Algebra 1: Expressions, Equations, and Applications (3^rd Edition)

Section I - Organization and Features

The student text for Algebra 1: Expressions, Equations and Applications (Third Edition) contains 721 pages organized into 14 chapters. The chapters are arranged and identified by math topics, not by context topics.

The student text contains an index with a moderate number of entries. Index entries contain references to math topics, not context references.

The student text also contains a glossary with a small number of entries. The entries in the glossary do not include page number references. The breadth of coverage of mathematics terms in the glossary is moderate.

There are many answers to problems for students to check their own work.

There are virtually no pictures within the text beyond those that clearly illustrate the material being presented.

The student text includes self-testing sections.

Section II - Major Topic Summaries

A) Linear equations in one variable

This book does an excellent job on solving linear equations. The exposition is clear and easy to follow. Subtopics grow in depth and complexity in a reasonable order, terms are clearly defined and a sufficient number of problems covering a range of difficulties are available at each level. Word problems of increasing sophistication are appropriately linked to increases in what the students can do. The text emphasizes analytical methods and mathematical logic both in the exposition and in the problem sets.

This book does a great job on this topic. All of the key properties and concepts are presented in a clear, easy to understand format. The word problems are both clever and appropriate.

This book has an excellent treatment of linear functions. The discussion of slope, slope intercept form, conversion between forms, and fast graphing is excellent. Some topics, especially graphs of parallel lines, direct and inverse variation and function notation are in chapter 14 and may not be reached in some classes. Some topics, such as parallel and perpendicular lines and their equations could use far more problems at the top level of sophistication.

This book does an excellent job of presenting factoring and the solution of quadratic equations and related word problems. If there is a problem in this presentation it is that simple factoring (trinomials, including those with lead coefficient >1, perfect squares, difference of two squares) occurs in chapter 5 while more advanced factoring (e.g. by grouping) and solution of quadratic equations are in chapter 10. Outside of this issue, however, the coverage of this important topic is sufficient to support student learning at high achievement levels.

The coverage of this major topic contains some very positive features, notable the detail with which the examples are worked out, the extent and creativeness of the word problems, and the overall number of problems. The more advanced topics of matrix solutions and systems of three equations are not covered.

The book adopts the attitude that the graphic method is both tedious and inaccurate. As such, the opening section on graphing simply talks about estimating the intercept, while the full discussion with definitions needed to address systems falls into the substitution section. The emphasis is thus decidedly on analytic approaches.

Problems are plentiful and often to medium levels, but the most difficult problems are less common.

In general, the quality of presentation, definitions of terms and concepts, clarity with which procedures are explained, and number of problems and detailed examples are outstanding. The topic could benefit from more difficult problems in some areas, and references to properties in working out examples and justifying steps.

In general, however, the treatment of this major topic is sufficient to promote student achievement at all but the very highest levels.

This major topic is addressed with clear explanations, lots of detailed examples, and lots of student exercises. Terms, concepts, and procedures are all clearly defined. Fractional exponents are not covered, although exponents of 1/n are addressed.

This text provides an outstanding opportunity for student learning to the moderate difficulty level. The highest difficulty level and an emphasis on proof and derivation are not sufficient to provide complete support for student learning at the very highest levels of achievement.

This text begins the introduction to radicals as a prelude to the presentation on the quadratic formula in chapter 6 of 14. Most of the introduction to the major topic appears here, including definitions and the closure axioms and the square root property of equalities and the roots of perfect squares and rational and irrational numbers are defined. Examples and problems address roots found in formulas. Some of these get the student to explore the properties of radicals using numbers as a prelude of work to come much later.

The bulk of the material appears in the radical expressions chapter (chapter 12 of 14). Radical expressions are defined and problems again are given in numeric form. The product and quotient properties are introduced with detailed examples, along with the criteria for simplest form. Many problems across levels are included, and the student is asked to prove these two properties.

Work on simplification of radicals continues with the introduction of conjugate form for products of radical binomials and with the procedure for rationalizing the denominator. Then, variables are introduced into the simplification process to lead to harder problems.

Solutions of radical equations are introduced by example with justifications of each step followed by problems at all levels.

The Pythagorean theorem is introduced by example and then stated. The rationale by area following the statement approximates a proof. Examples are given followed by several problems and the student is asked to outline the proof.

The distance formula, on the other hand, receives a rather weak treatment in this text, and must be arrived at by the student in the context of problems.

The treatment of n^th roots includes the exponent property of n^th roots and a problem set. Following this, rational and irrational numbers are discussed again and their relation to radicals is clarified.

Throughout the number and range of problems is extensive, and many creative application problems are included. The presentation is clear with sufficient examples and definitions of terms. Technology is incorporated but not to the extent of interfering with algebraic techniques. Proof and justification are required of the student.

In short, the opportunity for student learning in this major topic area is outstanding.

Section III - Overall Evaluation

Mathematical Depth and Breadth

The coverage of math topics is excellent. Nearly all specifics receive abundant attention.

The depth of coverage is outstanding. The support and experience that students need to achieve well beyond moderate levels is provided, although the highest achievement levels need a bit more support in some areas.

Overall the quality of presentation is excellent in terms of the depth of student learning supported.

Terms, concepts, and procedures are clearly and stated explicitly.

Examples are very effective and useful. They typically show steps on the left and explanations on the right. However, these explanations are often in terms of stating the procedure employed rather than in terms of the justification of the step. Examples also go well beyond the moderate cases in many instances.

The emphasis on properties is good, and proof is often presented or required.

The use of technology is not very frequent and is unlikely to be presented without underlying understanding.

The number of student exercises is outstanding across topic areas, including an extensive number of application problems that are often very creative and interesting.

The student work consistently extends into the moderate difficulty range, and the higher levels of difficulty are often provided. Thus, the exercises provide excellent experience to support moderate levels of achievement and very good support for high levels of achievement

The book provides an outstanding opportunity for student learning. Even achievement at the highest levels is supported, although sometimes only at good levels rather than outstanding levels.

Perhaps the greatest strength of this program lies in the abundance and quality of student exercises, especially application word problems. But, virtually all ratings of this program are outstanding. Simply put, it does a good job of the topic of introductory algebra.