By the end of grade twelve, students will:

D.12.1 Identify, describe, and use derived attributes* (e.g., density, speed, acceleration, pressure) to represent and solve problem situations

D.12.2 Select and use tools with appropriate degree of precision to determine measurements directly* within specified degrees of accuracy and error (tolerance)

D.12.3 Determine measurements indirectly*, using

• estimation
• proportional reasoning, including those involving squaring and cubing (e.g., reasoning that areas of circles are proportional to the squares of their radii)
• techniques of algebra, geometry, and right triangle trigonometry
• formulas in applications (e.g., for compound interest, distance formula)
• geometric formulas to derive lengths, areas, or volumes of shapes and objects (e.g., cones, parallelograms, cylinders, pyramids)
• geometric relationships and properties of circles and polygons (e.g., size of central angles, area of a sector of a circle)
• conversion constants to relate measures in one system to another (e.g., meters to feet, dollars to Deutschmarks

*See Glossary.

Content Standard D