Unit-attribute relations must be considered.

• Students invent novel measures and quantify their measurement properties.
  
• Students invent novel measures as needed.
  
• Unit-attribute relations are understood by recourse to criteria such as purpose, precision, and the like. For example, time can serve as a surrogate for length measure if we know rate, ratios of length can serve as measures of angle, if we have models of right triangle properties, etc.
  
• For example, area units of curved figures should have curvature or areas of rectangles are best measured by other rectangles.
  
• For example, area units of curved figures should have curvature or areas of rectangles are best measured by other rectangles.
  
• Unit-attribute relations are not considered. Generally, this means that length is the universal unit-everything is measured as a length.