Calling to Order: Comparing Real Numbers with Inequality Visuals

This example visually demonstrates how to compare real numbers by mapping inequality conditions to positions relative to interval boundaries on a coordinate plane. It highlights the relationship between order relations (greater/less than) and geometric placement of endpoints, using graph-based intuition. Key concepts include inequality reasoning, real-number interval representation, and linear-function style depiction of boundary relationships; it can also support probability intuition when random selections are used to generate sample points. Construction is driven by the provided GeoGebra commands and objects: Sequence is used to generate ordered collections, RandomElement selects sample values interactively, and Union combines sets/intervals that define the comparison regions. Diagram elements such as L, a, right/left, L1, b represent left/right bounds, while text1–text4 label the inequality or comparison outcome. button1 together with parameters c, d, e provides user interaction for updating the scenario. Suitable for secondary education (algebra & inequalities) through introductory college mathematics, especially for teaching graphing of inequalities and interval reasoning.