Publisher: Prentice Hall Title: Pre-Algebra

Reviewer’s Name: Wayne Bishop, Jane Friedman, Steve Kerkhoff, Yat-Sun Poon

__Conclusion__

A succinct statement summarizing the CRP’s evaluation.

With regard to mathematics content only, this program sufficiently
addresses the content standards and applicable evaluation criteria to be
recommended for adoption as submitted.

This program has made a concerted effort to meet the California Grade 7 Standards. Although it is not perfect, it is successful in the large. Besides having to hit the Standards bullets, this program also takes time to develop some of the most critical topics with appropriate thoroughness. Most successful is its treatment of NS 1.7, AF 4.1 and 4.2

This program can be improved by two editorial corrections.

1. There are occasions when Standard related materials are presented after the problems at the end of a section. This arrangement may subject the involved topics to neglect. (See comments on Criterion 1). Our positive evaluation is conditional subject to satisfactory adoption of the recommended editing suggestions. (See "Corrections and Edits").

2. There are some standards whose coverage depends, in part, on exercises that are listed as "Extension" problems in the Teacher Edition. These should be listed instead in the "Core" problems to insure that they are covered. (See comments on Criterion 1)

Assuming that these corrections are made, this program is recommended
for adoption.

Other suggestions for improvement will be contained in the comments
on individual criteria.

__Mathematics Content/Alignment with Standards__

A systematic review of determinations regarding the criteria in this section. Citations of standards not adequately addressed (if any) are of particular importance with regard to Content Criterion 1.

Content Criterion 1. The content supports teaching the mathematics
standards at each grade level (as detailed, discussed, and prioritized
in Chapters 2 and 3 of the framework).

MEETS

This text adequately covers all of the California Standards. Some are covered more thoroughly than others; this is commented on below. Also, corrections to the Teacher Edition are required to insure that certain material is not inadvertently omitted.

According to the Framework (Page 150), "one of the high points of the entire strand" in Grade 7 Number Sense is 1.7. This item is addressed by the concerned program in Section 6-7 (Page 311 on Commissions). Section 6-9 (Page 318 on Markup and Discount) after one chapter on fractions, decimals and percents; and addressed in Section 7-8 (Page 369 on Simple and Compound Interest) after one chapter of discussion on equations.

One of the highlighted items in the Grade 7 Algebra and Functions strand
is 4.1

(Framework Page 151). This program begins with a review of one-step
problems in Chapter 2 (2-5 Page 84, 2-6 Page 93) and completes the discussions
in Chapter 7 with details.

The above two examples demonstrate an appropriate development, emphasis and depth on key standards in this program.

One standard that is only weakly covered is AF 3.0. In particular, graphing non-linear functions (AF 3.1) is done only briefly, using quadratic and exponential functions (and no cubic equations); plotting values of volumes (AF 3.2) is done in a single exercise. However, the highlighted parts of this standard (AF 3.3, 3.4) are covered more thoroughly, providing adequate overall coverage of these standards.

The following materials are given after the end of Lessons, where they
are in danger of being neglected.:

- The second half of NS 2.2 is on Page 587, in "For use after Lesson I 1-5".
- The second half of MG 1.1 is on Page 282-283, in "For use after Lesson 6-1".
- MR 2.7 is on Page 156-157, in "For use after Lesson 3-7".
- MR 2.7 is on Page 250. in "For use after Lesson 5-5".

In the Teachers' Edition these items should be clearly marked as
necessary components in the coverage of the standards and they need to
be included in the Scheduling recommendations there as well. Currently,
it is unclear how they are to be fit into the curriculum. Details of editing
required to fix this problem are in the "Corrections and Edits" section.

The following exercises are part of the primary citations for certain
standards. They should be listed as "Core" problems in the in the "Assignment
Guide" in the Teachers' Edition, rather than as "Extension" problems.

