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Abacus Mathematics

Algebra I

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Elementary Algebra by Harold R. Jacobs is an atypical algebra text that has been around for almost forty years in essentially the same edition because it has been so popular. The Algebra (I) course covers the 1st half of the book from Chapters 1 through 8.

Elementary Algebra covers all concepts typical of a 2-year algebra course. It invites students to explore algebra concepts in a friendlier environment than other texts. Cartoons, comic strips (e.g., Broom Hilda, B.C., Wizard of Id, and Doonesbury), interesting and creative applications, puzzles, and even poetry capture the interest of students who struggle with abstract mathematics. For example, a lesson on mixture problems opens with the story of Archimedes and the King of Syracuse’s golden crown which the king suspected was not really solid gold. Jacobs then sets up a volume and weight equation based on the problem.

In addition to stories and practical applications, Jacobs uses the rectangle-building (or area-model) concept throughout the text to demonstrate how concepts work. This is the same rectangle building idea used by Math-U-See and some other manipulative systems. While Jacobs’ book shows pictures, not requiring the use of manipulatives, students can still use manipulatives if they are helpful. I think most students should really benefit from this approach when they are learning to multiply and factor polynomials. (This last feature makes this text a particularly good one to use after Math-U-See’s Pre-Algebra level. If you don’t already have manipulatives, you might want to check out the Algebra Tiles from Nasco.)

The hardcover textbook is divided into seventeen chapters, with each chapter subdivided into a number of lessons. Students should be able to read through the instructional material and examples on their own, working independently most of the time. If your student benefits from a teacher's presentation, you might want to get the optional DVD Instruction set. These six DVDs have about six hours of lesson presentation by Dr. Callahan.

In the original book, there were four exercise sets at the end of each lesson. The first set reviews concepts from earlier lessons along with some from the current lesson. The second set concentrates primarily on topics taught in the current lesson. The third set of problems is generally fairly similar to the second set. These three sets present problems ranging from simple computation through word and application problems. The most challenging problems are in the fourth set. These are often complex problems requiring critical thinking skills. Since the third set is similar to the second set in the level of difficulty, Master Books has removed the third set of problems from the textbook. They have put those sets in the teacher guide, so they are still available for those who might want to use them. Generally, you will have students work through at least the first two sets of problems. By assigning appropriate problems, you can use the text with students of varying capabilities. Answers to the second set from each lesson are in the back of the student text so students can see if they are getting the correct answers. (If students are tempted to look at answers ahead of time, you might assign problems from the third set instead.)

Each chapter concludes with a "Summary and Review" section that briefly summarizes key concepts. This is followed by two sets of problems that review concepts from the entire chapter. The text includes answers for only one of these sets of chapter review problems. The teacher’s guide is the source for the rest of the answers for chapter reviews as well as the answers for the first, third, and fourth problem sets from the lessons. The teacher guide also has tests and test answer keys. A complete solutions manual is also available for students who need help figuring out what steps they have missed when they can't solve a problem.

The student text and the teacher guide are the most critical components, but if you want the solutions manual or the DVDs, you will save purchasing either the curriculum pack with the textbook, teacher guide, and solutions manual or the curriculum pack that also includes the set of DVDs.

Jacob's Elementary Algebra provides solid coverage of first-year algebra and remains one of the easiest courses for students to use and understand.


The syllabus of Algebra (I) course includes the followings:

1 Addition
2 Subtraction
3 Multiplication
4 Division
5 Raising to a Power
6 Zero and One
7 Several Operations
8 Parentheses
9 The Distributive Rule
Summary and Review

1 An Introduction to Functions
2 The Coordinate Graph
3 More on Functions
4 Direct Variation
5 Linear Functions
6 Inverse Variation
7 Summary and Review

Chapter 3 THE INTEGERS (can be brief)
1 The Integers
2 More on the Coordinate Graph
3 Addition
4 Subtraction
5 Multiplication
6 Division
7 Several Operations
Summary and Review

