Mathematical literacy develops when learners mathematize a problem that feels real. Shopping comparison, route estimation, evidence from data, geometric design and random phenomena are contexts; a bare exercise with a person's name is not.
The task must require learners to identify quantities and relationships, solve or model, and communicate with an equation, diagram, table, graph, symbol or reasoned explanation.
Stage arcs:
Task design for compulsory-education “三会”:
Non-negotiables: one authentic mathematizable problem; at least one strategy comparison; a visible mathematical representation; and computation serving the problem rather than an isolated drill.
Typical misconceptions: choosing an operation from a keyword; obtaining a correct expression but being unable to explain its meaning; treating the first method as the only method. Build the activity and quiz distractors from these.
The transfer task changes the numbers, constraints or context surface while preserving the mathematical structure, and still asks learners to represent and justify.