How well does Heath Passport 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).

### Heath Passport 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 Heath Passport 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 — Minimal 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 is only minimal coverage of the first two ideas of the benchmark in grades 6 and 7 with somewhat more treatment in grade 8, but the coverage is not sufficient to address the substance of the concepts. The idea of "a compared to b" is presented briefly in grade 6 and addressed more completely later, especially in grade 8, where students have the opportunity to apply the concept; however, it is not developed beyond the sixth grade level of sophistication. Reviewers noted a statement in the grade 6 teacher’s edition that a "ratio cannot have a zero in it," which confuses ratio comparisons with rational numbers.

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 skills in this benchmark are substantively addressed and are distributed across grades 6, 7, and 8. The relationships between equivalent forms of fractions and decimals are developed more substantively than relationships involving percents. The material progresses from the use, comparison, and interpretation of integers, fractions, decimals, and expanded notation in grade 6 to exponents in grade 7 and negative exponents and scientific notation in grade 8.

Geometry Concepts — Most 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 ideas of this benchmark appear mainly in grades 6 and 8. The special properties of shapes are covered, but the substance of the coverage is somewhat inconsistent for some of the benchmark concepts, such as the rigidity of triangles and the area of circles. The material addresses this benchmark in grades 6 and 7 but does not progress in sophistication in grade 8. Examples of similarity and congruence are discussed in grade 6 with more treatment given to properties of triangles and quadrilaterals. Formal theorems and definitions appear in grade 7 and work on comparing solids and describing corresponding angles appears 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.)

All the skills in this benchmark are addressed and are distributed across the grade levels. The depth of sophistication of the skills does not increase significantly across the grades except when exercises progress from using two-dimensional to three-dimensional figures. The formula for the area of a parallelogram is provided and then used to find the area formula for a circle. Formulas for finding perimeter, circumference of circles, and volume of prisms are also provided. The perimeter of polygons is related to the distances between points in a coordinate system.

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.)

Many of the concepts in the benchmark appear in grades 6 and 8 with more substance attempted in grade 8. Much of the material presented is below the sophistication of the benchmark and shows little development from grades 6 to 7. Some growth is seen in grade 8 as students begin communicating ideas about relationships between variables. Linear graphs are used to represent a relationship in grade 6 and the idea culminates with work on linear equations and their graphs in grade 8. There is some very limited discussion about linear versus non-linear relationships in grade 8.

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.)

Most of the treatment of this benchmark occurs in grade 8, mainly in lessons dealing with functions. Some of the lessons do not precisely target the idea of using equations to summarize change. They focus more on patterns of change rather than on the response of a variable to different types of change in another variable. The development across the grades is somewhat inconsistent. Algebraic expressions are used to model quantitative relationships, and later in the material, the use of variables is explained when working with linear equations having two variables. These equations include showing changes over time.