Algebra I: Expressions, Equations, and Applications [Hardcover]

Paul A. Foerster (Author)

Book Description

ISBN-10: 0201860945 | ISBN-13: 978-0201860948 | Publication Date: January 1994 | Edition: 3rd

A beginning algebra textbook with instructions for the teacher on how to present the material to students.

--This text refers to an out of print or unavailable edition of this title.

Product Details

• Hardcover: 721 pages
• Publisher: Addison-Wesley; 3rd edition (January 1994)
• Language: English
• ISBN-10: 0201860945
• ISBN-13: 978-0201860948
• Product Dimensions: 9.5 x 7.8 x 1.3 inches
• Shipping Weight: 3.1 pounds
• Average Customer Review: 4.9 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #517,872 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

72 of 73 people found the following review helpful:

5.0 out of 5 stars This book is a great teacher!, November 8, 2001

By 

Paul C Glasser - See all my reviews

Amazon Verified Purchase

This review is from: Algebra I: Expressions, Equations, and Applications (Hardcover)

I searched long and hard for a text like this. It is well organized, well illustrated, and has plenty of example and practice problems with solutions to odd problems found in the back of the book. It is not like some of the newer algebra texts, which take an inductive approach and rely on "group discovery" of mathematical concepts. It delivers a thorough explanation of concepts in a logical and intuitive fashion, and proceeds at a deliberate pace that ensures a mastery of each concept before moving on to the next.

As a home schooling resource:
I use this for home schooling. It explains things so well that my 12 yr. old daughter is able to read a section and work the homework problems with little or no help from me. I supplement it with more drill and explanation found in the Key to Algebra workbooks from Key Press Curriculum. We proceed at a comfortable pace and have covered the first six chapters in one year. I plan to use Geometer's Sketchpad (also from Key Press Curriculum) as a supplemental graphing tool beginning in chapter seven.

I don't mean to infer that home school parents with no knowledge of algebra can successfully use this book. It does not have a teacher's guide and one probably is not appropriate. As with any home school scenario, you will need to understand the topic yourself so that you can answer questions. I far prefer this text to Saxon and other texts designed for home school use.

I spent over a year looking for a good algebra textbook and was surprised and disturbed to find that most are poor examples of how to explain a concept to a student. This book stands out as a wonderful exception. Compared to other algebra texts, it beats all I have found hands down.

Here is the table of contents:
1 Expressions and Equations
2 Operations with Negative Numbers
3 Distributing: Axioms and Other Properties
4 Harder Equations
5 Some Operations with Polynomials and Radicals
6 Quadratic Equations
7 Expressions and Equations Containing Two Variables
8 Linear Function, Scattered Data, and Probability
9 Properties of Exponents
10 More Operations with Polynomials
11 Rational Algebraic Expressions
12 Radical Algebraic Expressions
13 Inequalities
14 Functions and Advanced Topics

18 of 18 people found the following review helpful:

5.0 out of 5 stars Provides a strong foundation in algebra., July 2, 2006

By 

N. F. Taussig (Bronx, NY) - See all my reviews
(REAL NAME)   

This review is from: Algebra I: Expressions, Equations, and Applications (Hardcover)

Foerster's text provides the student with a strong foundation in algebra. Topics are introduced incrementally. Before Foerster introduces a new idea, he first makes sure that the reader has a strong understanding of the concepts on which the new idea is based. His exposition, which can seem pedantic at times, is clear and effective. The numerous examples he provides are explained in painstaking detail. He also warns the reader of potential pitfalls. The exercises are designed to build both the reader's algebra skills and conceptual understanding. Each chapter concludes with a section in which the reader applies the material learned in the chapter to real world problems. This material, which is a particular strength of the text, demonstrates how and why algebra is used.

The book begins with basic algebraic concepts that are sometimes covered in pre-algebra classes. Those concepts include operations on numbers, variables, constants, algebraic expressions and equations, signed numbers, and the rules of algebra such as the commutative, associative, and distributive laws.

Foerster then discusses linear equations in one variable. Rather than discussing equations of lines next, as many authors do, he defers that topic in order to cover operations on polynomials. That allows him to discuss quadratic equations before the midterm review. While he later discusses how to factor by grouping, in this chapter he treats the factoring of quadratic polynomials as a series of special cases. The chapter concludes with a discussion of the quadratic formula, the derivation of which he leaves as an exercise. If this book has a weakness, it is that Foerster teaches you how to do algebra without always justifying the methods he uses.

Following the midterm review, Foerster discusses equations of lines and systems of linear equations. This leads to a brief discussion of probability and statistics. Probability is revisited in the exercises later in the text.

The following chapters address exponents, operations on polynomials, rational expressions and equations, radical expressions and equations, and inequalities. The last chapter, which is followed by a final review, introduces concepts such as functions and right triangle trigonometry that are explored in more advanced algebra classes. The final sections of this chapter, which address quadratic inequalities, provide a capstone to the text because they tie together many of the concepts introduced earlier.

The exercises, which are numerous, vary from drills designed to develop the reader's facility with a particular type of algebraic manipulation to challenging application problems. For instance, Foerster poses the following problem: In some states, your state tax is based on your net income after your federal tax has been deducted and your federal tax is based on your net income after your state tax has been deducted. How do you determine how much tax you owe each entity if the tax you owe depends on the amount being collected by the other entity? The difficulty of the problems Foerster poses makes this text suitable for an honors course.

The text is quite comprehensive, discussing topics not found in other texts. For instance, one topic he introduces is a system comprised of a linear equation and a linear inequality. As is the case with other topics, he also introduces applications of such systems. Consequently, there is more material here than can comfortably be covered in one year. Instructors will need to be selective in their choice of topics. However, the text's clear exposition, detailed examples, and the provision of answers to the odd-number exercises make it suitable for self-study.

A less challenging alternative to this text is Harold R. Jacobs' Elementary Algebra. It is engagingly written, provides a strong foundation in algebra, and will not overwhelm the average student.

16 of 18 people found the following review helpful:

5.0 out of 5 stars A former student of Mr. Foerster's, November 2, 2001

By 

Laura Smith "fibersmith" (TX United States) - See all my reviews

This review is from: Algebra I: Expressions, Equations, and Applications (Hardcover)

Until I met Mr. Foerster, I thought I desperately hated math. I scored well in it, yet I just hated the whole subject.

Mr. Foerster is truly an inspiring man; the whole high school was in awe of him. His courses were reputed to be extremely tough. But the hallway gossip was soon dispelled. Although Algebra isn't always "easy", I was quite surprised and delighted to discover that Mr. Foerster's classes - and especially his textbooks - were extremely user-friendly! Mr. Foerster writes clearly, and is able to address Algebra from the beginning, rather than talking several levels over students' heads. His kindness, humor, and gentle personality show through in the books. Wow! Math is fun after all!

I am now homeschooling my three kids, and Foerster's books are the texts of choice in this family.