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List of Benchmarks for Mathematics

Standard 4.Understands and applies basic and advanced properties of the concepts of measurement
  Level Pre-K (Grade Pre-K)
   1. Understands basic concepts of time (e.g., today, tomorrow, morning, evening) and the sequence of various events (e.g., what comes after lunch)
   2. Measures objects with non-standard tools (e.g., string, hands, footsteps, unifix cubes, tiles)
   3. Estimates quantities in real-world situations
   4. Orders objects qualitatively by measurable attribute (e.g., smallest to largest, lightest to heaviest, shortest to longest)
   5. Knows the common language of measurement (e.g., "big," "little," "long," "short," "light," "heavy")
   6. Knows that different sized containers will hold more or less
  Level I (Grade K-2)
   1. Understands the basic measures length, width, height, weight, and temperature
   2. Understands the concept of time and how it is measured  A 
   3. Knows processes for telling time, counting money, and measuring length, weight, and temperature, using basic standard and non-standard units  A 
   4. Makes quantitative estimates of familiar linear dimensions, weights, and time intervals and checks them against measurements  A 
  Level II (Grade 3-5)
   1. Understands the basic measures perimeter, area, volume, capacity, mass, angle, and circumference  A 
   2. Selects and uses appropriate tools for given measurement situations (e.g., rulers for length, measuring cups for capacity, protractors for angle)  A 
   3. Knows approximate size of basic standard units (e.g., centimeters, feet, grams) and relationships between them (e.g., between inches and feet)  A 
   4. Understands relationships between measures (e.g., between length, perimeter, and area)  A 
   5. Understands that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times)
   6. Uses specific strategies to estimate quantities and measurements (e.g., estimating the whole by estimating the parts)
   7. Selects and uses appropriate units of measurement, according to type and size of unit  A 
  Level III (Grade 6-8)
   1. Understands the basic concept of rate as a measure (e.g., miles per gallon)
   2. Solves problems involving perimeter (circumference) and area of various shapes (e.g., parallelograms, triangles, circles)  A 
   3. Understands the relationships among linear dimensions, area, and volume and the corresponding uses of units, square units, and cubic units of measure  A 
   4. Solves problems involving units of measurement and converts answers to a larger or smaller unit within the same system (i.e., standard or metric)  A 
   5. Understands the concepts of precision and significant digits as they relate to measurement (e.g., how units indicate precision)  A 
   6. Selects and uses appropriate units and tools, depending on degree of accuracy required, to find measurements for real-world problems
   7. Understands formulas for finding measures (e.g., area, volume, surface area)  A 
   8. Selects and uses appropriate estimation techniques (e.g., overestimate, underestimate, range of estimates) to solve real-world problems  A 
   9. Understands procedures for basic indirect measurements (e.g., using grids to estimate area of irregular figures)
  Level IV (Grade 9-12)
   1. Solves problems involving rate as a measure (e.g., speed, density)  A 
   2. Understands the concepts of absolute and relative errors in measurement
   3. Selects and uses an appropriate direct or indirect method of measurement in a given situation (e.g., uses properties of similar triangles to measure indirectly the height of an inaccessible object)
   4. Solves real-world problems involving three-dimensional measures (e.g., volume, surface area)
   5. Uses unit analysis to solve problems involving measurement and unit conversion (e.g., between metric and U.S. customary systems, foreign currency conversions)
  Level V (Grade (College Readiness))
   1. Calculates the perimeter and area of irregular figures

 A  = Assessment items available