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