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).

MathScape 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 MathScape 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 — 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.)

Only the first and third ideas of the benchmark are explicitly covered in the material with connections made between the benchmark concepts. The greatest emphasis on these ideas is in grade 6. Related numbers skills are the focus in grades 7 and 8. The idea "a divided by b" is applied as assumed knowledge. The material develops sophistication in understanding fraction concepts across the grades emphasizing more informal conceptual understanding early on and moving to application of related skills in the later grades.

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.)

MathScape addresses all components of the benchmark and focuses on the skills of comparing and interpreting numbers in several equivalent forms in grades 6 and 7. In grade 8, the emphasis on the use and application of numbers increases, and many opportunities for applying and practicing computational skills are available. The grade 7 units cover skills with proportions through consumer applications and unit pricing. The grade 8 units examine equivalent ways of representing tangents and slopes with fractions and decimals.

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.)

The material does not address the special properties of triangular shapes and round shapes stated in the benchmark. Properties and relationships of shapes are covered in units that require making drawings and sketches of house plans and other figures. An understanding of congruence and similarity is developed through scale drawing and construction, but the terms themselves are not mentioned explicitly. The material includes properties of regular two-dimensional shapes and three-dimensional angles, relationships between properties, and formalized concepts such as the Pythagorean Theorem.

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.)

MathScape addresses the substance of all parts of the benchmark. Throughout the material, there are applications of calculating area, circumference, and volume. The sophistication progresses from visualization of two-dimensional shapes and properties in grades 6 and 7 to three-dimensional aspects of shapes in grade 8, and moves beyond consideration of basic properties. The material exceeds the expectations of the benchmark by addressing surface area and volume of three-dimensional figures other than rectangular solids.

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.)

MathScape only addresses the linear and quadratic ideas in the benchmark. The other ideas are not covered in the material. The sophistication level of the content increases appropriately from grade 6 through grade 8 starting with an early emphasis on patterns of numbers followed by linear relationships and graphs and then functions and quadratic relations.

Algebra Equation Concepts — Most 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 substance of the benchmark is addressed in depth with connections made between benchmark ideas. Units across grades 6 through 8 cover rules for patterns, then linear relationships and functions, and finally non-linear relationships. Equations are used throughout to develop an understanding of the effect changing one variable has on another. Real-world connections are made to the benchmark ideas and skills.