- Page 197, Ex. 30-33, for NS 2.5.
- Page 473, Ex. 24, for AF 3.4.
- Page 507, Ex. 20-22, for MG 2.2.
- Page 569, Ex. 43-44, for MG 3.6.

Content Criterion 2. A checklist of evidence accompanies the submission and includes page numbers or other references and demonstrates alignment with the mathematics content standards and, to the extent possible, the framework.

MEETS

A Standards Map provided by the publisher accurately demonstrates alignment with the Mathematics Content Standards.

Content Criterion 3. Mathematical terms are defined and used appropriately, precisely, and accurately.

MEETS

Mathematical terms are defined and highlighted. Definitions of terms that are used often in both Grade 7 and Grade 8, such as "proportion", are consistent. (Pre-Algebra 6-2, Page 284 and Algebra I 3-9, page 148).

Content Criterion 4. Concepts and procedures are explained and are accompanied by examples to reinforce the lessons.

MEETS

Section 7-5, Page 356, Example 2 is a good example on mult-step equations.

Section 8-7, Page 422, "Measurement" is a good example of a linear system and a good example to review equations with one variable.

Content Criterion 5. Opportunities for both mental and written calculations are provided.

MEETS

Yes, see Criterion 6 below.

Content Criterion 6. Many types of problems are provided: those that help develop a concept, those that provide practice in learning a skill, those that apply previously learned concepts and skills to new situations, those that are mathematically interesting and challenging, and those that require proofs.

MEETS

Various types of problems ("Mathematical Reasoning", "Critical Thought", "Mental Math") are included in most sections and, for the most part, their titles are an accurate reflection of what they are.

Content Criterion 7. Ample practice is provided with both routine calculations and more involved multi-step procedures in order to foster the automatic use of these procedures and to foster the development of mathematical understanding, which is described in Chapters 1 and 4.

MEETS

This program provides ample practice between examples, before lessons as well as after lessons. For example, the exercises for Section 6-5 on page 302-302 are concerned with fractions, decimals and percents. There are simple conversions between fractions and percents and between decimals and percents. It also has two-step problems that involve comparison between fractions and percents and comparison between decimals and percents. The "Assignment Guide" in Teacher Edition appropriately advises teachers to focus on the one-step problems first and the two-step problems second.

Content Criterion 8. Applications of mathematics are given when appropriate, both within mathematics and to problems arising from daily life. Applications must not dictate the scope and sequence of the mathematics program and the use of brand names and logos should be avoided. When the mathematics is understood, one can teach students how to apply it.

MEETS

For example, Section 7-2, Page 340-341, is on "Solving multi-step equations". Example 1 is a contextual problem. Example 2 is a mathematical problem given in words. Example 3 illustrates usage of the distributive property of arithmetic in computation. In the first two problems, the text produces detailed step-by-step development of an algebraic formulation from the problem statement, and then a step-by-step algebraic solution

Content Criterion 9. Selected solved examples and strategies for solving various classes of problems are provided.

MEETS

Each section of this program offers three to four solved examples for students. The Teachers' Edition offers 'Error Prevention" next to solved examples. For example, in Section 3.1, Page 122-125 on "Rounding and Estimating", it offers four examples to explain different ways to do rounding. The "Error Prevention" on Page 124 discusses common errors well. It finishes the discussion with a "Different ways to solve a Problem" on rounding. By Chapter 8, this program has completed "solving two-step linear equations". In Section 8-7, Page 420, it presents "solving systems of linear equations" by graphing through four examples. Each example is more difficult than the previous ones. It starts with a straightforward procedural type problem and finishes with a word problem. After the word problem is solved by the method of the section, it pleasantly surprises the readers with "Different ways to solve a problem" using an algebraic method in solving multi-step linear equations with one variable, a concept learned in a previous chapter.

Content Criterion 10. Materials must be written for individual study as well as for classroom instruction and for practice outside the classroom.

