These standards and benchmarks are from McREL's online database, Content Knowledge: A Compendium of Standards and Benchmarks for K-12 education (4th edition, 2004) (http://www.mcrel.org/standards-benchmarks/.) The mathematics portion of the database was developed using National Council of Teachers of Mathematics (NCTM) standards in addition to other nationally recognized standards documents.
Standard 1: Uses a variety of strategies in the problem-solving process
Grades K-2 Benchmark 2: Uses discussions with teachers and other students to understand problems
Benchmark 3: Explains to others how she or he went about solving a numerical problem
Grades 3-5 Benchmark 1: Uses a variety of strategies to understand problem situations (for example, discussing with peers, stating problems in own words, modeling problem with diagrams or physical objects, identifying a pattern)
Benchmark 2: Represents problems situations in a variety of forms (for example, translates from a diagram to a number or symbolic expression)
Benchmark 3: Understands that some ways of representing a problem are more helpful than others
Benchmark 4: Understands and applies basic and advanced properties of the concepts of measurement
Grades Pre-K Benchmark 2: Measures objects with non-standard tools (for example, string, hands, footsteps, unifix cubes, tiles)
Grades K-2 Benchmark 1: Understands the basic measures length, width, height, weight, and temperature
Grades 3-5 Benchmark 1: Understands the basic measures perimeter, area, volume, capacity, mass, angle, and circumference
Benchmark 2: Selects and uses appropriate tools for given measurement situations (for example, rulers for length, measuring cups for capacity, protractors for angle)
Benchmark 3: Knows approximate size of basic standard units (for example, centimeters, feet, grams) and relationships between them (for example, between inches and feet)
Benchmark 4: Understands relationships between measures (for example, between length, perimeter, and area)
Benchmark 5: Understands that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times)
Benchmark 6: Uses specific strategies to estimate quantities and measurements (for example, estimating the whole by estimating the parts)
Benchmark 7: Selects and uses appropriate units of measurement, according to type and size of unit