### How well does Heath Mathematics Connections 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 Mathematics Connections 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 Mathematics Connections 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.)

There is a reference to each part of the benchmark at some point in the material. While each part is addressed, there is little beyond a passing reference to a/b as meaning "a parts of size 1/b." The idea is mentioned once in grade 6 and once in grade 8. The substance of the concept is not explicitly presented. The meaning "a compared to b" is presented in grade 6 in an optional activity only and addressed more directly in grade 7. The idea that a/b means "a divided by b" is addressed thoroughly. Throughout grade 6, students are reminded of this meaning in lessons on dividing whole numbers and decimals. Finally, students revisit this meaning in grade 8 in a lesson on complex fractions.

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.)

All parts of this benchmark are treated in the material, particularly in grades 6 and 7. Ideas and representations progress in sophistication, but not depth, from one level to the next. Equivalencies are first noted in grade 6, where decimals are represented by their equivalents on a grid. By the end of grade 6, students are converting fractions to decimals to percents. In grade 7, a few lessons interpret and compare equivalent forms of numbers (exponents, scientific notation, positive and negative rational numbers, and decimals). Appropriate use of different forms is not addressed. By grade 8, there are only a few lessons that address equivalent forms of numbers other than references to equivalencies of fractions expressed as repeating decimals.

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.)

This benchmark receives minimal coverage throughout the material. A great deal of geometry instruction centers around measurement with little focus on the properties of shapes. In grade 6, the material deals with the properties and construction of quadrilaterals but draws no attention to distinguishing among the various figures. In grades 7 and 8, students encounter very similar lessons that examine properties of polygons including classification by shape. There is no reference to triangle rigidity or the boundary and area relation for circles. Congruence is studied very briefly in grades 7 and 8. Similarity receives more treatment across the grade levels beginning with scale drawings and projections in grade 6. A few lessons in grades 7 and 8 directly address the characteristics of similar polygons.

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 parts of this benchmark are fully addressed throughout Heath Mathematics Connections. While there is some overlap in the presentation of skills, for the most part they are developed appropriately across the grade levels, with connected ideas within the benchmark spiraled from one level to the next. In grade 6, students are introduced to calculations for all measurements included in the benchmark. In grades 7 and 8, students explore the measurements further, using them in a variety of problem solving situations. In grade 8, they apply what they know about these measurements to composite figures, estimation, and approximations.

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.)

Graphs are explored across all grade levels of Heath Mathematics Connections; however, most of the work involves simply reading, interpreting, and analyzing graphs. There are no opportunities to work with original data. Not all of the types of graphs described in the benchmark are addressed in the material. In grades 6 and 7, graphs illustrate the relationships in which one variable increases uniformly and the other increases or decreases steadily, step-wise, or alternately. In grade 8, the material examines graphs for functions, linear equations, and slope. There are a few lessons involving analysis of graphs in which students look at misleading graphs and make choices about appropriate graphs for particular needs.

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.)

Overall, while there is implicit instruction in the concepts of symbolic equations, the substance of the benchmark is addressed only briefly and with little depth. The second part of the benchmark, symbolic equations can be used to summarize how a quantity changes in response to other changes, receives greater coverage. There are a few examples showing how a quantity of something changes over time. Variables and symbolic equations are introduced in grade 6, although it is only implied that the equations represent change. They are explored further in grade 7 where this concept is more clearly demonstrated though not explicitly stated. In grades 7 and 8, the material briefly examines the relationship between symbolic equations and graphing.