How well does Middle Grades Math Thematics 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 Grades Math Thematics 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 Grades Math Thematics 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.)

The material addresses two parts of the benchmark substantively; the other part is mentioned but not fully developed. A fraction model is used to illustrate the number of equal-sized parts of the whole, building on early experiences with fractions. The idea "a divided by b" is used in grades 7 and 8 only to illustrate the procedure of changing a fraction to a decimal or a mixed number. A single example is shown as an illustration. The concept of ratio is introduced, and the text clearly states that a ratio can be written as a fraction. This idea is reinforced several times in grades 6 and 7, and developed further in lessons on ratios and proportions and on proportions and percents.

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 given in-depth treatment, primarily in grades 6 and 7. Representations and comparisons of fractions, mixed numbers, and equivalent fractions are addressed with manipulative materials. Relationships among fractions, decimals, and percents are treated comprehensively. Exponents, scientific notation, and integer and fractional equivalents of numbers are covered. In a section on percent and probability, ratios are expressed as fractions, decimals, and percents. The material is appropriate to these grade levels for it focuses on the interpretation and comparison of equivalent forms of numbers rather than simply on their use.

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 circumference and area relationship of circles is not addressed in this material. In early explorations of geometric figures, special terms and symbols are used to describe geometric figures and special properties of polygons and circles. Material covering the angles of triangles and properties of quadrilaterals and their diagonals address the idea of rigid structures. The concepts of similarity and congruence are addressed and then applied in scale drawings, coordinate graphing, direct and indirect measurement of angles and sides of figures, and fractals.

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 the benchmark are addressed in this material. Area and perimeter of rectangular figures are introduced in a lesson on equations and expressions and then covered in great detail through calculating areas of structures and estimating and measuring the area of the classroom. Volume of rectangular solids is covered by finding the volume of tall buildings. Circumference of a circle is introduced by measuring the distance around circular objects. A formula is then presented and students draw and measure circles and estimate the circumference of real objects. Further exploration and extension of the benchmark are found in grades 7 and 8 and include novel applications of measurements.

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.)

All but two parts of the benchmark are covered substantively in this material. Students first review how to plot points, then apply the idea to saving money and watching it double over time. Later, a lesson on population growth looks at rate of increase as exhibited by a graph. Finally, students explore and interpret line graphs and their shapes in many applications, including interpreting graphs that can be misleading. In grade 7, double line graphs compare two sets of data. Middle Grades Math Thematics uses many contexts to show the effects on a variable as the other variable increases uniformly.

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 benchmark is addressed in depth. The concept of symbolic equations is introduced in grade 6. The relationship between the elements of the equation is covered with an emphasis on the meaning of the equations and their parts. Solving equations comes much later when students are told that to solve the equation they must find the unknown value. In grade 7, a lesson on sequences reviews the idea that a variable represents a quantity that changes. The concept of symbolic equations is applied by writing and graphing equations. In grade 8, time is devoted to graphing and evaluating linear versus nonlinear equations, exploring slope, and using equations to make predictions.