MEETS

The pacing guide, math background, teaching notes and assignment guide in the Teachers' Edition support classroom instruction, but could also be used for individual study outside the classroom. The pacing guide offers teachers and individuals the option of moving through the same material at a slower pace for transitional students. The examples, exercises, quick review, and assessments in the Student Edition are sufficiently focused. The Student Edition also contains both an index and a Glossary/Study Guide. The latter is more than just a glossary in that it not only provides citations for page numbers and definitions but also general and specific examples. It is adequate for students' practice outside the classroom.

Content Criterion 11. Mathematical discussions are brought to closure. Discussion of a mathematical concept, once initiated, should be completed.

MEETS

The overall judgment is that this program meets this criterion. However there are places where it can be improved. For example: in Section 6-10, Page 33-324, it presents "making a table" as a reasoning strategy to solve a problem. The problem in question is concerned with population with a fixed annual growth rate. Although the discussion does finish off its usage of the table, it does not bring out a grade appropriate topic to explain the mathematics in the table. It could have pointed out that another approach, using compound interest, will to be studied in Chapter 7. Or it could have returned to this topic in Chapter 7 after the students understood compound interest.

Content Criterion 12. All formulas and theorems appropriate for
the grade level should be proved, and reasons should be given when an important
proof is not proved.

MEETS DOES NOT MEET

This program is not consistent with respect to this Criterion. Although examples are usually explained carefully in a step-by-step manner, there are a number of facts that are simply stated as true that could easily have been proved or explained at this grade level.

For example, the text does not explain the theorem that multiplication of an inequality by a negative number reverses the inequality relation. Instead, it appeals to "patterning" or "inductive reasoning" on Page 108. Ironically, "Method 2" in "Different Ways to Solve a Problem" on Page 110 actually provides the algebraic justification for this fact without pointing it out. So, though a formal proof may be out of place at this grade level, it clearly is possible to give an explanation that goes beyond checking a couple of examples.

Similarly, when compound interest is presented, an examp1e is worked
out where the interest is compounded yearly over 4 years. The form of this
example would have made ii quite easy to derive the general formula. Instead,
the formula is simply stated, without any connection to the example, as
a simpler method of computation. This is a completely unnecessary avoidance
of Mathematical Reasoning.

unnecessary avoidance of Mathematical Reasoning.

Content Criterion 13. Topics cover broad levels of difficulty. Materials must address mathematical content from the standards well beyond a minimal level of competence.

MEETS

Standards are generally covered well beyond the minimum level. Also, there are opportunities, through challenge problems and other questions, for students to go beyond the immediate content of the text.

Content Criterion 14. Attention and emphasis differ across the standards in accordance with (1) the emphasis given to standards in Chap--ter 3; and (2) the inherent complexity and difficulty of a given standard.

MEETS

Yes.

Content Criterion 15. Optional activities, advanced problems, discretionary activities, enrichment activities, and supplemental activities or examples are clearly identified and are easily accessible to teachers and students alike.

MEETS

This program offers optional and enrichment activities through "Math at Work" and "Multi-step Application". "Math at Work" is often limited to less than half-a-page and placed at the end of a section (e.g. Page 402). "Multi-step Application" is given at the end of a chapter and is not given a pacing recommendation.

Content Criterion 16. A substantial majority of the material relates directly to the mathematics standards for each grade level, although standards from earlier grades may be reinforced. The foundation for the mastery of later standards should be built at each grade level.

MEETS

Yes. The text does not spend too much time on review material.

Content Criterion 17. An overwhelming majority of the submission is devoted directly to mathematics. Extraneous topics that are not tied to meeting or exceeding the standards, or to the goals of the framework, are kept to a minimum; and extraneous material is not in conflict with the standards. Any non-mathe-matical content must be clearly relevant to mathematics. Mathematical content can include applications, worked problems, problem sets, and line drawings that represent and clarify the process of abstraction.

