In adding to the conversation regarding the use of the number line for modeling and reasoning quantitatively, what kinds of modeling on the number line would support the high school student?
For showing multiple representations of Real Numbers, the number line serves as a model for locating those Irrational Numbers and displaying their relationship with more familiar Rational Numbers. The locations of these Irrational Numbers can also be completed using constructions.
See Irrational numbers such as pi, e,√5, ∛6, …
For solving functional equations and inequalities, the number line model supports using reflections, slides, and change of scales for those solutions. Additionally and importantly, this conceptual understanding works for all function families (linear, quadratic, exponential, etc.) and thus enables students to think holistically in solving equations from those same functional families.
For solving the absolute value inequality: |2x – 1| > 5
The question remains, if the number line provides a visual model for students to display and operate with numbers and variables, why do we not see a number line in every classroom where it is prominently displayed, used, and referred to at all times?