Length relationships can be determined without placing two objects together by comparing each with the same intermediary object or by comparing their measurements in identical units. This reasoning supports transitivity—for example, if one length exceeds a third length and the third exceeds another, the first is longer than the other—and distinguishes length from an object’s position or visual size; more advanced unit conversions and generalized measurement comparisons are not included.
To compare two lengths indirectly, compare both objects with the same third object or use the same-sized units.
Example:
A ribbon is longer than a piece of string. The piece of string is longer than a pencil. Which is longer: the ribbon or the pencil?
Compare the ribbon and the string:
The ribbon is longer than the string.
Compare the string and the pencil:
The string is longer than the pencil.
The string is between the two comparisons. Since the ribbon is longer than the string, and the string is longer than the pencil, the ribbon must be longer than the pencil.
Answer: The ribbon is longer than the pencil. You did not need to place the ribbon and pencil together.
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