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).

Mathematics in Context 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 Mathematics in Context 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 parts of the benchmark are addressed in a variety of lessons and activities, primarily in grades 5/6 and 6/7. In grade 5/6, examples and exercises that apply the idea of equal parts of a whole include working with fractions to fill parts of cans and using measuring cups and fraction strips to create whole units from parts. The concept that a fraction means "a divided by b" is illustrated by modeling division with fraction notation. The idea is further developed by constructing pie charts in the unit on statistics in grade 6/7. The idea "a compared to b" is developed by relating fractions and ratios to scale factor and by a comparison of part-part and part-whole ratios.

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.)

Mathematics in Context addresses all of the benchmark ideas, beginning with building number skills, in grades 6/7 by accounting for several ways students would conceptualize writing money amounts. In grades 5/6, lessons also model different strategies to estimate fractions by using either a ratio table or number sense. Many applications and uses of fractions, decimals, and percents provide opportunities for skill development and practice with and without a calculator. In grades 7/8, the connection is made between powers of ten and scientific notation and large numbers. Exponential notation is used to compare, express, calculate, and recognize the inverse relationship between multiplication and division by powers of ten.

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.)

All ideas of the benchmark are addressed except for the special properties of round shapes. Special properties of triangles are investigated through many hands-on activities in grades 7/8 and 8/9. The difference between triangles and quadrilaterals is explored by considering their rigidity. Triangle classification is learned by building a hierarchy of side and angle relationships. Beginning in grades 5/6 and progressing through grades 8/9, concepts about polygons and circles are developed through hands-on work, as is the idea of congruence. The distinction between regular and irregular shapes is developed through the study of symmetry. Similar figures are developed and applied in several settings.

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 of the benchmark skills of calculating perimeters, circumferences, areas, and volumes are developed in the units. Hands-on work leads to generalizations and skills, including activities in which estimations, calculations, and their justifications are required.

The question of how perimeters of circles and squares are related and the effect of changing dimensions on perimeter, area, and volume are explored throughout all grade levels. Beginning in grades 6/7, the concept and role of pi in the circumference of a circle connects perimeter and circumference.

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 one of the benchmark ideas, reaching a limiting value, are addressed in depth. Graphs are used in modeling real life situations, and students learn to extract information, expand existing graphs to make predictions, become alert to missing information, and draw conclusions. Data in tables, graphs, and narrative descriptions are gathered, summarized, and compared. In grades 8/9, students examine the relationship of slope to the appearance of a graph. Beginning in grades 7/8, characteristics of periodic graphs, equations of lines, and linear regression are applied in describing relationships between two variables.

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.)

Mathematics in Context develops the concepts of the benchmark by having students create a table and graph to illustrate relationships between variables and write verbal statements and a formula. Equations and formulas are developed for a great variety of applications. In grades 7/8 and 8/9, linear growth over time is explored in depth in a variety of situations such as using a scatterplot, finding the relationship using linear regression, and using equations to predict future growth.