 1-15)

136 12.5 FINAL EXAM SOLUTIONS (Problems 16-24) 15:32

Final Exam Solutions Video (Problems 16-24)

Algebra 1 Course Description

In this course, I strive to provide all students with a dynamic mathematics education that balances a solid foundation of basic algebraic skills with a constructed understanding of concepts that challenges, supports, and instills an excitement for math. My goal is to help students develop as curious and flexible thinkers who are confident in their individual mathematical abilities, allowing them to feel prepared to meet the challenges of higher mathematics.  Topics mastered include number sense, graphing and solving linear and quadratic equations, solving systems of equations and inequalities, exponent rules, radical and rational expressions and equations, parabolas and real-life applications through word problems. It is a rich curriculm which is designed to challenge each student while at the same time help him/her begin to enjoy the world of mathematics.  Homework pdfs are included, as well as short videos to review the homework solutions.  Each homework has a few problems from previous lessons so that students practice recalling and implementing previously learned skills. 

This course includes:

  • 12 Chapters
  • 132 Homework Worksheets
  • 272 Videos Total
    • 138 Lesson Videos
    • 134 Homework Solutions Videos (I work out on the board the solutions to each problem step by step)
  • 4 Final Exam Review Lessons
  • 1 FINAL EXAM
  • Over 75 Hours of Video Instruction!

COURSE TOPICS

Chapter 1:  Foundations of Algebra

Lessons:

Introduction to Course

Classification of Real Numbers

Adding & Subtracting Positive and Negative Numbers (Part 1)

Adding & Subtracting Positive and Negative Numbers (Part 2)

Multiplying & Dividing Positive and Negative Numbers

Evaluating Algebraic Expressions

Order of Operations

Some Key Properties in Algebra

 

Chapter 2:  Linear Equations

Lessons:

Solving One-Step Equations

Solving Two-Step Equations

Solving Multi-Step Equations

Equations with Infinite and Zero Solutions

Solving Equations with Fractions (Same Denominators)

Solving Equations with Fractions (Different Denominators)

Solving Proportions

Solving Equations with Decimals

Solving Absolute Value Equations

Solving Literal Equations

Solving Percent Equations

Percent Increase or Decrease

 

Chapter 3:  Introduction to Word Problems

Lessons:

Translating English into Math

Number Word Problems

Consecutive Integer Word Problems (Part 1)

Consecutive Integer Word Problems (Part 2)

Geometry Word Problems

Age Word Problems

Ratio Word Problems

Percent Word Problems

Simple Interest Word Problems

Distance / Motion Word Problems (Parts 1,2 &3)

 

Chapter 4:  Linear Inequalities

Lessons:

Graphing and Writing Single-Variable Inequalities

Solving Single-Variable Inequalities

More Practice solving Inequalites; Examples of Zero and Infinite Solutions

Solving and Graphing Compound Inequalities with “AND” Statements

Solving and Graphing Compound Inequalities with “OR” Statements

Absolute Value Inequalities

 

Chapter 5: Graphing and Writing Functions

Lessons:

Introduction to Equations with Two Variables

Relations vs. Functions

Graphing on a Cartesian Plane with T-charts

Graphing Equations in Slope Intercept Form (Using Shortcut)

Graphing Equations in Point-Slope Form

Graphing Equations in Standard Form

Graphing Practice

Finding the Slope Using The Slope Formula

Writing Equations With Given Data

Converting Equations From One Form to Another

Parallel and Perpendicular Lines

Scatter Plots and Trend Lines

Direct Variation

Graphing Absolute Value Functions

Graphing One-Variable Inequalities on Cartesian Plane

Graphing Two-Variable Inequalities on Cartesian Plane

 

Chapter 6: Systems of Equations and Inequalities

Lessons:

Solving Systems of Equations by Graphing

Solving Systems of Equations by Substitution (Parts 1-2)

Solving Systems of Equations by Elimination (Parts 1-4)

Systems with No Solutions or Infinite Solutions

Systems of Equations Word Problems (5 Types)

