Benchmarks Used to Evaluate Textbooks

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.)

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.)

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.)

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.)

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.)

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.)

Criteria for Evaluating the Quality of Instructional Guidance

I.1 Conveying Unit Purpose
I.2 Conveying Lesson Purpose
I.3 Justifying Sequence of Activities

Category II: Building on Student Ideas about Mathematics

II.1 Specifying Prerequisite Knowledge
II.2 Alerting Teacher to Student Ideas
II.3 Assisting Teacher in Identifying Ideas
II.4 Addressing Misconceptions

Category III: Engaging Students in Mathematics

III.1 Providing Variety of Contexts
III.2 Providing First-hand Experiences

Category IV: Developing Mathematical Ideas

IV.1 Justifying Importance of Benchmark Ideas
IV.2 Introducing Terms or Procedures
IV.3 Representing Ideas Accurately
IV.4 Connecting Benchmark Ideas
IV.5 Demonstrating/Modeling Procedures

V.1 Encouraging Students to Explain Their Reasoning
V.2 Guiding Interpretation or Reasoning
V.3 Encouraging Students to Think about What They've Learned

Category VI: Assessing Student Progress in Mathematics

VI.1 Aligning Assessment
VI.2 Assessing through Applications
VI.3 Using Embedded Assessment

Category VII. Enhancing the Mathematics Learning Environment

VII.1 Providing Teacher Content Support
VII.2 Establishing Challenging Classroom Environment
VII.3 Supporting All Students