Why is absolute value taught to fifth graders?
On "Are you Smarter than a Fifth Grader?" last night, was the fifth grade math question "What is the Absolute Value of 9?" Absolute value is, of course, the distance of a value from the origin on a number line or coordinate grid.
That being the case, the absolute value function for scalars is a degenerate case and, IMHO, earns little more than a footnote, much less an entire chapter in the fifth grade curriculum.
I remember scratching my own head over this when it was presented as in "what possible use does absolute value serve?". A few years later, when it was applied to complex numbers, coordinate systems and vectors, yes it makes sense, but when applied to scalars, it makes about as much sense as spending a week on "how to multiply by 1" or "how to add zero to something".
lazy... That's part of my issue. It's a degenerate case and as such lacks meaningful context. It would be like trying to teach multiplication but only being allowed to explain n x 1.
Pedagogy is like building a wall out of bricks. You keep supplying bricks and mortar and suddenly, when you least expect it, you have a wall.
Absolute value has a role in teaching about the multiplication rules for negative numbers. It enables the teacher to parse the problem into the multiplication of the absolute value and then ascertaining the sign of the result as a separate step.
Fifth graders are taught absolute value so that when the pre-algebra curriculum for grades 6, 7 and 8 deals with multiplication involving negative numbers, the building blocks will be there.
The Math 9 curriculum that I teach from still treats the absolute value of a scalar and the magnitude of a vector as distinct objects of knowledge. Mathematically, they are equivalent, but pedagogically they are distinct. The purpose behind teaching absolute value to a fifth-grader is pedagogical, not mathematical. Children are not ready to do math at this level, but if you form the synapses they will find it much easier to grasp the concepts later on.
Pre-Calculus: Complex Numbers - Trig or Polar Form
