Introduction
This is part of a series of second, fifth, and seventh grade Mathematics Program Reviews. This review includes a summary of the structure of the program, evaluations of a selected set of content areas, and evaluations of program quality. Ratings in these areas were made on a scale from 1 (poor) to 5 (outstanding). The overall evaluation was made using the traditional system of letter grades. For details of the methods used in this evaluation see Methods for Seventh Grade Program Reviews.
Student Text Structure
The student text contains:The twelve chapters are arranged by mathematical topic.
Each chapter is divided into two or three parts of 3-5 lessons. At the end of each subchapter there is a "connect" exercise attempting to link the lesson to a real world situation and a section review. Each lesson begins with a short explore exercise, followed by a relatively short exposition and a set of about 3 examples, each of which comes with a short set of class exercises to reinforce the concept. Prior to the problem set there are a few (3-5) additional questions asking for explanations of some aspect of the lesson. The problem sets generally contain about 30 problems involving "mechanical" practice, word problems/critical thinking and a mixed review. At the end of each chapter there is a chapter summary containing both short bullets on key points in the chapter and review exercises, an assessment involving both a set of problems relatively closely related to the topic and a "performance task" open ended question. Each chapter is also followed by what is called a "cumulative review" of all chapters up to that point. Unfortunately, these really consist of choosing one of four open ended problems rather than actual reviews.
As with a number of other books there are lots of topical problems or examples (movies, sports) that will soon be outdated or silly.
The book is moderately illustrated, with 31 extraneous pictures in the 50 pages from page 101 to page 150. Unfortunately, the frequency and placement of illustrations tends to pull one's attention from the lessons.
The glossary has a moderate number of entries all linked to specific pages.
Content Area Evaluations
Properties, Order of Operations [4.0]
This book has a good treatment of properties, order of operations, and simplification of algebraic expressions. The practice problems do not involve negative numbers, however, since integers are not brought in until chapter 9. The potentially distracting and unnecessary technology pages can and should be ignored. They are extras and do not interrupt the flow of the regular lesson. Of course, there is always the danger that a teacher will choose to emphasize the extras and not the key points of the lesson. Similarly, the photos and tidbits thrown in are unnecessary and may distract students.
Exponents, squares, roots [3.0]
For what is covered this book has a better than average treatment of this topic. This includes whole number powers, squares and square roots and expressions involving these items. Scientific notation is nicely presented with positive powers of ten. Later, in an extension section that not all students may do, scientific notation with negative exponents is introduced. Negative exponents do not otherwise appear. Unfortunately, there is weak coverage of operations with exponents: There is little or no coverage of multiplication or division of exponents with a common base or of operations such as multiplication, division or simplification of fractions or monomials using exponents. The lessons themselves are not overly dependent on calculators and receive relatively high marks for objectives, explanations, examples efficiency and so on.
Fractions [4.0]
This is a good treatment of fractions and their conversion to percents. Equation solving with fractions is presented and there are a good number of practice problems, although none of the addition or subtraction problems are difficult enough to require prime factorization to find common denominators. As with some other topics, this one is placed in the book prior to the time at which operations with negative numbers have been introduced. This eliminates operations with negative fractions from the coverage. Some of the modeling with manipulatives is annoying.
Decimals [4.0]
The coverage of this topic is above average. Just about every subtopic is covered to reasonable depth. The lessons are clear and well presented with good marks in objectives, explanations examples and efficiency. The quantity and general difficulty of problems is reasonable, including the presence of equation solving with decimals. The deficiencies include failure to include negative numbers resulting from a relatively late presentation of negatives in the text and a failure to convert repeating decimals to reduced fractions. This is a common gap.
Percents [4.5]
This book provides excellent instruction in relating fractions, decimals and percents. It then devotes a whole chapter to solving various types of word problems including markups, discounts, and increase/decrease. In the examples variables are selected, proportions are set up and the steps to solving the problems are clearly justified. The only topic that is missing is simple interest. It is indirectly mentioned on a technology page requiring a computer spreadsheet. The I= prt formula should be presented for ordinary computation first.
Proportions [5.0]
This book's treatment of proportions is excellent. The explanations are thorough and sequential. Lots of attention is paid to unit and rate conversions, although there are no conversions between unit systems. The students are expected to remember customary and metric mass and volume units, but review boxes are provided.
