From "Lined Up" to Measured Alignment: A Simple Classroom Test that Turns "One Line" into a Ray Bundle

This teaching note presents a short, classroom-ready activity that makes measurement variability visible by contrasting constrained (1D) and unconstrained (2D) pointing. Using repeated aiming trials with a flashlight (or a low-power laser where permitted), students observe that “the same aim” produces a distribution rather than a single point. Strip-like versus blob-like outcome patterns provide an accessible bridge from ideal geometric language to practical ideas of tolerance, uncertainty, and operational alignment (“within a stated tolerance, under a stated method, at a stated distance”). The manuscript includes setup guidance, instructor notes, prompts, common misconceptions, a quick assessment with rubric, and optional extensions for distance scaling and data reasoning. The intended audience is introductory college and advanced high school STEM instruction, with preservice teacher programs as a secondary audience.