MEETS

There are several topics that are not tied to the standards. For example, Section 9-8A on matrices and translations, Section 9-10A on Tessellations and Section 12-9A on Random Numbers. As the presence of these topics is limited and may serve as mathematical enrichment for advanced students, it does not dilute the efficiency of this program.

However, the text would be improved by including fewer visual distractions.
The pages are much too busy, drawing students' attention from the mathematics
on the page. Also, standardized test preparation problems put the focus
on test-taking rather than on mathematical content. They would be much
better off in the Teachers Edition only.

Content Criterion 18. Factually accurate material is provided.

MEETS

There do not seem to be many errors in the text.

Content Criterion 19. Principles of instruction are reflective of current and confirmed research.

MEETS DOES NOT MEET

The CRP members generally agreed that they would not comment on this criterion.

Content Criterion 20. Materials drawn from other subject-matter areas are scholarly and accurate in relation to that other subject-matter area. For example, if a mathematics program includes an example related to science, the scientific references must be scholarly and accurate.

MEETS DOES NOT MEET

Content Criterion 21. Regular opportunities are provided for students to demonstrate mathematical reasoning. Such demonstrations may take a variety of forms, but they should always focus on logical reasoning, such as showing steps in calculations or giving oral and written explanations of how to solve a particular problem.

MEETS

In examples, this program offers both reasons and instructions alongside its computational procedures and examples. It offers "check" sections after completion of some computations and 'error analysis' in some of the problems in the Student Edition. It offers "Different Ways to Solve a Problem", which are generally quite good, in a limited number of pages.

However, it does miss opportunities to guide students in mathematical
reasoning, For example, Section 3-2, Pace 172-173, offers rules on divisibility
rules for 2,5, 10, 3 and 9 respectively. In the Student Edition. the rules
are given without proof. The rules for divisibility by 2, 5 and 10, at
least, could be worked through by the students. Inclusion of justification
of these rules would greatly improve the discussion. Since this is not
a key topic, this will not be required at this time, but it should be included
in the next edition.

Content Criterion 22. Homework assignments are provided beyond grade three (they are optional prior to grade three).

MEETS

This program provides ample practice between examples, before lessons as well as after lessons. For example, the exercises for Section 6-5 on page 302-302 are concerned with fractions, decimals and percents. There are simple conversions between fractions and percents and conversions between decimals and percents. It also has two-step problems that involve comparison between fractions and percents and comparison between decimals and percents. The "Assignment Guide" in Teacher Edition appropriately advises teachers to focus on the one-step problems first and the two-step problems second.

Additional Comments and Citations.

Corrections and Edits.

Typos:

Page 204. Example 2b. Typo in the question. It should have been {6b^{3}/{18b^{3}}.

Page 459. Heading "Polynomial" should be "Polygon".

A. As discussed in the summary and in Content Criterion 1, the material in the sections labeled "For use after Lesson 11-5 ", "...6-l ", "3-7", and "5-5" are necessary for adequate coverage of certain standards and are in danger of being neglected in their current position in the text. The following steps are REQUIRED:

1. Change the headings of these sections to "Lesson 11-5 A", Lesson 6-1 A", etc., in order to emphasize that they are a necessary part of the section. (Note: This labeling has already been done in the Table of Contents.)

2. State clearly in the Teachers' Edition that these sections are necessary for coverage of the Standards.

3. Include these sections in the pacing suggestions in the Teachers Edition.

A fourth, desirable editing change would be to move the pages containing this material so they appear before the problems associated to Lessons 11-5, etc. Since these sections and the problems are on individual pages, this appears to be a simple correction with little affect on the pagination, but this is left to the publishers' discretion. (Note: For consistency, the publisher may wish to treat all of the "For use after...." sections in the same way, which is fine. But the four above are the most crucial to coverage of the Standards.)

B. The problems listed at the end of Content Criterion 1 need to be
listed as "Core" problems, rather than "Extension" problems, in the "Assignment
Guide" in the Teachers' Edition. This is a simple editing change.