How well does Middle School Math 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).

### Middle School Math 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 Middle School Math 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.)

All ideas of the benchmark are addressed in Middle School Math. The idea "a parts of size 1/b" is introduced in the definition of a fraction as part of a whole. The idea "a divided by b" is covered in applications of converting fractions to decimals and improper fractions to mixed numbers and in descriptions of what the expression a/b means. The concept "a compared to b" is addressed in discussing rates in which a ratio is described as a special kind of fraction that compares two quantities. The ideas are explored at different times across the grade levels, but the greatest coverage is in grade 6.

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.)

The material addresses all parts of the benchmark. The text explores numbers written in standard form, powers, expanded, exponential, and scientific notation, fractions, decimals, and percents. The various equivalent forms of these numbers are introduced with definitions and examples and include demonstrations throughout grades 6 through 8 of how to compare, interpret, and apply them in various situations. The material includes comparison and use of integers, powers, and exponents, and exponential and scientific notation.

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.)

The benchmark ideas addressed in the material include the special properties of shapes and the concept of congruency and similarity of shapes. The rigid nature of a triangle and the boundary and area of a circle are not addressed. At all grade levels, most of the lessons and activities related to this benchmark involve exploring the properties and classifications of triangles, polygons, quadrilaterals, polyhedrons, and circles. A few lessons, for the most part in grade 8, discuss congruence and similarity and require measurement and examination of figures.

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.)

Middle School Math addresses all parts of the benchmark. In grades 6 and 7, the perimeters of rectangles and triangles are defined and calculated by adding the lengths of the sides of the figures. Procedures are given for finding the circumference of a circle by measurement or by using the formula C = p d. The area of rectangles, triangles, and circles is developed in grades 6 and 7, and the volume of rectangular solids is explored in grade 8. Formulas are developed for calculating area and volume.

Algebra Graph Concepts — Partial 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.)

Middle School Math does not address two of the benchmark ideas—those dealing with reaching a limit and an intermediate maximum or minimum. There are lessons across the three grade levels discussing line graphs and showing how data changes over time through using line and bar graphs and scatterplots. Tables and graphs illustrate the idea that a change in one variable causes a change in another. In grade 8, the graphs are constructed from symbolic equations or functions. The lessons involve drawing and interpreting straight-line graphs, quadratic functions that result in parabolas, and exponential and step functions.

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.)

Middle School Math addresses all ideas of the benchmark, primarily in grades 7 and 8, in applications of linear equations and functions, quadratic equations, and exponential functions. Most linear equations or functions are presented as relationships between the variables x and y. Quadratic and exponential functions are discussed in applications such as finding the area of a rectangle and using formulas for determining speed or growth.