Expressions and Equations - Simplifying and Solving [3.0]
Although this book covers many aspects of solving one and two step equations, including those with fractions and positive and negative integers, the coverage is average at best. The equations in the book do not require simplification using the distributive property, grouping of like terms or variables on both sides of the equal sign. Thus, only a fraction of the appropriate equation solving skills are covered or drilled. In addition, there is essentially nothing about inequalities and their solution. The material that is covered is well and clearly presented, with clear step by step examples and justification for each step. There are an adequate number of problems even if they fall short of the necessary depth or complexity. Unfortunately, each lesson on solving equations seems to begin with a modeling of the mathematical system using algebra tiles. It is not at all clear that introducing yet another formal system, with its own rules that may map onto the rules for the manipulation of numbers, actually makes things clearer. Indeed, it is easily conceivably that we would now have two formal systems confusing students and a lack of understanding of either. Luckily, teachers can easily choose to skip those parts of the lessons that use algebra tiles.
Expressions and Equations - Writing [3.5]
This book contains a good treatment of the writing equations, within the constraints, discussed in the last section, of not having problems requiring grouping of like terms, use of the distributive property are dealing with the variable on both sides of the equation. The students are taught to write proportions to solve a variety of problems. The sections dealing with proportions are quite thorough, including similarity, scale drawings, and rates. More word problems leading to practice of equation-writing skills would be useful. There are few or no problems dealing with writing or solving inequalities. Algebra tiles are noticeable in the presentation, although a teacher could choose to ignore them with no loss to the rest of the presentation.
Graphing [3.0]
This topic is well covered except for the failure to introduce the concept of slope and to use it in graphing linear equations. The rating would be higher without this omission. The presentation leading up to graphs of linear equations is nicely done. An "extension" page gives a brief intro to quadratic and absolute value graphs. Graphs of inequalities in two variables are omitted as are graphs of systems of two equations,
Shapes, Objects, Angles, Similarity, Congruence [4.0]
This topic is covered in an above average manner. The presentation is thorough and clear and almost all items of content are covered. Some vocabulary is missing, such as "diagonal", but overall the treatment is good, including a number of constructions.
Area, Volume, Perimeter, Distance [4.0]
The presentation and coverage of this topic is above average. Essentially all necessary topics are covered. A bit more derivation of formulas could be provided in the area chapter, but the problems are of good quality and include irregular shapes. Volumes and surface area of cylinders and prisms are well presented with helpful diagrams. Mercifully, there are no silly hands on exercises. Cones are not considered. This is a minor deficiency.
Program Quality Evaluations
Mathematical Depth [3.9]
This book has content at a level that could support many students in preparation for algebra in the next year, although it could also serve as a book for pre-pre-algebra. There are no really badly covered topics.
The content level of the proportions and percents sections is quite high while the content is weaker, but not to a disqualifying level, for exponents and writing and solving equations.
Quality of Presentation [2.9]
When concentrating on the core of each lesson, scores for such things as clarity of objectives, explanations, examples and quantity of student work are all high. Teachers will need to be careful in some lessons as some topics contain significant algebra tile lessons and use of calculators or computers. Luckily, the use of calculators and manipulatives is generally not distracting and can be ignored with no cost to student learning.
The book, as most books covering this grade level, is rather long. The lessons, technology activities, and review subsections add up to at least 160 items. This is without including time for tests or any additional activities such as preparing for outside examinations. Chapter 11, out of 12, contains most of the geometry material and chapter 10 contains most of the material on graphing and solving linear equations. Thus, it is critical that teachers using this course keep on a time schedule to get them to this point. This means choices will have to be made about time spent on various exploration activities, projects and enrichment activities.
Quality of Student Work [2.9]
The work in this book, with the elimination of various unnecessary or inappropriate calculator activities and activities with manipulatives, is likely to lead to reasonable levels of mastery of the topics covered.
Overall Program Evaluation
With recognition of and appropriate response to the content areas that could use supplementation, the need to cut out unnecessary lessons, and the need to avoid wasting any days, this book is of sufficiently high quality that it might well meet the needs of individual schools or districts in preparing their seventh graders for success in algebra. In choosing to use this book to teach seventh grade students who might be ready for algebra in eighth grade, districts may wish to look carefully at other books that are specifically designed as pre-algebra books, especially as such books have a substantial overlap in content with this book. On the other hand, districts may find that this book would work well as a pre-pre-algebra book and meet the needs of their students who are hoping to take a serious algebra course in two years.
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