1 The Rational Numbers
2 Absolute Value and Addition
3 More on Operations with Rational Numbers
4 Approximations
5 More on Graphing Functions
6 Summary and Review

Chapter 5 EQUATIONS IN ONE VARIABLE (can be brief)
1 Equations
2 Inverse Operations
3 Equivalent Equations
4 Equivalent Expressions
5 More on Solving Equations
6 Length and Area
7 Distance, Rate, and Time
8 Rate Problems
Summary and Review

1 Equations in Two Variables
2 Formulas
3 Graphing Linear Equations
4 Intercepts
5 Slope
6 The Slope-Intercept Form
Summary and Review

1 Solving by Addition
2 Solving by Subtraction
3 More on Solving by Addition and Subtraction
4 Graphing Simultaneous Equations
5 Inconsistent and Equivalent Equations
6 Solving by Substitution
7 Mixture Problems
Summary and Review

1 Large Numbers
2 A Fundamental Property of Exponents
3 Two More Properties of Exponents
4 Zero and Negative Exponents
5 Small Numbers
6 Powers of Products and Quotients
7 Exponential Functions
Summary and Review


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Ch 1. FUNDAMENTAL OPERATIONS: Summary and Review

Lesson 2.1. FUNCTIONS AND GRAPHS: An Introduction to Functions

Lesson 2.2. FUNCTIONS AND GRAPHS: The Coordinate Graph; 2.3. More on Functions

Lesson 2.4. FUNCTIONS AND GRAPHS: Direct Variation

Lesson 2.5. FUNCTIONS AND GRAPHS: Linear Functions

Lesson 2.6. FUNCTIONS AND GRAPHS: Inverse Variation

Lesson 3.1. THE INTEGERS: The Integers

Lesson 3.2. THE INTEGERS: More on the Coordinate Graph

Chapter 3. THE INTEGERS, Lesson 3.3. Addition; Lesson 3.4. Subtraction; Lesson 3.5. Multiplication

Lesson 3.6~3.7. THE INTEGERS: Division; Several Operations

Lesson 4.1. THE RATIONAL NUMBERS: The Rational Numbers

Lesson 4.2. THE RATIONAL NUMBERS: Absolute Value and Addition; Lesson 4.3. More on Operations with Rational Numbers

Lesson 4.5. THE RATIONAL NUMBERS: More on Graphing Functions

Lesson 5.2. EQUATIONS IN ONE VARIABLE: Inverse Operations

Lesson 5.5. EQUATIONS IN ONE VARIABLE: More on Solving Equations

Lesson 6.1. EQUATIONS IN TWO VARIABLES: Equations in Two Variables


Lesson 6.4. EQUATIONS IN TWO VARIABLES: Intercepts

Lesson 6.6. EQUATIONS IN TWO VARIABLES: The Slope-Intercept Form

Lesson 7.1. SIMULTANEOUS EQUATIONS: Solving by Addition

Lesson 7.2. SIMULTANEOUS EQUATIONS: Solving by Subtraction

Lesson 7.3. SIMULTANEOUS EQUATIONS: More on Solving by Addition and Subtraction

Lesson 7.4. SIMULTANEOUS EQUATIONS: Graphing Simultaneous Equations

Lesson 7.5. SIMULTANEOUS EQUATIONS: Inconsistent and Equivalent Equations

Lesson 7.6. SIMULTANEOUS EQUATIONS: Solving by Substitution

Lesson 7.7. SIMULTANEOUS EQUATIONS: Mixture Problem

Lesson 8.1. EXPONENTS: Large Numbers; Lesson 8.2. EXPONENTS: A Fundamental Property of Exponents

Lesson 8.3. EXPONENTS: Two More Properties of Exponents; Lesson 8.4. EXPONENTS: Zero and Negative Exponents

Lesson 8.5. EXPONENTS: Small Numbers 8.6. EXPONENTS: Powers of Products and Quotients

Lesson 8.7. EXPONENTS: Exponential Functions


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