Graphing Systems of Inequalities with Parallel Boundary Lines

Systems of Inequalities Word Problems

 

Chapter 7: Exponents and Exponential Functions

Lessons:

Introduction to Exponents; Rules for Zero and Negative Exponents

Multiplication Properties of Exponents

Division Properties of Exponents

Division Property: A Cool Little Trick

Scientific Notation

Exponential Functions and Their Graphs

Exponential Growth and Decay

Compound Interest

 

Chapter 8: Radicals and Radical Functions

Lessons:

Introduction to Radicals; Simplifying Radicals with Numbers

Simplifying Radicals with Variables

Adding and Subtracting Radicals

Multiplying Radicals (Parts 1 & 2)

Dividing Radicals and Rationalizing the Denominator

Practicing with Radicals

Solving Radical Equations (Parts 1 & 2)

Graphing Radical Equations

 

Chapter 9:  Polynomials: Combining, Multiplying and Factoring

Lessons:

Introduction to Polynomials

Adding and Subtracting Polynomials

Multiplying Polynomials

Multiplying Binomials using FOIL

Special Products of Binomials

Factoring Polynomials: Finding Factors, Tree Factorization, Greatest Common Factor

Factoring Out the Greatest Common Factor

Factoring Out the “Blobs” (…or Binomials)

Factoring by Grouping

Factoring Quadratic Trinomials: a = 1

Factoring Quadratic Trinomials: ”a” is Not 1

Gary’s Terrific Trick

Factoring the Difference of Two Squares

Factoring Practice

 

Chapter 10: Quadratic Functions and Equations

Lessons:

Understanding and Solving Quadratic Equations (Parts 1 & 2)

Using Square Roots to Solve Quadratic Equations

Vertical Motion Model Word Problems

Completing the Square

Deriving the Quadratic Formula

Using the Quadratic Formula

Understanding the Discriminant

Quadratic Word Problems – Rectangles

Finding the Axis of Symmetry and Vertex

More Quadratic Word Problems

Anatomy of a Quadratic Equation

Graphing Quadratics with “Standard Parabola Guy”

Reviewing Different Types of Graphs

Functions, Set Notation, Domain and Range

 

Chapter 11: Rational Expressions and Equations

Lessons:

Rational Expressions: Finding the Excluded Value

Simplifying Rational Expressions

Simplifying Rational Expressions with Opposite Binomials

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions (Parts 1 & 2)

Dividing Polynomials Using Long Division

Solving Rational Equations: Proportions

Solving Rational Equations: Multiplying by LCD

Solving Rational Equations: Extraneous Solutions

Understanding and Graphing Inverse Variation

Direct Variation vs. Inverse Variation

Graphing Rational Functions Using Asymptotes & T-charts

Work Word Problems

Inverse Variation Word Problems and Other Rational Word Problems

 

Chapter 12: End-of-Course Review

Lessons:

Final Exam Prep #1

Final Exam Prep #2

Final Exam Prep #3

Final Exam Prep #4

FINAL EXAM

  • Teacher: Gary
  • Areas of expertise: Algebra
  • Education: B.A. in Business Administration from Principia College; Tutoring and teaching middle school and High School math for over 20 years.
  • Interests: Math, music, sports, sailing, water, quantum physics, healing, woodworking, helping kids grow in their appreciation for their unique talents and skills
  • Skills: Teaching math to kids
  • Associations: State licensed educator. Chair of the Math Department at Santa Fe School for the Arts & Sciences in Santa Fe, NM
  • Issues I care about: I care deeply about making this world a kinder place where each person feels safe to be exactly who they are.

I have taught and tutored High School and Middle School math for over twenty years. My passion is to awaken the love of math in my students. It does not have to be a scary subject. I find that if students are allowed to question freely, they begin to enjoy the class, and their brilliance begins to shine. My best classes have been guided by the insightful questions of my students where we can explore and learn together. I have recorded many lectures on Youtube and now have a significant following of students from around the world. I'm inspired by the number of wonderful students who truly wish to learn this material.

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