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).

Math 65, Math 76, and Math 87 in Brief

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 Math 65, Math 76, and Math 87 attempt 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 — Partial 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.)

There are few sightings of any parts of the benchmark in this material. The idea "a parts of size 1/b" is addressed almost exclusively in grade 6, and the presentation in grades 7 and 8 is the same as the pictorial representation and commentary in grade 6 with no development beyond a one-page explanation. The meaning "a divided by b" is presented in grade 6 as one of three ways to show division when teaching the terms divisor, dividend, and quotient. In grade 7, two lessons about a/b are combined into one discussion about ways to write division. In grade 8, students are simply reminded that a/b is one of three ways to designate division. There are only three lessons for "a compared to b"—one in each grade. A few practice and problem set examples addressing this idea are found throughout the series.

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.)

There is extensive coverage of most of this benchmark throughout the material. Interpretation and comparison of equivalent forms of fractions, decimals, percents, rational numbers, and exponents are scattered equally throughout all three grades. There are very few examples of using equivalent forms other than fraction and percent equivalents, which are introduced early in grade 6. In grades 7 and 8, lessons on equivalent forms are similar to those in grade 6. The same skills are reiterated, often by using very similar examples. In grade 7, students are introduced to a chart for expressing fraction-decimal-percent equivalents, and in grade 8, they use words to express numbers or exponential expressions and to learn how to write equivalent forms of very large or very small numbers using scientific notation.

Geometry Concepts — Minimal 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.)

There is very limited coverage of this benchmark in the series. There is no reference to circles and the relationship between boundary and area nor to the rigid structure of triangular shapes. Each grade features one or two charts that identify special properties of different polygons. Other than the definitions of the terms polygon and quadrilateral, properties of shapes, specifically triangles, are found in one example in each of grades 7 and 8. Likewise, congruence is addressed only once, in grade 7. Similarity is given the most coverage, with a lesson in grades 7 and 8 on similar triangles and a few individual problems distributed in grades 6 and 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.)

There are many opportunities throughout the three levels of this material for students to practice the calculations designated in this benchmark, with most coverage in grades 7 and 8. There are only two related lessons in grade 6, one on the perimeter of polygons and measurement of circles, the other on the area of rectangles. There are a number of warm up activities in this book that may serve as prerequisites for studying the volume of rectangular solids. In grade 7 there are several lessons on calculating perimeters and areas of triangles, rectangles, and circles. In grade 8, circumference of a circle receives a great deal of attention.

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.)

There are very few lessons on graphs in this material. In grade 6, there are no lessons and only a few exercises asking what each graph shows or doesn’t show. This pattern is followed in grade 7 where there is one lesson on line graphs. In grade 8, the only material is a lesson about graphs in general, in which line graphs are one of four different types presented. Most graphs show discrete rather than continuous relationships. There are a few practice exercises on reading graphs as well as one lesson on graphing functions.

Algebra Equation Concepts — Minimal 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.)

Symbolic equations and variables receive very limited attention in this material. They are not addressed at all in grade 6. In grade 7, students use variables in formulas for calculating areas of geometric figures and circumference using pi and in a lesson on functions using variables in input-output charts. In grade 8, a few scattered lessons deal with symbolic expressions and equations, functions expressed as equations, literal equations, and transforming formulas. At the very end of grade 8, students are taught to substitute letters in literal equations with known quantities in order to solve them.