How well does Mathematics Plus address the content in the selected benchmarks?

This In Brief chart provides profiles showing how this textbook scored on content and instructional quality. For the content profile, the coverage of each specific mathematical idea in the selected benchmark was rated on a 0 to 3 scale (no coverage to substantive coverage). These ratings were then averaged to obtain an overall rating for each benchmark (Most content 2.6-3.0, Partial content 1.6-2.5, Minimal content 0-1.5). For the instruction profile, the score for each instructional category was computed by averaging the criterion ratings for the category. This was repeated for each benchmark, to produce ratings of instructional quality on a 0 to 3 scale (High potential for learning to take place 2.6-3.0, Some potential for learning to take place 1.6-2.5, Little potential for learning to take place 0.1-1.5, Not present 0).

### Mathematics Plus in Brief

 Benchmarks Number Concepts Number Skills Geometry Concepts Geometry Skills Algebra Graph Concepts Algebra Equation Concepts Content Instructional Categories Identifying a Sense of Purpose Building on Student Ideas about Mathematics Engaging Students in Mathematics Developing Mathematical Ideas Promoting Student Thinking about Mathematics Assessing Student Progress in Mathematics Enhancing the Mathematics Learning Environment
 Content Scale Instructional Categories Scale Most content Partial content Minimal content High potential for learning to take place Some potential for learning to take place Little potential for learning to take place Not present

The content ratings are estimates of what the textbook series attempts to present on only these benchmarks and are not an indication of overall content coverage or accuracy. The ratings also do not indicate whether or not the content will be learned. The instructional analysis provides information on the potential the series has for helping students actually learn the concepts and skills it attempts to present.

The following indicates how well Mathematics Plus attempts to address the substance, breadth, and sophistication of the ideas contained in each of the six mathematics benchmarks that were selected for the analysis.

Number Concepts — Most Content

 The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b. (Chapter 9A, grades 6-8, benchmark 5, pg. 213.)

Mathematics Plus covers all parts of the benchmark through definition, examples, demonstrations and practice exercises. "a parts of size 1/b" is given minimal coverage in grade 6 but developed further in grades 7 and 8. The concept of "a divided by b" is explored throughout the grade levels, primarily through lessons on converting fractions to decimals or percents. The idea "a compared to b" has the most in-depth coverage at all grade levels through many lessons on the meaning, use, and application of ratios.

Number Skills — Most Content

 Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents. (Chapter 12B, grades 6-8, benchmark 2, pg. 291.)

Mathematics Plus addresses the benchmark ideas substantively; however, for some ideas, the level of sophistication does not increase from one grade level to the next. At grades 6, 7, and 8, the lessons deal mainly with the basic skills of finding equivalent fractions, decimals, and percents, and simplifying fractions. Exercises and examples cover the use, interpretation, and comparison of all forms of these numbers, with greater emphasis on these areas in grade 8. Particularly in grades 7 and 8, students explore integers in activities that involve comparing and ordering integers and representing numbers in expanded form, scientific notation, powers, and roots.

Geometry Concepts — Partial Content

 Some shapes have special properties: Triangular shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes. (Chapter 9C, grades 6-8, benchmark 1, pg. 224.)

Although there is no reference to the special properties of round shapes, all other parts of this benchmark are addressed at all three grade levels. For the most part, the level of sophistication develops appropriately from grade 6 through grade 8, as students examine properties of shapes. Lessons explore basic characteristics of many figures, including squares, rectangles, triangles, and circles, as well as properties of solid figures. Similarity and congruence are introduced and studied with little development from grade 6 to grade 7; however, these concepts are expanded in grade 8.

Geometry Skills — Most Content

 Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids. (Chapter 12B, grades 6-8, benchmark 3, pg. 291.)

The geometry skills benchmark is addressed through written definitions that introduce area, volume, and circumference of figures and shapes, along with the application of their respective formulas. Although the material does address the substance of all parts of the benchmark, many lessons are redundant across the grades in their introduction, demonstration, and applications. There is a noticeable development from grades 7 to 8 in activities that relate the area of a triangle to the areas of parallelograms and trapezoids.

Algebra Graph Concepts — Minimal Content

 Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these. (Chapter 9B, grades 6-8, benchmark 3, pg. 219.)

The idea that graphs illustrate a variety of relationships between two variables is addressed in the chapters that involve graphing, statistics, and algebra. The treatment is limited to graphs of linear equations and functions to depict patterns of change. None of the other benchmark ideas about the relationship between two variables are addressed. The idea that the change in one variable reacts to the change in another variable tends to remain at the grade 6 level except that as the grade level increases, the questions require more precise interpretation of the graphs.

Algebra Equation Concepts — Partial Content

 Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes. (Chapter 11C, grades 6-8, benchmark 4, pg. 274.)

The material introduces symbolic equations in sections that discuss or introduce variables and algebraic expressions and in lessons dealing with graphing equations. The content of Mathematics Plus for this benchmark is appropriate for grades 6 and 7 and focuses on the changes in variables by examining graphs or equations. Equations that represent changes over time are only partially addressed in examples.