Although infinity-related content is not presented within a rigorous analytic framework at the lower-secondary level, ideas such as number-line unboundedness, the infinite expansion of repeating decimals, the intuitive notion of limits as “approaching infinitely closely,” and infinite processes such as repeated halving and accumulation have entered classroom instruction in multiple forms. In teaching practice, students are often influenced by a completability presupposition—the assumption that an object should be finitely writable and a process finitely executable. Together with semantic drift between everyday meanings and mathematical meanings of intuitive expressions, and additional difficulties in preserving meaning across multiple representations, this presupposition can give rise to stable conceptual misconceptions that readily transfer across topics. Drawing on linguistic evidence from classroom dialogue and written justifications in students’ work, this paper typologizes these misconceptions into eight categories (A–H), covering key themes including unboundedness and density, equivalence of repeating decimals, conceptions of limits, and judgments about infinite accumulation.To address these misconceptions, we propose a corrective instructional framework that is classroom-feasible, observable for evaluation, and transferable across topics. Centered on four justificatory templates—constructive reasoning, difference quantification and algebraic transformation, threshold language (error control), and upper-bound constraints—the framework organizes learning through a “diagnosis–justification–transfer” sequence to support students’ shift from process-based intuition to object-oriented understanding. The study further provides classroom cases on number-line unboundedness, the equivalence 0.999…, and limit intuition, and uses students’ justificatory behaviors and transfer performance as key evaluation indicators. These results offer an explanatory yet actionable pathway for improving instructional transitions in infinity-related content at the lower-secondary level.